{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Early math review8 units \u00b7 121 skills": ["Unit 1Counting", "Unit 2Addition and subtraction intro", "Unit 3Place value (tens and hundreds)", "Unit 4Addition and subtraction within 20", "Unit 5Addition and subtraction within 100", "Unit 6Addition and subtraction within 1000", "Unit 7Measurement and data", "Unit 8Geometry", "Start Course challenge", "Unit 1Unit 1: Counting", "Counting: Unit test", "Unit 2Unit 2: Addition and subtraction intro", "Addition and subtraction intro: Unit test", "Unit 3Unit 3: Place value (tens and hundreds)", "Place value (tens and hundreds): Unit test", "Unit 4Unit 4: Addition and subtraction within 20", "Addition and subtraction within 20: Unit test", "Unit 5Unit 5: Addition and subtraction within 100", "Addition and subtraction within 100: Unit test", "Unit 6Unit 6: Addition and subtraction within 1000", "Addition and subtraction within 1000: Unit test", "Unit 7Unit 7: Measurement and data", "Measurement and data: Unit test", "Unit 8Unit 8: Geometry", "Geometry: Unit test", "Start Course challenge", "Unit 1: Counting", "Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting", "Unit 2: Addition and subtraction intro", "What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro", "Unit 3: Place value (tens and hundreds)", "Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)", "Unit 4: Addition and subtraction within 20", "Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20", "Unit 5: Addition and subtraction within 100", "Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100", "Unit 6: Addition and subtraction within 1000", "Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000", "Unit 7: Measurement and data", "Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data", "Unit 8: Geometry", "Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"2nd grade8 units \u00b7 75 skills": ["Unit 1Add and subtract within 20", "Unit 2Place value", "Unit 3Add and subtract within 100", "Unit 4Add and subtract within 1,000", "Unit 5Money and time", "Unit 6Measurement", "Unit 7Data", "Unit 8Geometry", "Start Course challenge", "Unit 1Unit 1: Add and subtract within 20", "Add and subtract within 20: Unit test", "Unit 2Unit 2: Place value", "Place value: Unit test", "Unit 3Unit 3: Add and subtract within 100", "Add and subtract within 100: Unit test", "Unit 4Unit 4: Add and subtract within 1,000", "Add and subtract within 1,000: Unit test", "Unit 5Unit 5: Money and time", "Money and time: Unit test", "Unit 6Unit 6: Measurement", "Measurement: Unit test", "Unit 7Unit 7: Data", "Data: Unit test", "Unit 8Unit 8: Geometry", "Geometry: Unit test", "Start Course challenge", "Unit 1: Add and subtract within 20", "Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20", "Unit 2: Place value", "Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value", "Unit 3: Add and subtract within 100", "Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100", "Unit 4: Add and subtract within 1,000", "Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000", "Unit 5: Money and time", "Time: Money and time", "Unit 6: Measurement", "Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement", "Unit 7: Data", "Bar graphs: Data", "Line plots: Data", "Unit 8: Geometry", "Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"3rd grade14 units \u00b7 141 skills": ["Unit 1Intro to multiplication", "Unit 21-digit multiplication", "Unit 3Addition, subtraction, and estimation", "Unit 4Intro to division", "Unit 5Understand fractions", "Unit 6Equivalent fractions and comparing fractions", "Unit 7More with multiplication and division", "Unit 8Arithmetic patterns and problem solving", "Unit 9Quadrilaterals", "Unit 10Area", "Unit 11Perimeter", "Unit 12Time", "Unit 13Measurement", "Unit 14Represent and interpret data", "Start Course challenge", "Unit 1Unit 1: Intro to multiplication", "Intro to multiplication: Unit test", "Unit 2Unit 2: 1-digit multiplication", "1-digit multiplication: Unit test", "Unit 3Unit 3: Addition, subtraction, and estimation", "Addition, subtraction, and estimation: Unit test", "Unit 4Unit 4: Intro to division", "Intro to division: Unit test", "Unit 5Unit 5: Understand fractions", "Understand fractions: Unit test", "Unit 6Unit 6: Equivalent fractions and comparing fractions", "Equivalent fractions and comparing fractions: Unit test", "Unit 7Unit 7: More with multiplication and division", "More with multiplication and division: Unit test", "Unit 8Unit 8: Arithmetic patterns and problem solving", "Arithmetic patterns and problem solving: Unit test", "Unit 9Unit 9: Quadrilaterals", "Quadrilaterals: Unit test", "Unit 10Unit 10: Area", "Area: Unit test", "Unit 11Unit 11: Perimeter", "Perimeter: Unit test", "Unit 12Unit 12: Time", "Time: Unit test", "Unit 13Unit 13: Measurement", "Measurement: Unit test", "Unit 14Unit 14: Represent and interpret data", "Represent and interpret data: Unit test", "Start Course challenge", "Unit 1: Intro to multiplication", "Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication", "Unit 2: 1-digit multiplication", "Distributive property: 1-digit multiplication", "Unit 3: Addition, subtraction, and estimation", "Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation", "Unit 4: Intro to division", "Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division", "Unit 5: Understand fractions", "Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions", "Unit 6: Equivalent fractions and comparing fractions", "Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions", "Unit 7: More with multiplication and division", "Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division", "Unit 8: Arithmetic patterns and problem solving", "2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving", "Unit 9: Quadrilaterals", "Quadrilaterals : Quadrilaterals", "Unit 10: Area", "Count unit squares to find area: Area", "Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area", "Unit 11: Perimeter", "Perimeter: Perimeter", "Perimeter word problems: Perimeter", "Unit 12: Time", "Time on number line: Time", "Telling time: Time", "Elapsed time: Time", "Unit 13: Measurement", "Mass: Measurement", "Volume: Measurement", "Unit 14: Represent and interpret data", "Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"4th grade14 units \u00b7 154 skills": ["Unit 1Place value", "Unit 2Addition, subtraction, and estimation", "Unit 3Multiply by 1-digit numbers", "Unit 4Multiply by 2-digit numbers", "Unit 5Division", "Unit 6Factors, multiples and patterns", "Unit 7Equivalent fractions and comparing fractions", "Unit 8Add and subtract fractions", "Unit 9Multiply fractions", "Unit 10Understand decimals", "Unit 11Plane figures", "Unit 12Measuring angles", "Unit 13Area and perimeter", "Unit 14Units of measurement", "Start Course challenge", "Unit 1Unit 1: Place value", "Place value: Unit test", "Unit 2Unit 2: Addition, subtraction, and estimation", "Addition, subtraction, and estimation: Unit test", "Unit 3Unit 3: Multiply by 1-digit numbers", "Multiply by 1-digit numbers: Unit test", "Unit 4Unit 4: Multiply by 2-digit numbers", "Multiply by 2-digit numbers: Unit test", "Unit 5Unit 5: Division", "Division: Unit test", "Unit 6Unit 6: Factors, multiples and patterns", "Factors, multiples and patterns: Unit test", "Unit 7Unit 7: Equivalent fractions and comparing fractions", "Equivalent fractions and comparing fractions: Unit test", "Unit 8Unit 8: Add and subtract fractions", "Add and subtract fractions: Unit test", "Unit 9Unit 9: Multiply fractions", "Multiply fractions: Unit test", "Unit 10Unit 10: Understand decimals", "Understand decimals: Unit test", "Unit 11Unit 11: Plane figures", "Plane figures: Unit test", "Unit 12Unit 12: Measuring angles", "Measuring angles: Unit test", "Unit 13Unit 13: Area and perimeter", "Area and perimeter: Unit test", "Unit 14Unit 14: Units of measurement", "Units of measurement: Unit test", "Start Course challenge", "Unit 1: Place value", "Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value", "Unit 2: Addition, subtraction, and estimation", "Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation", "Unit 3: Multiply by 1-digit numbers", "Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers", "Unit 4: Multiply by 2-digit numbers", "Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers", "Unit 5: Division", "Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division", "Unit 6: Factors, multiples and patterns", "Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns", "Unit 7: Equivalent fractions and comparing fractions", "Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions", "Unit 8: Add and subtract fractions", "Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions", "Unit 9: Multiply fractions", "Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions", "Unit 10: Understand decimals", "Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals", "Unit 11: Plane figures", "Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures", "Unit 12: Measuring angles", "Measuring angles: Measuring angles", "Decomposing angles: Measuring angles", "Unit 13: Area and perimeter", "Area and perimeter: Area and perimeter", "Unit 14: Units of measurement", "Estimating volume: Units of measurement", "Estimating length: Units of measurement", "Time: Units of measurement", "Converting units of mass: Units of measurement", "Converting units of volume: Units of measurement", "Converting units of length: Units of measurement", "Converting units of time: Units of measurement", "Money word problems: Units of measurement", "Conversion word problems: Units of measurement", "Start Course challenge"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"5th grade16 units \u00b7 130 skills": ["Unit 1Decimal place value", "Unit 2Add decimals", "Unit 3Subtract decimals", "Unit 4Add and subtract fractions", "Unit 5Multi-digit multiplication and division", "Unit 6Multiply fractions", "Unit 7Divide fractions", "Unit 8Multiply decimals", "Unit 9Divide decimals", "Unit 10Powers of ten", "Unit 11Volume", "Unit 12Coordinate plane", "Unit 13Algebraic thinking", "Unit 14Converting units of measure", "Unit 15Line plots", "Unit 16Properties of shapes", "Start Course challenge", "Unit 1Unit 1: Decimal place value", "Decimal place value: Unit test", "Unit 2Unit 2: Add decimals", "Add decimals: Unit test", "Unit 3Unit 3: Subtract decimals", "Subtract decimals: Unit test", "Unit 4Unit 4: Add and subtract fractions", "Add and subtract fractions: Unit test", "Unit 5Unit 5: Multi-digit multiplication and division", "Multi-digit multiplication and division: Unit test", "Unit 6Unit 6: Multiply fractions", "Multiply fractions: Unit test", "Unit 7Unit 7: Divide fractions", "Divide fractions: Unit test", "Unit 8Unit 8: Multiply decimals", "Multiply decimals: Unit test", "Unit 9Unit 9: Divide decimals", "Divide decimals: Unit test", "Unit 10Unit 10: Powers of ten", "Powers of ten: Unit test", "Unit 11Unit 11: Volume", "Volume: Unit test", "Unit 12Unit 12: Coordinate plane", "Coordinate plane: Unit test", "Unit 13Unit 13: Algebraic thinking", "Algebraic thinking: Unit test", "Unit 14Unit 14: Converting units of measure", "Converting units of measure: Unit test", "Unit 15Unit 15: Line plots", "Line plots: Unit test", "Unit 16Unit 16: Properties of shapes", "Properties of shapes: Unit test", "Start Course challenge", "Unit 1: Decimal place value", "Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value", "Unit 2: Add decimals", "Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals", "Unit 3: Subtract decimals", "Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals", "Unit 4: Add and subtract fractions", "Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions", "Unit 5: Multi-digit multiplication and division", "Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division", "Unit 6: Multiply fractions", "Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions", "Unit 7: Divide fractions", "Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions", "Dividing unit fractions by whole numbers: Divide fractions", "Dividing whole numbers by unit fractions: Divide fractions", "Dividing fractions and whole numbers word problems: Divide fractions", "Unit 8: Multiply decimals", "Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals", "Unit 9: Divide decimals", "Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals", "Unit 10: Powers of ten", "Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten", "Unit 11: Volume", "Volume with unit cubes: Volume", "Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume", "Unit 12: Coordinate plane", "Intro to the coordinate plane : Coordinate plane", "Unit 13: Algebraic thinking", "Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking", "Unit 14: Converting units of measure", "Converting units of time: Converting units of measure", "Converting metric units: Converting units of measure", "Converting metric units word problems: Converting units of measure", "Converting US Customary units: Converting units of measure", "Converting US Customary units word problems: Converting units of measure", "Unit 15: Line plots", "Graph data on line plots: Line plots", "Interpret data on line plots: Line plots", "Unit 16: Properties of shapes", "Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"6th grade11 units \u00b7 148 skills": ["Unit 1Ratios", "Unit 2Arithmetic with rational numbers", "Unit 3Rates and percentages", "Unit 4Exponents and order of operations", "Unit 5Negative numbers", "Unit 6Variables & expressions", "Unit 7Equations & inequalities", "Unit 8Plane figures", "Unit 9Coordinate plane", "Unit 103D figures", "Unit 11Data and statistics", "Start Course challenge", "Unit 1Unit 1: Ratios", "Ratios: Unit test", "Unit 2Unit 2: Arithmetic with rational numbers", "Arithmetic with rational numbers: Unit test", "Unit 3Unit 3: Rates and percentages", "Rates and percentages: Unit test", "Unit 4Unit 4: Exponents and order of operations", "Exponents and order of operations: Unit test", "Unit 5Unit 5: Negative numbers", "Negative numbers: Unit test", "Unit 6Unit 6: Variables & expressions", "Variables & expressions: Unit test", "Unit 7Unit 7: Equations & inequalities", "Equations & inequalities: Unit test", "Unit 8Unit 8: Plane figures", "Plane figures: Unit test", "Unit 9Unit 9: Coordinate plane", "Coordinate plane: Unit test", "Unit 10Unit 10: 3D figures", "3D figures: Unit test", "Unit 11Unit 11: Data and statistics", "Data and statistics: Unit test", "Start Course challenge", "Unit 1: Ratios", "Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios", "Unit 2: Arithmetic with rational numbers", "Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers", "Unit 3: Rates and percentages", "Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages", "Unit 4: Exponents and order of operations", "Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations", "Unit 5: Negative numbers", "Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers", "Unit 6: Variables & expressions", "Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions", "Unit 7: Equations & inequalities", "Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities", "Unit 8: Plane figures", "Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures", "Unit 9: Coordinate plane", "Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane", "Unit 10: 3D figures", "Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures", "Unit 11: Data and statistics", "Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"7th grade9 units \u00b7 119 skills": ["Unit 1Proportional relationships", "Unit 2Rates and percentages", "Unit 3Integers: addition and subtraction", "Unit 4Rational numbers: addition and subtraction", "Unit 5Negative numbers: multiplication and division", "Unit 6Expressions, equations, & inequalities", "Unit 7Statistics and probability", "Unit 8Scale copies", "Unit 9Geometry", "Start Course challenge", "Unit 1Unit 1: Proportional relationships", "Proportional relationships: Unit test", "Unit 2Unit 2: Rates and percentages", "Rates and percentages: Unit test", "Unit 3Unit 3: Integers: addition and subtraction", "Integers: addition and subtraction: Unit test", "Unit 4Unit 4: Rational numbers: addition and subtraction", "Rational numbers: addition and subtraction: Unit test", "Unit 5Unit 5: Negative numbers: multiplication and division", "Negative numbers: multiplication and division: Unit test", "Unit 6Unit 6: Expressions, equations, & inequalities", "Expressions, equations, & inequalities: Unit test", "Unit 7Unit 7: Statistics and probability", "Statistics and probability: Unit test", "Unit 8Unit 8: Scale copies", "Scale copies: Unit test", "Unit 9Unit 9: Geometry", "Geometry: Unit test", "Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles", "Unit 1: Proportional relationships", "Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships", "Unit 2: Rates and percentages", "Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages", "Unit 3: Integers: addition and subtraction", "Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction", "Unit 4: Rational numbers: addition and subtraction", "Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction", "Unit 5: Negative numbers: multiplication and division", "Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division", "Unit 6: Expressions, equations, & inequalities", "The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities", "Unit 7: Statistics and probability", "Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability", "Unit 8: Scale copies", "Scale copies: Scale copies", "Scale drawings: Scale copies", "Unit 9: Geometry", "Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"8th grade7 units \u00b7 121 skills": ["Unit 1Numbers and operations", "Unit 2Solving equations with one unknown", "Unit 3Linear equations and functions", "Unit 4Systems of equations", "Unit 5Geometry", "Unit 6Geometric transformations", "Unit 7Data and modeling", "Start Course challenge", "Unit 1Unit 1: Numbers and operations", "Numbers and operations: Unit test", "Unit 2Unit 2: Solving equations with one unknown", "Solving equations with one unknown: Unit test", "Unit 3Unit 3: Linear equations and functions", "Linear equations and functions: Unit test", "Unit 4Unit 4: Systems of equations", "Systems of equations: Unit test", "Unit 5Unit 5: Geometry", "Geometry: Unit test", "Unit 6Unit 6: Geometric transformations", "Geometric transformations: Unit test", "Unit 7Unit 7: Data and modeling", "Data and modeling: Unit test", "Start Course challenge", "Unit 1: Numbers and operations", "Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations", "Unit 2: Solving equations with one unknown", "Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown", "Unit 3: Linear equations and functions", "Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions", "Unit 4: Systems of equations", "Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations", "Unit 5: Geometry", "Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry", "Unit 6: Geometric transformations", "Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations", "Unit 7: Data and modeling", "Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 3rd grade7 units \u00b7 38 skills": ["Unit 1Get ready for addition and subtraction", "Unit 2Get ready for multiplication and division", "Unit 3Get ready for fractions", "Unit 4Get ready for patterns and problem solving", "Unit 5Get ready for area and perimeter", "Unit 6Get ready for telling time", "Unit 7Get ready for data", "Start Course challenge", "Unit 1Unit 1: Get ready for addition and subtraction", "Get ready for addition and subtraction: Unit test", "Unit 2Unit 2: Get ready for multiplication and division", "Get ready for multiplication and division: Unit test", "Unit 3Unit 3: Get ready for fractions", "Get ready for fractions: Unit test", "Unit 4Unit 4: Get ready for patterns and problem solving", "Get ready for patterns and problem solving: Unit test", "Unit 5Unit 5: Get ready for area and perimeter", "Get ready for area and perimeter: Unit test", "Unit 6Unit 6: Get ready for telling time", "Get ready for telling time: Unit test", "Unit 7Unit 7: Get ready for data", "Get ready for data: Unit test", "Start Course challenge", "Unit 1: Get ready for addition and subtraction", "Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction", "Unit 2: Get ready for multiplication and division", "Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division", "Unit 3: Get ready for fractions", "Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions", "Unit 4: Get ready for patterns and problem solving", "Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving", "Unit 5: Get ready for area and perimeter", "Units of length: Get ready for area and perimeter", "Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter", "Unit 6: Get ready for telling time", "Telling time: Get ready for telling time", "Unit 7: Get ready for data", "Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 4th grade7 units \u00b7 56 skills": ["Unit 1Get ready for place value", "Unit 2Get ready for addition, subtraction, and estimation", "Unit 3Get ready for multiplication", "Unit 4Get ready for division", "Unit 5Get ready for fractions", "Unit 6Get ready for plane figures", "Unit 7Get ready for area and perimeter", "Start Course challenge", "Unit 1Unit 1: Get ready for place value", "Get ready for place value: Unit test", "Unit 2Unit 2: Get ready for addition, subtraction, and estimation", "Get ready for addition, subtraction, and estimation: Unit test", "Unit 3Unit 3: Get ready for multiplication", "Get ready for multiplication: Unit test", "Unit 4Unit 4: Get ready for division", "Get ready for division: Unit test", "Unit 5Unit 5: Get ready for fractions", "Get ready for fractions: Unit test", "Unit 6Unit 6: Get ready for plane figures", "Get ready for plane figures : Unit test", "Unit 7Unit 7: Get ready for area and perimeter", "Get ready for area and perimeter: Unit test", "Start Course challenge", "Unit 1: Get ready for place value", "Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value", "Unit 2: Get ready for addition, subtraction, and estimation", "Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation", "Unit 3: Get ready for multiplication", "Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication", "Unit 4: Get ready for division", "Division intro: Get ready for division", "Relate multiplication and division: Get ready for division", "Unit 5: Get ready for fractions", "Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions", "Unit 6: Get ready for plane figures", "Quadrilaterals: Get ready for plane figures", "Unit 7: Get ready for area and perimeter", "Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 5th grade8 units \u00b7 62 skills": ["Unit 1Get ready for decimal place value", "Unit 2Get ready for adding and subtracting decimals", "Unit 3Get ready for adding and subtracting fractions", "Unit 4Get ready for multiplication and division with whole numbers and decimals", "Unit 5Get ready for multiplying and dividing fractions", "Unit 6Get ready for powers of 10", "Unit 7Get ready for volume", "Unit 8Get ready for properties of shapes", "Start Course challenge", "Unit 1Unit 1: Get ready for decimal place value", "Get ready for decimal place value: Unit test", "Unit 2Unit 2: Get ready for adding and subtracting decimals", "Get ready for adding and subtracting decimals: Unit test", "Unit 3Unit 3: Get ready for adding and subtracting fractions", "Get ready for adding and subtracting fractions: Unit test", "Unit 4Unit 4: Get ready for multiplication and division with whole numbers and decimals", "Get ready for multiplication and division with whole numbers and decimals: Unit test", "Unit 5Unit 5: Get ready for multiplying and dividing fractions", "Get ready for multiplying and dividing fractions: Unit test", "Unit 6Unit 6: Get ready for powers of 10", "Get ready for powers of 10: Unit test", "Unit 7Unit 7: Get ready for volume", "Get ready for volume: Unit test", "Unit 8Unit 8: Get ready for properties of shapes", "Get ready for properties of shapes: Unit test", "Start Course challenge", "Unit 1: Get ready for decimal place value", "Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value", "Unit 2: Get ready for adding and subtracting decimals", "Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals", "Unit 3: Get ready for adding and subtracting fractions", "Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions", "Unit 4: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals", "Unit 5: Get ready for multiplying and dividing fractions", "Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions", "Unit 6: Get ready for powers of 10", "How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10", "Unit 7: Get ready for volume", "Introduction to area: Get ready for volume", "Unit 8: Get ready for properties of shapes", "Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 6th grade5 units \u00b7 60 skills": ["Unit 1Get ready for ratios, rates, and percentages", "Unit 2Get ready for arithmetic operations", "Unit 3Get ready for negative numbers", "Unit 4Get ready for equations, expressions, and inequalities", "Unit 5Get ready for geometry", "Start Course challenge", "Unit 1Unit 1: Get ready for ratios, rates, and percentages", "Get ready for ratios, rates, and percentages: Unit test", "Unit 2Unit 2: Get ready for arithmetic operations", "Get ready for arithmetic operations: Unit test", "Unit 3Unit 3: Get ready for negative numbers", "Get ready for negative numbers: Unit test", "Unit 4Unit 4: Get ready for equations, expressions, and inequalities", "Get ready for equations, expressions, and inequalities: Unit test", "Unit 5Unit 5: Get ready for geometry", "Get ready for geometry: Unit test", "Start Course challenge", "Unit 1: Get ready for ratios, rates, and percentages", "Multiplication and division word problems: Get ready for ratios, rates, and percentages", "Convert units of measure: Get ready for ratios, rates, and percentages", "Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages", "Unit 2: Get ready for arithmetic operations", "Divide whole numbers by unit fractions: Get ready for arithmetic operations", "Divide unit fractions by whole numbers: Get ready for arithmetic operations", "Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations", "Unit 3: Get ready for negative numbers", "Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers", "Unit 4: Get ready for equations, expressions, and inequalities", "Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities", "Unit 5: Get ready for geometry", "Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 7th grade6 units \u00b7 63 skills": ["Unit 1Get ready for negative number operations", "Unit 2Get ready for fractions, decimals, & percentages", "Unit 3Get ready for rates & proportional relationships", "Unit 4Get ready for expressions, equations, & inequalities", "Unit 5Get ready for geometry", "Unit 6Get ready for statistics & probability", "Start Course challenge", "Unit 1Unit 1: Get ready for negative number operations", "Get ready for negative number operations: Unit test", "Unit 2Unit 2: Get ready for fractions, decimals, & percentages", "Get ready for fractions, decimals, & percentages: Unit test", "Unit 3Unit 3: Get ready for rates & proportional relationships", "Get ready for rates & proportional relationships: Unit test", "Unit 4Unit 4: Get ready for expressions, equations, & inequalities", "Get ready for expressions, equations, & inequalities: Unit test", "Unit 5Unit 5: Get ready for geometry", "Get ready for geometry: Unit test", "Unit 6Unit 6: Get ready for statistics & probability", "Get ready for statistics & probability: Unit test", "Start Course challenge", "Unit 1: Get ready for negative number operations", "Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations", "Unit 2: Get ready for fractions, decimals, & percentages", "Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages", "Unit 3: Get ready for rates & proportional relationships", "Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships", "Unit 4: Get ready for expressions, equations, & inequalities", "Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities", "Unit 5: Get ready for geometry", "Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry", "Unit 6: Get ready for statistics & probability", "Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 8th grade4 units \u00b7 44 skills": ["Unit 1Get ready for numbers and operations", "Unit 2Get ready for solving equations and systems of equations", "Unit 3Get ready for linear equations and functions", "Unit 4Get ready for geometry", "Start Course challenge", "Unit 1Unit 1: Get ready for numbers and operations", "Get ready for numbers and operations: Unit test", "Unit 2Unit 2: Get ready for solving equations and systems of equations", "Get ready for solving equations and systems of equations: Unit test", "Unit 3Unit 3: Get ready for linear equations and functions", "Get ready for linear equations and functions: Unit test", "Unit 4Unit 4: Get ready for geometry", "Get ready for geometry: Unit test", "Start Course challenge", "Unit 1: Get ready for numbers and operations", "Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations", "Unit 2: Get ready for solving equations and systems of equations", "Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations", "Unit 3: Get ready for linear equations and functions", "Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions", "Unit 4: Get ready for geometry", "Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Get ready for Algebra 16 units \u00b7 87 skills": ["Unit 1Get ready for equations & inequalities", "Unit 2Get ready for working with units", "Unit 3Get ready for linear relationships", "Unit 4Get ready for functions & sequences", "Unit 5Get ready for exponents, radicals, & irrational numbers", "Unit 6Get ready for quadratics", "Start Course challenge", "Unit 1Unit 1: Get ready for equations & inequalities", "Get ready for equations & inequalities: Unit test", "Unit 2Unit 2: Get ready for working with units", "Get ready for working with units: Unit test", "Unit 3Unit 3: Get ready for linear relationships", "Get ready for linear relationships: Unit test", "Unit 4Unit 4: Get ready for functions & sequences", "Get ready for functions & sequences: Unit test", "Unit 5Unit 5: Get ready for exponents, radicals, & irrational numbers", "Get ready for exponents, radicals, & irrational numbers: Unit test", "Unit 6Unit 6: Get ready for quadratics", "Get ready for quadratics: Unit test", "Start Course challenge", "Unit 1: Get ready for equations & inequalities", "Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities", "Unit 2: Get ready for working with units", "Intro to ratios: Get ready for working with units", "Equivalent ratios: Get ready for working with units", "Ratio application: Get ready for working with units", "Intro to rates: Get ready for working with units", "Rate problems: Get ready for working with units", "Unit 3: Get ready for linear relationships", "Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships", "Unit 4: Get ready for functions & sequences", "Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences", "Unit 5: Get ready for exponents, radicals, & irrational numbers", "Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers", "Unit 6: Get ready for quadratics", "Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Get ready for Geometry4 units \u00b7 51 skills": ["Unit 1Get ready for congruence, similarity, and triangle trigonometry", "Unit 2Get ready for analytic geometry", "Unit 3Get ready for conic sections", "Unit 4Get ready for circles and solid geometry", "Start Course challenge", "Unit 1Unit 1: Get ready for congruence, similarity, and triangle trigonometry", "Get ready for congruence, similarity, and triangle trigonometry: Unit test", "Unit 2Unit 2: Get ready for analytic geometry", "Get ready for analytic geometry: Unit test", "Unit 3Unit 3: Get ready for conic sections", "Get ready for conic sections: Unit test", "Unit 4Unit 4: Get ready for circles and solid geometry", "Get ready for circles and solid geometry: Unit test", "Start Course challenge", "Unit 1: Get ready for congruence, similarity, and triangle trigonometry", "Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry", "Unit 2: Get ready for analytic geometry", "Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry", "Unit 3: Get ready for conic sections", "Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections", "Unit 4: Get ready for circles and solid geometry", "Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Get ready for Algebra 26 units \u00b7 96 skills": ["Unit 1Get ready for polynomial operations and complex numbers", "Unit 2Get ready for equations", "Unit 3Get ready for transformations of functions and modeling with functions", "Unit 4Get ready for exponential and logarithmic relationships", "Unit 5Get ready for trigonometry", "Unit 6Get ready for rational functions", "Start Course challenge", "Unit 1Unit 1: Get ready for polynomial operations and complex numbers", "Get ready for polynomial operations and complex numbers: Unit test", "Unit 2Unit 2: Get ready for equations", "Get ready for equations: Unit test", "Unit 3Unit 3: Get ready for transformations of functions and modeling with functions", "Get ready for transformations of functions and modeling with functions: Unit test", "Unit 4Unit 4: Get ready for exponential and logarithmic relationships", "Get ready for exponential and logarithmic relationships: Unit test", "Unit 5Unit 5: Get ready for trigonometry", "Get ready for trigonometry: Unit test", "Unit 6Unit 6: Get ready for rational functions", "Get ready for rational functions: Unit test", "Start Course challenge", "Unit 1: Get ready for polynomial operations and complex numbers", "Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers", "Unit 2: Get ready for equations", "Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations", "Unit 3: Get ready for transformations of functions and modeling with functions", "Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions", "Unit 4: Get ready for exponential and logarithmic relationships", "Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships", "Unit 5: Get ready for trigonometry", "Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry", "Unit 6: Get ready for rational functions", "Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Get ready for Precalculus", "course_url": "/math/get-ready-for-precalculus", "page_contents": {"syllabus": {"topics": {"Get ready for Precalculus8 units \u00b7 88 skills": ["Unit 1Get ready for complex numbers", "Unit 2Get ready for polynomials", "Unit 3Get ready for composite and inverse functions", "Unit 4Get ready for trigonometry", "Unit 5Get ready for vectors and matrices", "Unit 6Get ready for series", "Unit 7Get ready for conic sections", "Unit 8Get ready for probability and combinatorics", "Start Course challenge", "Unit 1Unit 1: Get ready for complex numbers", "Get ready for complex numbers: Unit test", "Unit 2Unit 2: Get ready for polynomials", "Get ready for polynomials: Unit test", "Unit 3Unit 3: Get ready for composite and inverse functions", "Get ready for composite and inverse functions: Unit test", "Unit 4Unit 4: Get ready for trigonometry", "Get ready for trigonometry: Unit test", "Unit 5Unit 5: Get ready for vectors and matrices", "Get ready for vectors and matrices: Unit test", "Unit 6Unit 6: Get ready for series", "Get ready for series: Unit test", "Unit 7Unit 7: Get ready for conic sections", "Get ready for conic sections: Unit test", "Unit 8Unit 8: Get ready for probability and combinatorics", "Get ready for probability and combinatorics: Unit test", "Start Course challenge", "Unit 1: Get ready for complex numbers", "The imaginary unit i: Get ready for complex numbers", "Complex numbers introduction: Get ready for complex numbers", "The complex plane: Get ready for complex numbers", "Adding and subtracting complex numbers: Get ready for complex numbers", "Quadratic equations with complex solutions: Get ready for complex numbers", "Unit 2: Get ready for polynomials", "Adding and subtracting polynomials: Get ready for polynomials", "Multiplying binomials by polynomials: Get ready for polynomials", "Special products of polynomials: Get ready for polynomials", "Factoring higher degree polynomials: Get ready for polynomials", "Factoring using structure: Get ready for polynomials", "Zeros of polynomials: Get ready for polynomials", "Dividing polynomials by x: Get ready for polynomials", "Dividing quadratics by linear factors: Get ready for polynomials", "Dividing polynomials by linear factors: Get ready for polynomials", "Unit 3: Get ready for composite and inverse functions", "Shifting functions: Get ready for composite and inverse functions", "Reflecting functions: Get ready for composite and inverse functions", "Scaling functions: Get ready for composite and inverse functions", "Identifying function transformations: Get ready for composite and inverse functions", "Intro to domain and range of a function: Get ready for composite and inverse functions", "Intro to inverse functions: Get ready for composite and inverse functions", "Unit 4: Get ready for trigonometry", "Unit circle introduction: Get ready for trigonometry", "Radians: Get ready for trigonometry", "The Pythagorean identity: Get ready for trigonometry", "Trigonometric values of special angles: Get ready for trigonometry", "Graphing sinusoidal functions: Get ready for trigonometry", "Sinusoidal models: Get ready for trigonometry", "Unit 5: Get ready for vectors and matrices", "Equivalent systems of equations and the elimination method: Get ready for vectors and matrices", "Dilations: Get ready for vectors and matrices", "Solving triangles using the trigonometric ratios: Get ready for vectors and matrices", "Unit circle introduction: Get ready for vectors and matrices", "Distance formula: Get ready for vectors and matrices", "Unit 6: Get ready for series", "Intro to sequences: Get ready for series", "Constructing arithmetic sequences: Get ready for series", "Constructing geometric sequences: Get ready for series", "Modeling with sequences: Get ready for series", "General sequences: Get ready for series", "Geometric series: Get ready for series", "Unit 7: Get ready for conic sections", "Graphs of circles intro: Get ready for conic sections", "Standard equation of a circle: Get ready for conic sections", "Expanded equation of a circle: Get ready for conic sections", "Focus and directrix of a parabola: Get ready for conic sections", "Unit 8: Get ready for probability and combinatorics", "Basic theoretical probability: Get ready for probability and combinatorics", "Probability using sample spaces: Get ready for probability and combinatorics", "Basic set operations: Get ready for probability and combinatorics", "Experimental probability: Get ready for probability and combinatorics", "Randomness, probability, and simulation: Get ready for probability and combinatorics", "Addition rule: Get ready for probability and combinatorics", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Calculus", "course_url": "/math/get-ready-for-ap-calc", "page_contents": {"syllabus": {"topics": {"Get ready for AP\u00ae Calculus9 units \u00b7 112 skills": ["Unit 1Get ready for limits and continuity", "Unit 2Get ready for differentiation: definition and basic derivative rules", "Unit 3Get ready for differentiation: composite, implicit, and inverse functions", "Unit 4Get ready for contextual applications of differentiation", "Unit 5Get ready for applying derivatives to analyze functions", "Unit 6Get ready for integration and accumulation of change", "Unit 7Get ready for applications of integration", "Unit 8Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Unit 9Get ready for infinite sequences and series (BC only)", "Start Course challenge", "Unit 1Unit 1: Get ready for limits and continuity", "Get ready for limits and continuity: Unit test", "Unit 2Unit 2: Get ready for differentiation: definition and basic derivative rules", "Get ready for differentiation: definition and basic derivative rules: Unit test", "Unit 3Unit 3: Get ready for differentiation: composite, implicit, and inverse functions", "Get ready for differentiation: composite, implicit, and inverse functions: Unit test", "Unit 4Unit 4: Get ready for contextual applications of differentiation", "Get ready for contextual applications of differentiation: Unit test", "Unit 5Unit 5: Get ready for applying derivatives to analyze functions", "Get ready for applying derivatives to analyze functions : Unit test", "Unit 6Unit 6: Get ready for integration and accumulation of change", "Get ready for integration and accumulation of change: Unit test", "Unit 7Unit 7: Get ready for applications of integration", "Get ready for applications of integration: Unit test", "Unit 8Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only): Unit test", "Unit 9Unit 9: Get ready for infinite sequences and series (BC only)", "Get ready for infinite sequences and series (BC only): Unit test", "Start Course challenge", "Unit 1: Get ready for limits and continuity", "Evaluating functions: Get ready for limits and continuity", "Inputs and outputs of a function: Get ready for limits and continuity", "Composing functions: Get ready for limits and continuity", "Piecewise functions: Get ready for limits and continuity", "Introduction to factoring: Get ready for limits and continuity", "Factoring quadratics intro: Get ready for limits and continuity", "Factoring quadratics by grouping: Get ready for limits and continuity", "Factoring quadratics with difference of squares: Get ready for limits and continuity", "Factoring quadratics with perfect squares: Get ready for limits and continuity", "Factoring higher degree polynomials: Get ready for limits and continuity", "Introduction to the trigonometric ratios: Get ready for limits and continuity", "Unit circle introduction: Get ready for limits and continuity", "Radians: Get ready for limits and continuity", "The Pythagorean identity: Get ready for limits and continuity", "Special trigonometric values in the first quadrant: Get ready for limits and continuity", "Trigonometric identities on the unit circle: Get ready for limits and continuity", "Angle addition identities: Get ready for limits and continuity", "Reducing rational expressions to lowest terms: Get ready for limits and continuity", "End behavior of rational functions: Get ready for limits and continuity", "Discontinuities of rational functions: Get ready for limits and continuity", "Multiplying and dividing rational expressions: Get ready for limits and continuity", "Unit 2: Get ready for differentiation: definition and basic derivative rules", "Intro to slope-intercept form: Get ready for differentiation: definition and basic derivative rules", "Writing slope-intercept equations: Get ready for differentiation: definition and basic derivative rules", "Point-slope form: Get ready for differentiation: definition and basic derivative rules", "Average rate of change: Get ready for differentiation: definition and basic derivative rules", "Rational exponents: Get ready for differentiation: definition and basic derivative rules", "Properties of exponents: Get ready for differentiation: definition and basic derivative rules", "Introduction to logarithms: Get ready for differentiation: definition and basic derivative rules", "Unit 3: Get ready for differentiation: composite, implicit, and inverse functions", "Composing functions: Get ready for differentiation: composite, implicit, and inverse functions", "Linear equations with unknown coefficients: Get ready for differentiation: composite, implicit, and inverse functions", "Intro to inverse functions: Get ready for differentiation: composite, implicit, and inverse functions", "Invertible functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse trigonometric functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse functions in graphs and tables: Get ready for differentiation: composite, implicit, and inverse functions", "Verifying inverse functions by composition: Get ready for differentiation: composite, implicit, and inverse functions", "Unit 4: Get ready for contextual applications of differentiation", "Word problems with multiple units: Get ready for contextual applications of differentiation", "Linear equations word problems: Get ready for contextual applications of differentiation", "Interpreting function notation: Get ready for contextual applications of differentiation", "Average rate of change word problems: Get ready for contextual applications of differentiation", "Modeling with composite functions: Get ready for contextual applications of differentiation", "Modeling with right triangles: Get ready for contextual applications of differentiation", "Volume and surface area: Get ready for contextual applications of differentiation", "Unit 5: Get ready for applying derivatives to analyze functions", "Maximum and minimum points: Get ready for applying derivatives to analyze functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for applying derivatives to analyze functions", "Interpreting features of graphs: Get ready for applying derivatives to analyze functions", "Distance formula: Get ready for applying derivatives to analyze functions", "Square-root equations: Get ready for applying derivatives to analyze functions", "Zeros of polynomials: Get ready for applying derivatives to analyze functions", "Positive and negative intervals of polynomials: Get ready for applying derivatives to analyze functions", "Unit 6: Get ready for integration and accumulation of change", "Completing the square: Get ready for integration and accumulation of change", "Dividing quadratics by linear factors: Get ready for integration and accumulation of change", "Dividing polynomials by linear factors: Get ready for integration and accumulation of change", "Partial fraction expansion: Get ready for integration and accumulation of change", "Summation notation: Get ready for integration and accumulation of change", "Unit 7: Get ready for applications of integration", "Rational equations: Get ready for applications of integration", "Square-root equations: Get ready for applications of integration", "Extraneous solutions: Get ready for applications of integration", "Sinusoidal equations: Get ready for applications of integration", "Manipulating formulas: Get ready for applications of integration", "Solving equations by graphing: Get ready for applications of integration", "Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Sectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vectors introduction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Magnitude of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Scalar multiplication: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Direction of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components from magnitude & direction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Unit 9: Get ready for infinite sequences and series (BC only)", "Arithmetic sequences: Get ready for infinite sequences and series (BC only)", "Geometric sequences: Get ready for infinite sequences and series (BC only)", "Summation notation: Get ready for infinite sequences and series (BC only)", "Arithmetic series: Get ready for infinite sequences and series (BC only)", "Geometric series: Get ready for infinite sequences and series (BC only)", "End behavior of rational functions: Get ready for infinite sequences and series (BC only)", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Statistics", "course_url": "/math/get-ready-for-ap-statistics", "page_contents": {"syllabus": {"topics": {"Get ready for AP\u00ae Statistics5 units \u00b7 37 skills": ["Unit 1Get ready for exploring categorical data", "Unit 2Get ready for exploring one-variable quantitative data", "Unit 3Get ready for exploring two-variable quantitative data", "Unit 4Get ready for probability", "Unit 5Get ready for random variables and probability distributions", "Start Course challenge", "Unit 1Unit 1: Get ready for exploring categorical data", "Get ready for exploring categorical data: Unit test", "Unit 2Unit 2: Get ready for exploring one-variable quantitative data", "Get ready for exploring one-variable quantitative data: Unit test", "Unit 3Unit 3: Get ready for exploring two-variable quantitative data", "Get ready for exploring two-variable quantitative data: Unit test", "Unit 4Unit 4: Get ready for probability", "Get ready for probability: Unit test", "Unit 5Unit 5: Get ready for random variables and probability distributions", "Get ready for random variables and probability distributions: Unit test", "Start Course challenge", "Unit 1: Get ready for exploring categorical data", "Frequency tables: Get ready for exploring categorical data", "Bar graphs: Get ready for exploring categorical data", "Fractions, decimals, and percentages: Get ready for exploring categorical data", "Unit 2: Get ready for exploring one-variable quantitative data", "Frequency tables and dot plots: Get ready for exploring one-variable quantitative data", "Box and whisker plots: Get ready for exploring one-variable quantitative data", "Comparing data displays: Get ready for exploring one-variable quantitative data", "Mean, median, and mode: Get ready for exploring one-variable quantitative data", "Mean absolute deviation: Get ready for exploring one-variable quantitative data", "Linear equations with variables on both sides: Get ready for exploring one-variable quantitative data", "Linear equations with unknown coefficients: Get ready for exploring one-variable quantitative data", "Unit 3: Get ready for exploring two-variable quantitative data", "Introduction to scatter plots: Get ready for exploring two-variable quantitative data", "Estimating with trend lines: Get ready for exploring two-variable quantitative data", "Logarithms: Get ready for exploring two-variable quantitative data", "Unit 4: Get ready for probability", "Fractions, decimals, and percentages: Get ready for probability", "Comparing decimals and fractions: Get ready for probability", "Arithmetic with fractions: Get ready for probability", "Probability introduction: Get ready for probability", "Experimental probability: Get ready for probability", "Unit 5: Get ready for random variables and probability distributions", "Predictions with probability: Get ready for random variables and probability distributions", "The counting principle: Get ready for random variables and probability distributions", "Probability distributions introduction: Get ready for random variables and probability distributions", "Start Course challenge"]}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Early math review8 units \u00b7 121 skills": ["Unit 1Counting", "Unit 2Addition and subtraction intro", "Unit 3Place value (tens and hundreds)", "Unit 4Addition and subtraction within 20", "Unit 5Addition and subtraction within 100", "Unit 6Addition and subtraction within 1000", "Unit 7Measurement and data", "Unit 8Geometry", "Start Course challenge", "Unit 1Unit 1: Counting", "Counting: Unit test", "Unit 2Unit 2: Addition and subtraction intro", "Addition and subtraction intro: Unit test", "Unit 3Unit 3: Place value (tens and hundreds)", "Place value (tens and hundreds): Unit test", "Unit 4Unit 4: Addition and subtraction within 20", "Addition and subtraction within 20: Unit test", "Unit 5Unit 5: Addition and subtraction within 100", "Addition and subtraction within 100: Unit test", "Unit 6Unit 6: Addition and subtraction within 1000", "Addition and subtraction within 1000: Unit test", "Unit 7Unit 7: Measurement and data", "Measurement and data: Unit test", "Unit 8Unit 8: Geometry", "Geometry: Unit test", "Start Course challenge", "Unit 1: Counting", "Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting", "Unit 2: Addition and subtraction intro", "What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro", "Unit 3: Place value (tens and hundreds)", "Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)", "Unit 4: Addition and subtraction within 20", "Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20", "Unit 5: Addition and subtraction within 100", "Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100", "Unit 6: Addition and subtraction within 1000", "Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000", "Unit 7: Measurement and data", "Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data", "Unit 8: Geometry", "Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"2nd grade8 units \u00b7 75 skills": ["Unit 1Add and subtract within 20", "Unit 2Place value", "Unit 3Add and subtract within 100", "Unit 4Add and subtract within 1,000", "Unit 5Money and time", "Unit 6Measurement", "Unit 7Data", "Unit 8Geometry", "Start Course challenge", "Unit 1Unit 1: Add and subtract within 20", "Add and subtract within 20: Unit test", "Unit 2Unit 2: Place value", "Place value: Unit test", "Unit 3Unit 3: Add and subtract within 100", "Add and subtract within 100: Unit test", "Unit 4Unit 4: Add and subtract within 1,000", "Add and subtract within 1,000: Unit test", "Unit 5Unit 5: Money and time", "Money and time: Unit test", "Unit 6Unit 6: Measurement", "Measurement: Unit test", "Unit 7Unit 7: Data", "Data: Unit test", "Unit 8Unit 8: Geometry", "Geometry: Unit test", "Start Course challenge", "Unit 1: Add and subtract within 20", "Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20", "Unit 2: Place value", "Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value", "Unit 3: Add and subtract within 100", "Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100", "Unit 4: Add and subtract within 1,000", "Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000", "Unit 5: Money and time", "Time: Money and time", "Unit 6: Measurement", "Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement", "Unit 7: Data", "Bar graphs: Data", "Line plots: Data", "Unit 8: Geometry", "Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"3rd grade14 units \u00b7 141 skills": ["Unit 1Intro to multiplication", "Unit 21-digit multiplication", "Unit 3Addition, subtraction, and estimation", "Unit 4Intro to division", "Unit 5Understand fractions", "Unit 6Equivalent fractions and comparing fractions", "Unit 7More with multiplication and division", "Unit 8Arithmetic patterns and problem solving", "Unit 9Quadrilaterals", "Unit 10Area", "Unit 11Perimeter", "Unit 12Time", "Unit 13Measurement", "Unit 14Represent and interpret data", "Start Course challenge", "Unit 1Unit 1: Intro to multiplication", "Intro to multiplication: Unit test", "Unit 2Unit 2: 1-digit multiplication", "1-digit multiplication: Unit test", "Unit 3Unit 3: Addition, subtraction, and estimation", "Addition, subtraction, and estimation: Unit test", "Unit 4Unit 4: Intro to division", "Intro to division: Unit test", "Unit 5Unit 5: Understand fractions", "Understand fractions: Unit test", "Unit 6Unit 6: Equivalent fractions and comparing fractions", "Equivalent fractions and comparing fractions: Unit test", "Unit 7Unit 7: More with multiplication and division", "More with multiplication and division: Unit test", "Unit 8Unit 8: Arithmetic patterns and problem solving", "Arithmetic patterns and problem solving: Unit test", "Unit 9Unit 9: Quadrilaterals", "Quadrilaterals: Unit test", "Unit 10Unit 10: Area", "Area: Unit test", "Unit 11Unit 11: Perimeter", "Perimeter: Unit test", "Unit 12Unit 12: Time", "Time: Unit test", "Unit 13Unit 13: Measurement", "Measurement: Unit test", "Unit 14Unit 14: Represent and interpret data", "Represent and interpret data: Unit test", "Start Course challenge", "Unit 1: Intro to multiplication", "Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication", "Unit 2: 1-digit multiplication", "Distributive property: 1-digit multiplication", "Unit 3: Addition, subtraction, and estimation", "Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation", "Unit 4: Intro to division", "Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division", "Unit 5: Understand fractions", "Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions", "Unit 6: Equivalent fractions and comparing fractions", "Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions", "Unit 7: More with multiplication and division", "Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division", "Unit 8: Arithmetic patterns and problem solving", "2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving", "Unit 9: Quadrilaterals", "Quadrilaterals : Quadrilaterals", "Unit 10: Area", "Count unit squares to find area: Area", "Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area", "Unit 11: Perimeter", "Perimeter: Perimeter", "Perimeter word problems: Perimeter", "Unit 12: Time", "Time on number line: Time", "Telling time: Time", "Elapsed time: Time", "Unit 13: Measurement", "Mass: Measurement", "Volume: Measurement", "Unit 14: Represent and interpret data", "Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"4th grade14 units \u00b7 154 skills": ["Unit 1Place value", "Unit 2Addition, subtraction, and estimation", "Unit 3Multiply by 1-digit numbers", "Unit 4Multiply by 2-digit numbers", "Unit 5Division", "Unit 6Factors, multiples and patterns", "Unit 7Equivalent fractions and comparing fractions", "Unit 8Add and subtract fractions", "Unit 9Multiply fractions", "Unit 10Understand decimals", "Unit 11Plane figures", "Unit 12Measuring angles", "Unit 13Area and perimeter", "Unit 14Units of measurement", "Start Course challenge", "Unit 1Unit 1: Place value", "Place value: Unit test", "Unit 2Unit 2: Addition, subtraction, and estimation", "Addition, subtraction, and estimation: Unit test", "Unit 3Unit 3: Multiply by 1-digit numbers", "Multiply by 1-digit numbers: Unit test", "Unit 4Unit 4: Multiply by 2-digit numbers", "Multiply by 2-digit numbers: Unit test", "Unit 5Unit 5: Division", "Division: Unit test", "Unit 6Unit 6: Factors, multiples and patterns", "Factors, multiples and patterns: Unit test", "Unit 7Unit 7: Equivalent fractions and comparing fractions", "Equivalent fractions and comparing fractions: Unit test", "Unit 8Unit 8: Add and subtract fractions", "Add and subtract fractions: Unit test", "Unit 9Unit 9: Multiply fractions", "Multiply fractions: Unit test", "Unit 10Unit 10: Understand decimals", "Understand decimals: Unit test", "Unit 11Unit 11: Plane figures", "Plane figures: Unit test", "Unit 12Unit 12: Measuring angles", "Measuring angles: Unit test", "Unit 13Unit 13: Area and perimeter", "Area and perimeter: Unit test", "Unit 14Unit 14: Units of measurement", "Units of measurement: Unit test", "Start Course challenge", "Unit 1: Place value", "Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value", "Unit 2: Addition, subtraction, and estimation", "Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation", "Unit 3: Multiply by 1-digit numbers", "Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers", "Unit 4: Multiply by 2-digit numbers", "Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers", "Unit 5: Division", "Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division", "Unit 6: Factors, multiples and patterns", "Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns", "Unit 7: Equivalent fractions and comparing fractions", "Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions", "Unit 8: Add and subtract fractions", "Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions", "Unit 9: Multiply fractions", "Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions", "Unit 10: Understand decimals", "Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals", "Unit 11: Plane figures", "Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures", "Unit 12: Measuring angles", "Measuring angles: Measuring angles", "Decomposing angles: Measuring angles", "Unit 13: Area and perimeter", "Area and perimeter: Area and perimeter", "Unit 14: Units of measurement", "Estimating volume: Units of measurement", "Estimating length: Units of measurement", "Time: Units of measurement", "Converting units of mass: Units of measurement", "Converting units of volume: Units of measurement", "Converting units of length: Units of measurement", "Converting units of time: Units of measurement", "Money word problems: Units of measurement", "Conversion word problems: Units of measurement", "Start Course challenge"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"5th grade16 units \u00b7 130 skills": ["Unit 1Decimal place value", "Unit 2Add decimals", "Unit 3Subtract decimals", "Unit 4Add and subtract fractions", "Unit 5Multi-digit multiplication and division", "Unit 6Multiply fractions", "Unit 7Divide fractions", "Unit 8Multiply decimals", "Unit 9Divide decimals", "Unit 10Powers of ten", "Unit 11Volume", "Unit 12Coordinate plane", "Unit 13Algebraic thinking", "Unit 14Converting units of measure", "Unit 15Line plots", "Unit 16Properties of shapes", "Start Course challenge", "Unit 1Unit 1: Decimal place value", "Decimal place value: Unit test", "Unit 2Unit 2: Add decimals", "Add decimals: Unit test", "Unit 3Unit 3: Subtract decimals", "Subtract decimals: Unit test", "Unit 4Unit 4: Add and subtract fractions", "Add and subtract fractions: Unit test", "Unit 5Unit 5: Multi-digit multiplication and division", "Multi-digit multiplication and division: Unit test", "Unit 6Unit 6: Multiply fractions", "Multiply fractions: Unit test", "Unit 7Unit 7: Divide fractions", "Divide fractions: Unit test", "Unit 8Unit 8: Multiply decimals", "Multiply decimals: Unit test", "Unit 9Unit 9: Divide decimals", "Divide decimals: Unit test", "Unit 10Unit 10: Powers of ten", "Powers of ten: Unit test", "Unit 11Unit 11: Volume", "Volume: Unit test", "Unit 12Unit 12: Coordinate plane", "Coordinate plane: Unit test", "Unit 13Unit 13: Algebraic thinking", "Algebraic thinking: Unit test", "Unit 14Unit 14: Converting units of measure", "Converting units of measure: Unit test", "Unit 15Unit 15: Line plots", "Line plots: Unit test", "Unit 16Unit 16: Properties of shapes", "Properties of shapes: Unit test", "Start Course challenge", "Unit 1: Decimal place value", "Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value", "Unit 2: Add decimals", "Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals", "Unit 3: Subtract decimals", "Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals", "Unit 4: Add and subtract fractions", "Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions", "Unit 5: Multi-digit multiplication and division", "Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division", "Unit 6: Multiply fractions", "Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions", "Unit 7: Divide fractions", "Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions", "Dividing unit fractions by whole numbers: Divide fractions", "Dividing whole numbers by unit fractions: Divide fractions", "Dividing fractions and whole numbers word problems: Divide fractions", "Unit 8: Multiply decimals", "Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals", "Unit 9: Divide decimals", "Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals", "Unit 10: Powers of ten", "Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten", "Unit 11: Volume", "Volume with unit cubes: Volume", "Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume", "Unit 12: Coordinate plane", "Intro to the coordinate plane : Coordinate plane", "Unit 13: Algebraic thinking", "Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking", "Unit 14: Converting units of measure", "Converting units of time: Converting units of measure", "Converting metric units: Converting units of measure", "Converting metric units word problems: Converting units of measure", "Converting US Customary units: Converting units of measure", "Converting US Customary units word problems: Converting units of measure", "Unit 15: Line plots", "Graph data on line plots: Line plots", "Interpret data on line plots: Line plots", "Unit 16: Properties of shapes", "Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"6th grade11 units \u00b7 148 skills": ["Unit 1Ratios", "Unit 2Arithmetic with rational numbers", "Unit 3Rates and percentages", "Unit 4Exponents and order of operations", "Unit 5Negative numbers", "Unit 6Variables & expressions", "Unit 7Equations & inequalities", "Unit 8Plane figures", "Unit 9Coordinate plane", "Unit 103D figures", "Unit 11Data and statistics", "Start Course challenge", "Unit 1Unit 1: Ratios", "Ratios: Unit test", "Unit 2Unit 2: Arithmetic with rational numbers", "Arithmetic with rational numbers: Unit test", "Unit 3Unit 3: Rates and percentages", "Rates and percentages: Unit test", "Unit 4Unit 4: Exponents and order of operations", "Exponents and order of operations: Unit test", "Unit 5Unit 5: Negative numbers", "Negative numbers: Unit test", "Unit 6Unit 6: Variables & expressions", "Variables & expressions: Unit test", "Unit 7Unit 7: Equations & inequalities", "Equations & inequalities: Unit test", "Unit 8Unit 8: Plane figures", "Plane figures: Unit test", "Unit 9Unit 9: Coordinate plane", "Coordinate plane: Unit test", "Unit 10Unit 10: 3D figures", "3D figures: Unit test", "Unit 11Unit 11: Data and statistics", "Data and statistics: Unit test", "Start Course challenge", "Unit 1: Ratios", "Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios", "Unit 2: Arithmetic with rational numbers", "Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers", "Unit 3: Rates and percentages", "Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages", "Unit 4: Exponents and order of operations", "Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations", "Unit 5: Negative numbers", "Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers", "Unit 6: Variables & expressions", "Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions", "Unit 7: Equations & inequalities", "Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities", "Unit 8: Plane figures", "Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures", "Unit 9: Coordinate plane", "Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane", "Unit 10: 3D figures", "Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures", "Unit 11: Data and statistics", "Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"7th grade9 units \u00b7 119 skills": ["Unit 1Proportional relationships", "Unit 2Rates and percentages", "Unit 3Integers: addition and subtraction", "Unit 4Rational numbers: addition and subtraction", "Unit 5Negative numbers: multiplication and division", "Unit 6Expressions, equations, & inequalities", "Unit 7Statistics and probability", "Unit 8Scale copies", "Unit 9Geometry", "Start Course challenge", "Unit 1Unit 1: Proportional relationships", "Proportional relationships: Unit test", "Unit 2Unit 2: Rates and percentages", "Rates and percentages: Unit test", "Unit 3Unit 3: Integers: addition and subtraction", "Integers: addition and subtraction: Unit test", "Unit 4Unit 4: Rational numbers: addition and subtraction", "Rational numbers: addition and subtraction: Unit test", "Unit 5Unit 5: Negative numbers: multiplication and division", "Negative numbers: multiplication and division: Unit test", "Unit 6Unit 6: Expressions, equations, & inequalities", "Expressions, equations, & inequalities: Unit test", "Unit 7Unit 7: Statistics and probability", "Statistics and probability: Unit test", "Unit 8Unit 8: Scale copies", "Scale copies: Unit test", "Unit 9Unit 9: Geometry", "Geometry: Unit test", "Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles", "Unit 1: Proportional relationships", "Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships", "Unit 2: Rates and percentages", "Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages", "Unit 3: Integers: addition and subtraction", "Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction", "Unit 4: Rational numbers: addition and subtraction", "Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction", "Unit 5: Negative numbers: multiplication and division", "Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division", "Unit 6: Expressions, equations, & inequalities", "The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities", "Unit 7: Statistics and probability", "Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability", "Unit 8: Scale copies", "Scale copies: Scale copies", "Scale drawings: Scale copies", "Unit 9: Geometry", "Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"8th grade7 units \u00b7 121 skills": ["Unit 1Numbers and operations", "Unit 2Solving equations with one unknown", "Unit 3Linear equations and functions", "Unit 4Systems of equations", "Unit 5Geometry", "Unit 6Geometric transformations", "Unit 7Data and modeling", "Start Course challenge", "Unit 1Unit 1: Numbers and operations", "Numbers and operations: Unit test", "Unit 2Unit 2: Solving equations with one unknown", "Solving equations with one unknown: Unit test", "Unit 3Unit 3: Linear equations and functions", "Linear equations and functions: Unit test", "Unit 4Unit 4: Systems of equations", "Systems of equations: Unit test", "Unit 5Unit 5: Geometry", "Geometry: Unit test", "Unit 6Unit 6: Geometric transformations", "Geometric transformations: Unit test", "Unit 7Unit 7: Data and modeling", "Data and modeling: Unit test", "Start Course challenge", "Unit 1: Numbers and operations", "Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations", "Unit 2: Solving equations with one unknown", "Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown", "Unit 3: Linear equations and functions", "Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions", "Unit 4: Systems of equations", "Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations", "Unit 5: Geometry", "Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry", "Unit 6: Geometric transformations", "Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations", "Unit 7: Data and modeling", "Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 3rd grade7 units \u00b7 38 skills": ["Unit 1Get ready for addition and subtraction", "Unit 2Get ready for multiplication and division", "Unit 3Get ready for fractions", "Unit 4Get ready for patterns and problem solving", "Unit 5Get ready for area and perimeter", "Unit 6Get ready for telling time", "Unit 7Get ready for data", "Start Course challenge", "Unit 1Unit 1: Get ready for addition and subtraction", "Get ready for addition and subtraction: Unit test", "Unit 2Unit 2: Get ready for multiplication and division", "Get ready for multiplication and division: Unit test", "Unit 3Unit 3: Get ready for fractions", "Get ready for fractions: Unit test", "Unit 4Unit 4: Get ready for patterns and problem solving", "Get ready for patterns and problem solving: Unit test", "Unit 5Unit 5: Get ready for area and perimeter", "Get ready for area and perimeter: Unit test", "Unit 6Unit 6: Get ready for telling time", "Get ready for telling time: Unit test", "Unit 7Unit 7: Get ready for data", "Get ready for data: Unit test", "Start Course challenge", "Unit 1: Get ready for addition and subtraction", "Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction", "Unit 2: Get ready for multiplication and division", "Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division", "Unit 3: Get ready for fractions", "Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions", "Unit 4: Get ready for patterns and problem solving", "Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving", "Unit 5: Get ready for area and perimeter", "Units of length: Get ready for area and perimeter", "Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter", "Unit 6: Get ready for telling time", "Telling time: Get ready for telling time", "Unit 7: Get ready for data", "Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 4th grade7 units \u00b7 56 skills": ["Unit 1Get ready for place value", "Unit 2Get ready for addition, subtraction, and estimation", "Unit 3Get ready for multiplication", "Unit 4Get ready for division", "Unit 5Get ready for fractions", "Unit 6Get ready for plane figures", "Unit 7Get ready for area and perimeter", "Start Course challenge", "Unit 1Unit 1: Get ready for place value", "Get ready for place value: Unit test", "Unit 2Unit 2: Get ready for addition, subtraction, and estimation", "Get ready for addition, subtraction, and estimation: Unit test", "Unit 3Unit 3: Get ready for multiplication", "Get ready for multiplication: Unit test", "Unit 4Unit 4: Get ready for division", "Get ready for division: Unit test", "Unit 5Unit 5: Get ready for fractions", "Get ready for fractions: Unit test", "Unit 6Unit 6: Get ready for plane figures", "Get ready for plane figures : Unit test", "Unit 7Unit 7: Get ready for area and perimeter", "Get ready for area and perimeter: Unit test", "Start Course challenge", "Unit 1: Get ready for place value", "Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value", "Unit 2: Get ready for addition, subtraction, and estimation", "Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation", "Unit 3: Get ready for multiplication", "Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication", "Unit 4: Get ready for division", "Division intro: Get ready for division", "Relate multiplication and division: Get ready for division", "Unit 5: Get ready for fractions", "Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions", "Unit 6: Get ready for plane figures", "Quadrilaterals: Get ready for plane figures", "Unit 7: Get ready for area and perimeter", "Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 5th grade8 units \u00b7 62 skills": ["Unit 1Get ready for decimal place value", "Unit 2Get ready for adding and subtracting decimals", "Unit 3Get ready for adding and subtracting fractions", "Unit 4Get ready for multiplication and division with whole numbers and decimals", "Unit 5Get ready for multiplying and dividing fractions", "Unit 6Get ready for powers of 10", "Unit 7Get ready for volume", "Unit 8Get ready for properties of shapes", "Start Course challenge", "Unit 1Unit 1: Get ready for decimal place value", "Get ready for decimal place value: Unit test", "Unit 2Unit 2: Get ready for adding and subtracting decimals", "Get ready for adding and subtracting decimals: Unit test", "Unit 3Unit 3: Get ready for adding and subtracting fractions", "Get ready for adding and subtracting fractions: Unit test", "Unit 4Unit 4: Get ready for multiplication and division with whole numbers and decimals", "Get ready for multiplication and division with whole numbers and decimals: Unit test", "Unit 5Unit 5: Get ready for multiplying and dividing fractions", "Get ready for multiplying and dividing fractions: Unit test", "Unit 6Unit 6: Get ready for powers of 10", "Get ready for powers of 10: Unit test", "Unit 7Unit 7: Get ready for volume", "Get ready for volume: Unit test", "Unit 8Unit 8: Get ready for properties of shapes", "Get ready for properties of shapes: Unit test", "Start Course challenge", "Unit 1: Get ready for decimal place value", "Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value", "Unit 2: Get ready for adding and subtracting decimals", "Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals", "Unit 3: Get ready for adding and subtracting fractions", "Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions", "Unit 4: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals", "Unit 5: Get ready for multiplying and dividing fractions", "Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions", "Unit 6: Get ready for powers of 10", "How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10", "Unit 7: Get ready for volume", "Introduction to area: Get ready for volume", "Unit 8: Get ready for properties of shapes", "Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 6th grade5 units \u00b7 60 skills": ["Unit 1Get ready for ratios, rates, and percentages", "Unit 2Get ready for arithmetic operations", "Unit 3Get ready for negative numbers", "Unit 4Get ready for equations, expressions, and inequalities", "Unit 5Get ready for geometry", "Start Course challenge", "Unit 1Unit 1: Get ready for ratios, rates, and percentages", "Get ready for ratios, rates, and percentages: Unit test", "Unit 2Unit 2: Get ready for arithmetic operations", "Get ready for arithmetic operations: Unit test", "Unit 3Unit 3: Get ready for negative numbers", "Get ready for negative numbers: Unit test", "Unit 4Unit 4: Get ready for equations, expressions, and inequalities", "Get ready for equations, expressions, and inequalities: Unit test", "Unit 5Unit 5: Get ready for geometry", "Get ready for geometry: Unit test", "Start Course challenge", "Unit 1: Get ready for ratios, rates, and percentages", "Multiplication and division word problems: Get ready for ratios, rates, and percentages", "Convert units of measure: Get ready for ratios, rates, and percentages", "Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages", "Unit 2: Get ready for arithmetic operations", "Divide whole numbers by unit fractions: Get ready for arithmetic operations", "Divide unit fractions by whole numbers: Get ready for arithmetic operations", "Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations", "Unit 3: Get ready for negative numbers", "Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers", "Unit 4: Get ready for equations, expressions, and inequalities", "Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities", "Unit 5: Get ready for geometry", "Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 7th grade6 units \u00b7 63 skills": ["Unit 1Get ready for negative number operations", "Unit 2Get ready for fractions, decimals, & percentages", "Unit 3Get ready for rates & proportional relationships", "Unit 4Get ready for expressions, equations, & inequalities", "Unit 5Get ready for geometry", "Unit 6Get ready for statistics & probability", "Start Course challenge", "Unit 1Unit 1: Get ready for negative number operations", "Get ready for negative number operations: Unit test", "Unit 2Unit 2: Get ready for fractions, decimals, & percentages", "Get ready for fractions, decimals, & percentages: Unit test", "Unit 3Unit 3: Get ready for rates & proportional relationships", "Get ready for rates & proportional relationships: Unit test", "Unit 4Unit 4: Get ready for expressions, equations, & inequalities", "Get ready for expressions, equations, & inequalities: Unit test", "Unit 5Unit 5: Get ready for geometry", "Get ready for geometry: Unit test", "Unit 6Unit 6: Get ready for statistics & probability", "Get ready for statistics & probability: Unit test", "Start Course challenge", "Unit 1: Get ready for negative number operations", "Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations", "Unit 2: Get ready for fractions, decimals, & percentages", "Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages", "Unit 3: Get ready for rates & proportional relationships", "Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships", "Unit 4: Get ready for expressions, equations, & inequalities", "Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities", "Unit 5: Get ready for geometry", "Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry", "Unit 6: Get ready for statistics & probability", "Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 8th grade4 units \u00b7 44 skills": ["Unit 1Get ready for numbers and operations", "Unit 2Get ready for solving equations and systems of equations", "Unit 3Get ready for linear equations and functions", "Unit 4Get ready for geometry", "Start Course challenge", "Unit 1Unit 1: Get ready for numbers and operations", "Get ready for numbers and operations: Unit test", "Unit 2Unit 2: Get ready for solving equations and systems of equations", "Get ready for solving equations and systems of equations: Unit test", "Unit 3Unit 3: Get ready for linear equations and functions", "Get ready for linear equations and functions: Unit test", "Unit 4Unit 4: Get ready for geometry", "Get ready for geometry: Unit test", "Start Course challenge", "Unit 1: Get ready for numbers and operations", "Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations", "Unit 2: Get ready for solving equations and systems of equations", "Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations", "Unit 3: Get ready for linear equations and functions", "Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions", "Unit 4: Get ready for geometry", "Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Get ready for Algebra 16 units \u00b7 87 skills": ["Unit 1Get ready for equations & inequalities", "Unit 2Get ready for working with units", "Unit 3Get ready for linear relationships", "Unit 4Get ready for functions & sequences", "Unit 5Get ready for exponents, radicals, & irrational numbers", "Unit 6Get ready for quadratics", "Start Course challenge", "Unit 1Unit 1: Get ready for equations & inequalities", "Get ready for equations & inequalities: Unit test", "Unit 2Unit 2: Get ready for working with units", "Get ready for working with units: Unit test", "Unit 3Unit 3: Get ready for linear relationships", "Get ready for linear relationships: Unit test", "Unit 4Unit 4: Get ready for functions & sequences", "Get ready for functions & sequences: Unit test", "Unit 5Unit 5: Get ready for exponents, radicals, & irrational numbers", "Get ready for exponents, radicals, & irrational numbers: Unit test", "Unit 6Unit 6: Get ready for quadratics", "Get ready for quadratics: Unit test", "Start Course challenge", "Unit 1: Get ready for equations & inequalities", "Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities", "Unit 2: Get ready for working with units", "Intro to ratios: Get ready for working with units", "Equivalent ratios: Get ready for working with units", "Ratio application: Get ready for working with units", "Intro to rates: Get ready for working with units", "Rate problems: Get ready for working with units", "Unit 3: Get ready for linear relationships", "Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships", "Unit 4: Get ready for functions & sequences", "Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences", "Unit 5: Get ready for exponents, radicals, & irrational numbers", "Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers", "Unit 6: Get ready for quadratics", "Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Get ready for Geometry4 units \u00b7 51 skills": ["Unit 1Get ready for congruence, similarity, and triangle trigonometry", "Unit 2Get ready for analytic geometry", "Unit 3Get ready for conic sections", "Unit 4Get ready for circles and solid geometry", "Start Course challenge", "Unit 1Unit 1: Get ready for congruence, similarity, and triangle trigonometry", "Get ready for congruence, similarity, and triangle trigonometry: Unit test", "Unit 2Unit 2: Get ready for analytic geometry", "Get ready for analytic geometry: Unit test", "Unit 3Unit 3: Get ready for conic sections", "Get ready for conic sections: Unit test", "Unit 4Unit 4: Get ready for circles and solid geometry", "Get ready for circles and solid geometry: Unit test", "Start Course challenge", "Unit 1: Get ready for congruence, similarity, and triangle trigonometry", "Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry", "Unit 2: Get ready for analytic geometry", "Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry", "Unit 3: Get ready for conic sections", "Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections", "Unit 4: Get ready for circles and solid geometry", "Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Get ready for Algebra 26 units \u00b7 96 skills": ["Unit 1Get ready for polynomial operations and complex numbers", "Unit 2Get ready for equations", "Unit 3Get ready for transformations of functions and modeling with functions", "Unit 4Get ready for exponential and logarithmic relationships", "Unit 5Get ready for trigonometry", "Unit 6Get ready for rational functions", "Start Course challenge", "Unit 1Unit 1: Get ready for polynomial operations and complex numbers", "Get ready for polynomial operations and complex numbers: Unit test", "Unit 2Unit 2: Get ready for equations", "Get ready for equations: Unit test", "Unit 3Unit 3: Get ready for transformations of functions and modeling with functions", "Get ready for transformations of functions and modeling with functions: Unit test", "Unit 4Unit 4: Get ready for exponential and logarithmic relationships", "Get ready for exponential and logarithmic relationships: Unit test", "Unit 5Unit 5: Get ready for trigonometry", "Get ready for trigonometry: Unit test", "Unit 6Unit 6: Get ready for rational functions", "Get ready for rational functions: Unit test", "Start Course challenge", "Unit 1: Get ready for polynomial operations and complex numbers", "Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers", "Unit 2: Get ready for equations", "Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations", "Unit 3: Get ready for transformations of functions and modeling with functions", "Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions", "Unit 4: Get ready for exponential and logarithmic relationships", "Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships", "Unit 5: Get ready for trigonometry", "Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry", "Unit 6: Get ready for rational functions", "Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Early math review8 units \u00b7 121 skills": ["Unit 1Counting", "Unit 2Addition and subtraction intro", "Unit 3Place value (tens and hundreds)", "Unit 4Addition and subtraction within 20", "Unit 5Addition and subtraction within 100", "Unit 6Addition and subtraction within 1000", "Unit 7Measurement and data", "Unit 8Geometry", "Start Course challenge", "Unit 1Unit 1: Counting", "Counting: Unit test", "Unit 2Unit 2: Addition and subtraction intro", "Addition and subtraction intro: Unit test", "Unit 3Unit 3: Place value (tens and hundreds)", "Place value (tens and hundreds): Unit test", "Unit 4Unit 4: Addition and subtraction within 20", "Addition and subtraction within 20: Unit test", "Unit 5Unit 5: Addition and subtraction within 100", "Addition and subtraction within 100: Unit test", "Unit 6Unit 6: Addition and subtraction within 1000", "Addition and subtraction within 1000: Unit test", "Unit 7Unit 7: Measurement and data", "Measurement and data: Unit test", "Unit 8Unit 8: Geometry", "Geometry: Unit test", "Start Course challenge", "Unit 1: Counting", "Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting", "Unit 2: Addition and subtraction intro", "What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro", "Unit 3: Place value (tens and hundreds)", "Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)", "Unit 4: Addition and subtraction within 20", "Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20", "Unit 5: Addition and subtraction within 100", "Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100", "Unit 6: Addition and subtraction within 1000", "Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000", "Unit 7: Measurement and data", "Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data", "Unit 8: Geometry", "Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"2nd grade8 units \u00b7 75 skills": ["Unit 1Add and subtract within 20", "Unit 2Place value", "Unit 3Add and subtract within 100", "Unit 4Add and subtract within 1,000", "Unit 5Money and time", "Unit 6Measurement", "Unit 7Data", "Unit 8Geometry", "Start Course challenge", "Unit 1Unit 1: Add and subtract within 20", "Add and subtract within 20: Unit test", "Unit 2Unit 2: Place value", "Place value: Unit test", "Unit 3Unit 3: Add and subtract within 100", "Add and subtract within 100: Unit test", "Unit 4Unit 4: Add and subtract within 1,000", "Add and subtract within 1,000: Unit test", "Unit 5Unit 5: Money and time", "Money and time: Unit test", "Unit 6Unit 6: Measurement", "Measurement: Unit test", "Unit 7Unit 7: Data", "Data: Unit test", "Unit 8Unit 8: Geometry", "Geometry: Unit test", "Start Course challenge", "Unit 1: Add and subtract within 20", "Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20", "Unit 2: Place value", "Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value", "Unit 3: Add and subtract within 100", "Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100", "Unit 4: Add and subtract within 1,000", "Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000", "Unit 5: Money and time", "Time: Money and time", "Unit 6: Measurement", "Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement", "Unit 7: Data", "Bar graphs: Data", "Line plots: Data", "Unit 8: Geometry", "Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"3rd grade14 units \u00b7 141 skills": ["Unit 1Intro to multiplication", "Unit 21-digit multiplication", "Unit 3Addition, subtraction, and estimation", "Unit 4Intro to division", "Unit 5Understand fractions", "Unit 6Equivalent fractions and comparing fractions", "Unit 7More with multiplication and division", "Unit 8Arithmetic patterns and problem solving", "Unit 9Quadrilaterals", "Unit 10Area", "Unit 11Perimeter", "Unit 12Time", "Unit 13Measurement", "Unit 14Represent and interpret data", "Start Course challenge", "Unit 1Unit 1: Intro to multiplication", "Intro to multiplication: Unit test", "Unit 2Unit 2: 1-digit multiplication", "1-digit multiplication: Unit test", "Unit 3Unit 3: Addition, subtraction, and estimation", "Addition, subtraction, and estimation: Unit test", "Unit 4Unit 4: Intro to division", "Intro to division: Unit test", "Unit 5Unit 5: Understand fractions", "Understand fractions: Unit test", "Unit 6Unit 6: Equivalent fractions and comparing fractions", "Equivalent fractions and comparing fractions: Unit test", "Unit 7Unit 7: More with multiplication and division", "More with multiplication and division: Unit test", "Unit 8Unit 8: Arithmetic patterns and problem solving", "Arithmetic patterns and problem solving: Unit test", "Unit 9Unit 9: Quadrilaterals", "Quadrilaterals: Unit test", "Unit 10Unit 10: Area", "Area: Unit test", "Unit 11Unit 11: Perimeter", "Perimeter: Unit test", "Unit 12Unit 12: Time", "Time: Unit test", "Unit 13Unit 13: Measurement", "Measurement: Unit test", "Unit 14Unit 14: Represent and interpret data", "Represent and interpret data: Unit test", "Start Course challenge", "Unit 1: Intro to multiplication", "Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication", "Unit 2: 1-digit multiplication", "Distributive property: 1-digit multiplication", "Unit 3: Addition, subtraction, and estimation", "Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation", "Unit 4: Intro to division", "Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division", "Unit 5: Understand fractions", "Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions", "Unit 6: Equivalent fractions and comparing fractions", "Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions", "Unit 7: More with multiplication and division", "Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division", "Unit 8: Arithmetic patterns and problem solving", "2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving", "Unit 9: Quadrilaterals", "Quadrilaterals : Quadrilaterals", "Unit 10: Area", "Count unit squares to find area: Area", "Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area", "Unit 11: Perimeter", "Perimeter: Perimeter", "Perimeter word problems: Perimeter", "Unit 12: Time", "Time on number line: Time", "Telling time: Time", "Elapsed time: Time", "Unit 13: Measurement", "Mass: Measurement", "Volume: Measurement", "Unit 14: Represent and interpret data", "Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"4th grade14 units \u00b7 154 skills": ["Unit 1Place value", "Unit 2Addition, subtraction, and estimation", "Unit 3Multiply by 1-digit numbers", "Unit 4Multiply by 2-digit numbers", "Unit 5Division", "Unit 6Factors, multiples and patterns", "Unit 7Equivalent fractions and comparing fractions", "Unit 8Add and subtract fractions", "Unit 9Multiply fractions", "Unit 10Understand decimals", "Unit 11Plane figures", "Unit 12Measuring angles", "Unit 13Area and perimeter", "Unit 14Units of measurement", "Start Course challenge", "Unit 1Unit 1: Place value", "Place value: Unit test", "Unit 2Unit 2: Addition, subtraction, and estimation", "Addition, subtraction, and estimation: Unit test", "Unit 3Unit 3: Multiply by 1-digit numbers", "Multiply by 1-digit numbers: Unit test", "Unit 4Unit 4: Multiply by 2-digit numbers", "Multiply by 2-digit numbers: Unit test", "Unit 5Unit 5: Division", "Division: Unit test", "Unit 6Unit 6: Factors, multiples and patterns", "Factors, multiples and patterns: Unit test", "Unit 7Unit 7: Equivalent fractions and comparing fractions", "Equivalent fractions and comparing fractions: Unit test", "Unit 8Unit 8: Add and subtract fractions", "Add and subtract fractions: Unit test", "Unit 9Unit 9: Multiply fractions", "Multiply fractions: Unit test", "Unit 10Unit 10: Understand decimals", "Understand decimals: Unit test", "Unit 11Unit 11: Plane figures", "Plane figures: Unit test", "Unit 12Unit 12: Measuring angles", "Measuring angles: Unit test", "Unit 13Unit 13: Area and perimeter", "Area and perimeter: Unit test", "Unit 14Unit 14: Units of measurement", "Units of measurement: Unit test", "Start Course challenge", "Unit 1: Place value", "Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value", "Unit 2: Addition, subtraction, and estimation", "Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation", "Unit 3: Multiply by 1-digit numbers", "Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers", "Unit 4: Multiply by 2-digit numbers", "Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers", "Unit 5: Division", "Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division", "Unit 6: Factors, multiples and patterns", "Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns", "Unit 7: Equivalent fractions and comparing fractions", "Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions", "Unit 8: Add and subtract fractions", "Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions", "Unit 9: Multiply fractions", "Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions", "Unit 10: Understand decimals", "Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals", "Unit 11: Plane figures", "Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures", "Unit 12: Measuring angles", "Measuring angles: Measuring angles", "Decomposing angles: Measuring angles", "Unit 13: Area and perimeter", "Area and perimeter: Area and perimeter", "Unit 14: Units of measurement", "Estimating volume: Units of measurement", "Estimating length: Units of measurement", "Time: Units of measurement", "Converting units of mass: Units of measurement", "Converting units of volume: Units of measurement", "Converting units of length: Units of measurement", "Converting units of time: Units of measurement", "Money word problems: Units of measurement", "Conversion word problems: Units of measurement", "Start Course challenge"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"5th grade16 units \u00b7 130 skills": ["Unit 1Decimal place value", "Unit 2Add decimals", "Unit 3Subtract decimals", "Unit 4Add and subtract fractions", "Unit 5Multi-digit multiplication and division", "Unit 6Multiply fractions", "Unit 7Divide fractions", "Unit 8Multiply decimals", "Unit 9Divide decimals", "Unit 10Powers of ten", "Unit 11Volume", "Unit 12Coordinate plane", "Unit 13Algebraic thinking", "Unit 14Converting units of measure", "Unit 15Line plots", "Unit 16Properties of shapes", "Start Course challenge", "Unit 1Unit 1: Decimal place value", "Decimal place value: Unit test", "Unit 2Unit 2: Add decimals", "Add decimals: Unit test", "Unit 3Unit 3: Subtract decimals", "Subtract decimals: Unit test", "Unit 4Unit 4: Add and subtract fractions", "Add and subtract fractions: Unit test", "Unit 5Unit 5: Multi-digit multiplication and division", "Multi-digit multiplication and division: Unit test", "Unit 6Unit 6: Multiply fractions", "Multiply fractions: Unit test", "Unit 7Unit 7: Divide fractions", "Divide fractions: Unit test", "Unit 8Unit 8: Multiply decimals", "Multiply decimals: Unit test", "Unit 9Unit 9: Divide decimals", "Divide decimals: Unit test", "Unit 10Unit 10: Powers of ten", "Powers of ten: Unit test", "Unit 11Unit 11: Volume", "Volume: Unit test", "Unit 12Unit 12: Coordinate plane", "Coordinate plane: Unit test", "Unit 13Unit 13: Algebraic thinking", "Algebraic thinking: Unit test", "Unit 14Unit 14: Converting units of measure", "Converting units of measure: Unit test", "Unit 15Unit 15: Line plots", "Line plots: Unit test", "Unit 16Unit 16: Properties of shapes", "Properties of shapes: Unit test", "Start Course challenge", "Unit 1: Decimal place value", "Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value", "Unit 2: Add decimals", "Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals", "Unit 3: Subtract decimals", "Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals", "Unit 4: Add and subtract fractions", "Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions", "Unit 5: Multi-digit multiplication and division", "Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division", "Unit 6: Multiply fractions", "Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions", "Unit 7: Divide fractions", "Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions", "Dividing unit fractions by whole numbers: Divide fractions", "Dividing whole numbers by unit fractions: Divide fractions", "Dividing fractions and whole numbers word problems: Divide fractions", "Unit 8: Multiply decimals", "Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals", "Unit 9: Divide decimals", "Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals", "Unit 10: Powers of ten", "Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten", "Unit 11: Volume", "Volume with unit cubes: Volume", "Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume", "Unit 12: Coordinate plane", "Intro to the coordinate plane : Coordinate plane", "Unit 13: Algebraic thinking", "Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking", "Unit 14: Converting units of measure", "Converting units of time: Converting units of measure", "Converting metric units: Converting units of measure", "Converting metric units word problems: Converting units of measure", "Converting US Customary units: Converting units of measure", "Converting US Customary units word problems: Converting units of measure", "Unit 15: Line plots", "Graph data on line plots: Line plots", "Interpret data on line plots: Line plots", "Unit 16: Properties of shapes", "Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"6th grade11 units \u00b7 148 skills": ["Unit 1Ratios", "Unit 2Arithmetic with rational numbers", "Unit 3Rates and percentages", "Unit 4Exponents and order of operations", "Unit 5Negative numbers", "Unit 6Variables & expressions", "Unit 7Equations & inequalities", "Unit 8Plane figures", "Unit 9Coordinate plane", "Unit 103D figures", "Unit 11Data and statistics", "Start Course challenge", "Unit 1Unit 1: Ratios", "Ratios: Unit test", "Unit 2Unit 2: Arithmetic with rational numbers", "Arithmetic with rational numbers: Unit test", "Unit 3Unit 3: Rates and percentages", "Rates and percentages: Unit test", "Unit 4Unit 4: Exponents and order of operations", "Exponents and order of operations: Unit test", "Unit 5Unit 5: Negative numbers", "Negative numbers: Unit test", "Unit 6Unit 6: Variables & expressions", "Variables & expressions: Unit test", "Unit 7Unit 7: Equations & inequalities", "Equations & inequalities: Unit test", "Unit 8Unit 8: Plane figures", "Plane figures: Unit test", "Unit 9Unit 9: Coordinate plane", "Coordinate plane: Unit test", "Unit 10Unit 10: 3D figures", "3D figures: Unit test", "Unit 11Unit 11: Data and statistics", "Data and statistics: Unit test", "Start Course challenge", "Unit 1: Ratios", "Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios", "Unit 2: Arithmetic with rational numbers", "Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers", "Unit 3: Rates and percentages", "Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages", "Unit 4: Exponents and order of operations", "Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations", "Unit 5: Negative numbers", "Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers", "Unit 6: Variables & expressions", "Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions", "Unit 7: Equations & inequalities", "Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities", "Unit 8: Plane figures", "Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures", "Unit 9: Coordinate plane", "Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane", "Unit 10: 3D figures", "Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures", "Unit 11: Data and statistics", "Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"7th grade9 units \u00b7 119 skills": ["Unit 1Proportional relationships", "Unit 2Rates and percentages", "Unit 3Integers: addition and subtraction", "Unit 4Rational numbers: addition and subtraction", "Unit 5Negative numbers: multiplication and division", "Unit 6Expressions, equations, & inequalities", "Unit 7Statistics and probability", "Unit 8Scale copies", "Unit 9Geometry", "Start Course challenge", "Unit 1Unit 1: Proportional relationships", "Proportional relationships: Unit test", "Unit 2Unit 2: Rates and percentages", "Rates and percentages: Unit test", "Unit 3Unit 3: Integers: addition and subtraction", "Integers: addition and subtraction: Unit test", "Unit 4Unit 4: Rational numbers: addition and subtraction", "Rational numbers: addition and subtraction: Unit test", "Unit 5Unit 5: Negative numbers: multiplication and division", "Negative numbers: multiplication and division: Unit test", "Unit 6Unit 6: Expressions, equations, & inequalities", "Expressions, equations, & inequalities: Unit test", "Unit 7Unit 7: Statistics and probability", "Statistics and probability: Unit test", "Unit 8Unit 8: Scale copies", "Scale copies: Unit test", "Unit 9Unit 9: Geometry", "Geometry: Unit test", "Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles", "Unit 1: Proportional relationships", "Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships", "Unit 2: Rates and percentages", "Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages", "Unit 3: Integers: addition and subtraction", "Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction", "Unit 4: Rational numbers: addition and subtraction", "Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction", "Unit 5: Negative numbers: multiplication and division", "Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division", "Unit 6: Expressions, equations, & inequalities", "The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities", "Unit 7: Statistics and probability", "Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability", "Unit 8: Scale copies", "Scale copies: Scale copies", "Scale drawings: Scale copies", "Unit 9: Geometry", "Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"8th grade7 units \u00b7 121 skills": ["Unit 1Numbers and operations", "Unit 2Solving equations with one unknown", "Unit 3Linear equations and functions", "Unit 4Systems of equations", "Unit 5Geometry", "Unit 6Geometric transformations", "Unit 7Data and modeling", "Start Course challenge", "Unit 1Unit 1: Numbers and operations", "Numbers and operations: Unit test", "Unit 2Unit 2: Solving equations with one unknown", "Solving equations with one unknown: Unit test", "Unit 3Unit 3: Linear equations and functions", "Linear equations and functions: Unit test", "Unit 4Unit 4: Systems of equations", "Systems of equations: Unit test", "Unit 5Unit 5: Geometry", "Geometry: Unit test", "Unit 6Unit 6: Geometric transformations", "Geometric transformations: Unit test", "Unit 7Unit 7: Data and modeling", "Data and modeling: Unit test", "Start Course challenge", "Unit 1: Numbers and operations", "Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations", "Unit 2: Solving equations with one unknown", "Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown", "Unit 3: Linear equations and functions", "Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions", "Unit 4: Systems of equations", "Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations", "Unit 5: Geometry", "Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry", "Unit 6: Geometric transformations", "Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations", "Unit 7: Data and modeling", "Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 3rd grade7 units \u00b7 38 skills": ["Unit 1Get ready for addition and subtraction", "Unit 2Get ready for multiplication and division", "Unit 3Get ready for fractions", "Unit 4Get ready for patterns and problem solving", "Unit 5Get ready for area and perimeter", "Unit 6Get ready for telling time", "Unit 7Get ready for data", "Start Course challenge", "Unit 1Unit 1: Get ready for addition and subtraction", "Get ready for addition and subtraction: Unit test", "Unit 2Unit 2: Get ready for multiplication and division", "Get ready for multiplication and division: Unit test", "Unit 3Unit 3: Get ready for fractions", "Get ready for fractions: Unit test", "Unit 4Unit 4: Get ready for patterns and problem solving", "Get ready for patterns and problem solving: Unit test", "Unit 5Unit 5: Get ready for area and perimeter", "Get ready for area and perimeter: Unit test", "Unit 6Unit 6: Get ready for telling time", "Get ready for telling time: Unit test", "Unit 7Unit 7: Get ready for data", "Get ready for data: Unit test", "Start Course challenge", "Unit 1: Get ready for addition and subtraction", "Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction", "Unit 2: Get ready for multiplication and division", "Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division", "Unit 3: Get ready for fractions", "Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions", "Unit 4: Get ready for patterns and problem solving", "Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving", "Unit 5: Get ready for area and perimeter", "Units of length: Get ready for area and perimeter", "Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter", "Unit 6: Get ready for telling time", "Telling time: Get ready for telling time", "Unit 7: Get ready for data", "Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 4th grade7 units \u00b7 56 skills": ["Unit 1Get ready for place value", "Unit 2Get ready for addition, subtraction, and estimation", "Unit 3Get ready for multiplication", "Unit 4Get ready for division", "Unit 5Get ready for fractions", "Unit 6Get ready for plane figures", "Unit 7Get ready for area and perimeter", "Start Course challenge", "Unit 1Unit 1: Get ready for place value", "Get ready for place value: Unit test", "Unit 2Unit 2: Get ready for addition, subtraction, and estimation", "Get ready for addition, subtraction, and estimation: Unit test", "Unit 3Unit 3: Get ready for multiplication", "Get ready for multiplication: Unit test", "Unit 4Unit 4: Get ready for division", "Get ready for division: Unit test", "Unit 5Unit 5: Get ready for fractions", "Get ready for fractions: Unit test", "Unit 6Unit 6: Get ready for plane figures", "Get ready for plane figures : Unit test", "Unit 7Unit 7: Get ready for area and perimeter", "Get ready for area and perimeter: Unit test", "Start Course challenge", "Unit 1: Get ready for place value", "Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value", "Unit 2: Get ready for addition, subtraction, and estimation", "Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation", "Unit 3: Get ready for multiplication", "Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication", "Unit 4: Get ready for division", "Division intro: Get ready for division", "Relate multiplication and division: Get ready for division", "Unit 5: Get ready for fractions", "Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions", "Unit 6: Get ready for plane figures", "Quadrilaterals: Get ready for plane figures", "Unit 7: Get ready for area and perimeter", "Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 5th grade8 units \u00b7 62 skills": ["Unit 1Get ready for decimal place value", "Unit 2Get ready for adding and subtracting decimals", "Unit 3Get ready for adding and subtracting fractions", "Unit 4Get ready for multiplication and division with whole numbers and decimals", "Unit 5Get ready for multiplying and dividing fractions", "Unit 6Get ready for powers of 10", "Unit 7Get ready for volume", "Unit 8Get ready for properties of shapes", "Start Course challenge", "Unit 1Unit 1: Get ready for decimal place value", "Get ready for decimal place value: Unit test", "Unit 2Unit 2: Get ready for adding and subtracting decimals", "Get ready for adding and subtracting decimals: Unit test", "Unit 3Unit 3: Get ready for adding and subtracting fractions", "Get ready for adding and subtracting fractions: Unit test", "Unit 4Unit 4: Get ready for multiplication and division with whole numbers and decimals", "Get ready for multiplication and division with whole numbers and decimals: Unit test", "Unit 5Unit 5: Get ready for multiplying and dividing fractions", "Get ready for multiplying and dividing fractions: Unit test", "Unit 6Unit 6: Get ready for powers of 10", "Get ready for powers of 10: Unit test", "Unit 7Unit 7: Get ready for volume", "Get ready for volume: Unit test", "Unit 8Unit 8: Get ready for properties of shapes", "Get ready for properties of shapes: Unit test", "Start Course challenge", "Unit 1: Get ready for decimal place value", "Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value", "Unit 2: Get ready for adding and subtracting decimals", "Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals", "Unit 3: Get ready for adding and subtracting fractions", "Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions", "Unit 4: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals", "Unit 5: Get ready for multiplying and dividing fractions", "Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions", "Unit 6: Get ready for powers of 10", "How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10", "Unit 7: Get ready for volume", "Introduction to area: Get ready for volume", "Unit 8: Get ready for properties of shapes", "Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 6th grade5 units \u00b7 60 skills": ["Unit 1Get ready for ratios, rates, and percentages", "Unit 2Get ready for arithmetic operations", "Unit 3Get ready for negative numbers", "Unit 4Get ready for equations, expressions, and inequalities", "Unit 5Get ready for geometry", "Start Course challenge", "Unit 1Unit 1: Get ready for ratios, rates, and percentages", "Get ready for ratios, rates, and percentages: Unit test", "Unit 2Unit 2: Get ready for arithmetic operations", "Get ready for arithmetic operations: Unit test", "Unit 3Unit 3: Get ready for negative numbers", "Get ready for negative numbers: Unit test", "Unit 4Unit 4: Get ready for equations, expressions, and inequalities", "Get ready for equations, expressions, and inequalities: Unit test", "Unit 5Unit 5: Get ready for geometry", "Get ready for geometry: Unit test", "Start Course challenge", "Unit 1: Get ready for ratios, rates, and percentages", "Multiplication and division word problems: Get ready for ratios, rates, and percentages", "Convert units of measure: Get ready for ratios, rates, and percentages", "Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages", "Unit 2: Get ready for arithmetic operations", "Divide whole numbers by unit fractions: Get ready for arithmetic operations", "Divide unit fractions by whole numbers: Get ready for arithmetic operations", "Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations", "Unit 3: Get ready for negative numbers", "Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers", "Unit 4: Get ready for equations, expressions, and inequalities", "Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities", "Unit 5: Get ready for geometry", "Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 7th grade6 units \u00b7 63 skills": ["Unit 1Get ready for negative number operations", "Unit 2Get ready for fractions, decimals, & percentages", "Unit 3Get ready for rates & proportional relationships", "Unit 4Get ready for expressions, equations, & inequalities", "Unit 5Get ready for geometry", "Unit 6Get ready for statistics & probability", "Start Course challenge", "Unit 1Unit 1: Get ready for negative number operations", "Get ready for negative number operations: Unit test", "Unit 2Unit 2: Get ready for fractions, decimals, & percentages", "Get ready for fractions, decimals, & percentages: Unit test", "Unit 3Unit 3: Get ready for rates & proportional relationships", "Get ready for rates & proportional relationships: Unit test", "Unit 4Unit 4: Get ready for expressions, equations, & inequalities", "Get ready for expressions, equations, & inequalities: Unit test", "Unit 5Unit 5: Get ready for geometry", "Get ready for geometry: Unit test", "Unit 6Unit 6: Get ready for statistics & probability", "Get ready for statistics & probability: Unit test", "Start Course challenge", "Unit 1: Get ready for negative number operations", "Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations", "Unit 2: Get ready for fractions, decimals, & percentages", "Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages", "Unit 3: Get ready for rates & proportional relationships", "Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships", "Unit 4: Get ready for expressions, equations, & inequalities", "Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities", "Unit 5: Get ready for geometry", "Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry", "Unit 6: Get ready for statistics & probability", "Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Get ready for 8th grade4 units \u00b7 44 skills": ["Unit 1Get ready for numbers and operations", "Unit 2Get ready for solving equations and systems of equations", "Unit 3Get ready for linear equations and functions", "Unit 4Get ready for geometry", "Start Course challenge", "Unit 1Unit 1: Get ready for numbers and operations", "Get ready for numbers and operations: Unit test", "Unit 2Unit 2: Get ready for solving equations and systems of equations", "Get ready for solving equations and systems of equations: Unit test", "Unit 3Unit 3: Get ready for linear equations and functions", "Get ready for linear equations and functions: Unit test", "Unit 4Unit 4: Get ready for geometry", "Get ready for geometry: Unit test", "Start Course challenge", "Unit 1: Get ready for numbers and operations", "Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations", "Unit 2: Get ready for solving equations and systems of equations", "Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations", "Unit 3: Get ready for linear equations and functions", "Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions", "Unit 4: Get ready for geometry", "Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Get ready for Algebra 16 units \u00b7 87 skills": ["Unit 1Get ready for equations & inequalities", "Unit 2Get ready for working with units", "Unit 3Get ready for linear relationships", "Unit 4Get ready for functions & sequences", "Unit 5Get ready for exponents, radicals, & irrational numbers", "Unit 6Get ready for quadratics", "Start Course challenge", "Unit 1Unit 1: Get ready for equations & inequalities", "Get ready for equations & inequalities: Unit test", "Unit 2Unit 2: Get ready for working with units", "Get ready for working with units: Unit test", "Unit 3Unit 3: Get ready for linear relationships", "Get ready for linear relationships: Unit test", "Unit 4Unit 4: Get ready for functions & sequences", "Get ready for functions & sequences: Unit test", "Unit 5Unit 5: Get ready for exponents, radicals, & irrational numbers", "Get ready for exponents, radicals, & irrational numbers: Unit test", "Unit 6Unit 6: Get ready for quadratics", "Get ready for quadratics: Unit test", "Start Course challenge", "Unit 1: Get ready for equations & inequalities", "Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities", "Unit 2: Get ready for working with units", "Intro to ratios: Get ready for working with units", "Equivalent ratios: Get ready for working with units", "Ratio application: Get ready for working with units", "Intro to rates: Get ready for working with units", "Rate problems: Get ready for working with units", "Unit 3: Get ready for linear relationships", "Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships", "Unit 4: Get ready for functions & sequences", "Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences", "Unit 5: Get ready for exponents, radicals, & irrational numbers", "Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers", "Unit 6: Get ready for quadratics", "Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Get ready for Geometry4 units \u00b7 51 skills": ["Unit 1Get ready for congruence, similarity, and triangle trigonometry", "Unit 2Get ready for analytic geometry", "Unit 3Get ready for conic sections", "Unit 4Get ready for circles and solid geometry", "Start Course challenge", "Unit 1Unit 1: Get ready for congruence, similarity, and triangle trigonometry", "Get ready for congruence, similarity, and triangle trigonometry: Unit test", "Unit 2Unit 2: Get ready for analytic geometry", "Get ready for analytic geometry: Unit test", "Unit 3Unit 3: Get ready for conic sections", "Get ready for conic sections: Unit test", "Unit 4Unit 4: Get ready for circles and solid geometry", "Get ready for circles and solid geometry: Unit test", "Start Course challenge", "Unit 1: Get ready for congruence, similarity, and triangle trigonometry", "Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry", "Unit 2: Get ready for analytic geometry", "Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry", "Unit 3: Get ready for conic sections", "Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections", "Unit 4: Get ready for circles and solid geometry", "Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Get ready for Algebra 26 units \u00b7 96 skills": ["Unit 1Get ready for polynomial operations and complex numbers", "Unit 2Get ready for equations", "Unit 3Get ready for transformations of functions and modeling with functions", "Unit 4Get ready for exponential and logarithmic relationships", "Unit 5Get ready for trigonometry", "Unit 6Get ready for rational functions", "Start Course challenge", "Unit 1Unit 1: Get ready for polynomial operations and complex numbers", "Get ready for polynomial operations and complex numbers: Unit test", "Unit 2Unit 2: Get ready for equations", "Get ready for equations: Unit test", "Unit 3Unit 3: Get ready for transformations of functions and modeling with functions", "Get ready for transformations of functions and modeling with functions: Unit test", "Unit 4Unit 4: Get ready for exponential and logarithmic relationships", "Get ready for exponential and logarithmic relationships: Unit test", "Unit 5Unit 5: Get ready for trigonometry", "Get ready for trigonometry: Unit test", "Unit 6Unit 6: Get ready for rational functions", "Get ready for rational functions: Unit test", "Start Course challenge", "Unit 1: Get ready for polynomial operations and complex numbers", "Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers", "Unit 2: Get ready for equations", "Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations", "Unit 3: Get ready for transformations of functions and modeling with functions", "Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions", "Unit 4: Get ready for exponential and logarithmic relationships", "Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships", "Unit 5: Get ready for trigonometry", "Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry", "Unit 6: Get ready for rational functions", "Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Get ready for Precalculus", "course_url": "/math/get-ready-for-precalculus", "page_contents": {"syllabus": {"topics": {"Get ready for Precalculus8 units \u00b7 88 skills": ["Unit 1Get ready for complex numbers", "Unit 2Get ready for polynomials", "Unit 3Get ready for composite and inverse functions", "Unit 4Get ready for trigonometry", "Unit 5Get ready for vectors and matrices", "Unit 6Get ready for series", "Unit 7Get ready for conic sections", "Unit 8Get ready for probability and combinatorics", "Start Course challenge", "Unit 1Unit 1: Get ready for complex numbers", "Get ready for complex numbers: Unit test", "Unit 2Unit 2: Get ready for polynomials", "Get ready for polynomials: Unit test", "Unit 3Unit 3: Get ready for composite and inverse functions", "Get ready for composite and inverse functions: Unit test", "Unit 4Unit 4: Get ready for trigonometry", "Get ready for trigonometry: Unit test", "Unit 5Unit 5: Get ready for vectors and matrices", "Get ready for vectors and matrices: Unit test", "Unit 6Unit 6: Get ready for series", "Get ready for series: Unit test", "Unit 7Unit 7: Get ready for conic sections", "Get ready for conic sections: Unit test", "Unit 8Unit 8: Get ready for probability and combinatorics", "Get ready for probability and combinatorics: Unit test", "Start Course challenge", "Unit 1: Get ready for complex numbers", "The imaginary unit i: Get ready for complex numbers", "Complex numbers introduction: Get ready for complex numbers", "The complex plane: Get ready for complex numbers", "Adding and subtracting complex numbers: Get ready for complex numbers", "Quadratic equations with complex solutions: Get ready for complex numbers", "Unit 2: Get ready for polynomials", "Adding and subtracting polynomials: Get ready for polynomials", "Multiplying binomials by polynomials: Get ready for polynomials", "Special products of polynomials: Get ready for polynomials", "Factoring higher degree polynomials: Get ready for polynomials", "Factoring using structure: Get ready for polynomials", "Zeros of polynomials: Get ready for polynomials", "Dividing polynomials by x: Get ready for polynomials", "Dividing quadratics by linear factors: Get ready for polynomials", "Dividing polynomials by linear factors: Get ready for polynomials", "Unit 3: Get ready for composite and inverse functions", "Shifting functions: Get ready for composite and inverse functions", "Reflecting functions: Get ready for composite and inverse functions", "Scaling functions: Get ready for composite and inverse functions", "Identifying function transformations: Get ready for composite and inverse functions", "Intro to domain and range of a function: Get ready for composite and inverse functions", "Intro to inverse functions: Get ready for composite and inverse functions", "Unit 4: Get ready for trigonometry", "Unit circle introduction: Get ready for trigonometry", "Radians: Get ready for trigonometry", "The Pythagorean identity: Get ready for trigonometry", "Trigonometric values of special angles: Get ready for trigonometry", "Graphing sinusoidal functions: Get ready for trigonometry", "Sinusoidal models: Get ready for trigonometry", "Unit 5: Get ready for vectors and matrices", "Equivalent systems of equations and the elimination method: Get ready for vectors and matrices", "Dilations: Get ready for vectors and matrices", "Solving triangles using the trigonometric ratios: Get ready for vectors and matrices", "Unit circle introduction: Get ready for vectors and matrices", "Distance formula: Get ready for vectors and matrices", "Unit 6: Get ready for series", "Intro to sequences: Get ready for series", "Constructing arithmetic sequences: Get ready for series", "Constructing geometric sequences: Get ready for series", "Modeling with sequences: Get ready for series", "General sequences: Get ready for series", "Geometric series: Get ready for series", "Unit 7: Get ready for conic sections", "Graphs of circles intro: Get ready for conic sections", "Standard equation of a circle: Get ready for conic sections", "Expanded equation of a circle: Get ready for conic sections", "Focus and directrix of a parabola: Get ready for conic sections", "Unit 8: Get ready for probability and combinatorics", "Basic theoretical probability: Get ready for probability and combinatorics", "Probability using sample spaces: Get ready for probability and combinatorics", "Basic set operations: Get ready for probability and combinatorics", "Experimental probability: Get ready for probability and combinatorics", "Randomness, probability, and simulation: Get ready for probability and combinatorics", "Addition rule: Get ready for probability and combinatorics", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Calculus", "course_url": "/math/get-ready-for-ap-calc", "page_contents": {"syllabus": {"topics": {"Get ready for AP\u00ae Calculus9 units \u00b7 112 skills": ["Unit 1Get ready for limits and continuity", "Unit 2Get ready for differentiation: definition and basic derivative rules", "Unit 3Get ready for differentiation: composite, implicit, and inverse functions", "Unit 4Get ready for contextual applications of differentiation", "Unit 5Get ready for applying derivatives to analyze functions", "Unit 6Get ready for integration and accumulation of change", "Unit 7Get ready for applications of integration", "Unit 8Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Unit 9Get ready for infinite sequences and series (BC only)", "Start Course challenge", "Unit 1Unit 1: Get ready for limits and continuity", "Get ready for limits and continuity: Unit test", "Unit 2Unit 2: Get ready for differentiation: definition and basic derivative rules", "Get ready for differentiation: definition and basic derivative rules: Unit test", "Unit 3Unit 3: Get ready for differentiation: composite, implicit, and inverse functions", "Get ready for differentiation: composite, implicit, and inverse functions: Unit test", "Unit 4Unit 4: Get ready for contextual applications of differentiation", "Get ready for contextual applications of differentiation: Unit test", "Unit 5Unit 5: Get ready for applying derivatives to analyze functions", "Get ready for applying derivatives to analyze functions : Unit test", "Unit 6Unit 6: Get ready for integration and accumulation of change", "Get ready for integration and accumulation of change: Unit test", "Unit 7Unit 7: Get ready for applications of integration", "Get ready for applications of integration: Unit test", "Unit 8Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only): Unit test", "Unit 9Unit 9: Get ready for infinite sequences and series (BC only)", "Get ready for infinite sequences and series (BC only): Unit test", "Start Course challenge", "Unit 1: Get ready for limits and continuity", "Evaluating functions: Get ready for limits and continuity", "Inputs and outputs of a function: Get ready for limits and continuity", "Composing functions: Get ready for limits and continuity", "Piecewise functions: Get ready for limits and continuity", "Introduction to factoring: Get ready for limits and continuity", "Factoring quadratics intro: Get ready for limits and continuity", "Factoring quadratics by grouping: Get ready for limits and continuity", "Factoring quadratics with difference of squares: Get ready for limits and continuity", "Factoring quadratics with perfect squares: Get ready for limits and continuity", "Factoring higher degree polynomials: Get ready for limits and continuity", "Introduction to the trigonometric ratios: Get ready for limits and continuity", "Unit circle introduction: Get ready for limits and continuity", "Radians: Get ready for limits and continuity", "The Pythagorean identity: Get ready for limits and continuity", "Special trigonometric values in the first quadrant: Get ready for limits and continuity", "Trigonometric identities on the unit circle: Get ready for limits and continuity", "Angle addition identities: Get ready for limits and continuity", "Reducing rational expressions to lowest terms: Get ready for limits and continuity", "End behavior of rational functions: Get ready for limits and continuity", "Discontinuities of rational functions: Get ready for limits and continuity", "Multiplying and dividing rational expressions: Get ready for limits and continuity", "Unit 2: Get ready for differentiation: definition and basic derivative rules", "Intro to slope-intercept form: Get ready for differentiation: definition and basic derivative rules", "Writing slope-intercept equations: Get ready for differentiation: definition and basic derivative rules", "Point-slope form: Get ready for differentiation: definition and basic derivative rules", "Average rate of change: Get ready for differentiation: definition and basic derivative rules", "Rational exponents: Get ready for differentiation: definition and basic derivative rules", "Properties of exponents: Get ready for differentiation: definition and basic derivative rules", "Introduction to logarithms: Get ready for differentiation: definition and basic derivative rules", "Unit 3: Get ready for differentiation: composite, implicit, and inverse functions", "Composing functions: Get ready for differentiation: composite, implicit, and inverse functions", "Linear equations with unknown coefficients: Get ready for differentiation: composite, implicit, and inverse functions", "Intro to inverse functions: Get ready for differentiation: composite, implicit, and inverse functions", "Invertible functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse trigonometric functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse functions in graphs and tables: Get ready for differentiation: composite, implicit, and inverse functions", "Verifying inverse functions by composition: Get ready for differentiation: composite, implicit, and inverse functions", "Unit 4: Get ready for contextual applications of differentiation", "Word problems with multiple units: Get ready for contextual applications of differentiation", "Linear equations word problems: Get ready for contextual applications of differentiation", "Interpreting function notation: Get ready for contextual applications of differentiation", "Average rate of change word problems: Get ready for contextual applications of differentiation", "Modeling with composite functions: Get ready for contextual applications of differentiation", "Modeling with right triangles: Get ready for contextual applications of differentiation", "Volume and surface area: Get ready for contextual applications of differentiation", "Unit 5: Get ready for applying derivatives to analyze functions", "Maximum and minimum points: Get ready for applying derivatives to analyze functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for applying derivatives to analyze functions", "Interpreting features of graphs: Get ready for applying derivatives to analyze functions", "Distance formula: Get ready for applying derivatives to analyze functions", "Square-root equations: Get ready for applying derivatives to analyze functions", "Zeros of polynomials: Get ready for applying derivatives to analyze functions", "Positive and negative intervals of polynomials: Get ready for applying derivatives to analyze functions", "Unit 6: Get ready for integration and accumulation of change", "Completing the square: Get ready for integration and accumulation of change", "Dividing quadratics by linear factors: Get ready for integration and accumulation of change", "Dividing polynomials by linear factors: Get ready for integration and accumulation of change", "Partial fraction expansion: Get ready for integration and accumulation of change", "Summation notation: Get ready for integration and accumulation of change", "Unit 7: Get ready for applications of integration", "Rational equations: Get ready for applications of integration", "Square-root equations: Get ready for applications of integration", "Extraneous solutions: Get ready for applications of integration", "Sinusoidal equations: Get ready for applications of integration", "Manipulating formulas: Get ready for applications of integration", "Solving equations by graphing: Get ready for applications of integration", "Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Sectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vectors introduction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Magnitude of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Scalar multiplication: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Direction of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components from magnitude & direction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Unit 9: Get ready for infinite sequences and series (BC only)", "Arithmetic sequences: Get ready for infinite sequences and series (BC only)", "Geometric sequences: Get ready for infinite sequences and series (BC only)", "Summation notation: Get ready for infinite sequences and series (BC only)", "Arithmetic series: Get ready for infinite sequences and series (BC only)", "Geometric series: Get ready for infinite sequences and series (BC only)", "End behavior of rational functions: Get ready for infinite sequences and series (BC only)", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Statistics", "course_url": "/math/get-ready-for-ap-statistics", "page_contents": {"syllabus": {"topics": {"Get ready for AP\u00ae Statistics5 units \u00b7 37 skills": ["Unit 1Get ready for exploring categorical data", "Unit 2Get ready for exploring one-variable quantitative data", "Unit 3Get ready for exploring two-variable quantitative data", "Unit 4Get ready for probability", "Unit 5Get ready for random variables and probability distributions", "Start Course challenge", "Unit 1Unit 1: Get ready for exploring categorical data", "Get ready for exploring categorical data: Unit test", "Unit 2Unit 2: Get ready for exploring one-variable quantitative data", "Get ready for exploring one-variable quantitative data: Unit test", "Unit 3Unit 3: Get ready for exploring two-variable quantitative data", "Get ready for exploring two-variable quantitative data: Unit test", "Unit 4Unit 4: Get ready for probability", "Get ready for probability: Unit test", "Unit 5Unit 5: Get ready for random variables and probability distributions", "Get ready for random variables and probability distributions: Unit test", "Start Course challenge", "Unit 1: Get ready for exploring categorical data", "Frequency tables: Get ready for exploring categorical data", "Bar graphs: Get ready for exploring categorical data", "Fractions, decimals, and percentages: Get ready for exploring categorical data", "Unit 2: Get ready for exploring one-variable quantitative data", "Frequency tables and dot plots: Get ready for exploring one-variable quantitative data", "Box and whisker plots: Get ready for exploring one-variable quantitative data", "Comparing data displays: Get ready for exploring one-variable quantitative data", "Mean, median, and mode: Get ready for exploring one-variable quantitative data", "Mean absolute deviation: Get ready for exploring one-variable quantitative data", "Linear equations with variables on both sides: Get ready for exploring one-variable quantitative data", "Linear equations with unknown coefficients: Get ready for exploring one-variable quantitative data", "Unit 3: Get ready for exploring two-variable quantitative data", "Introduction to scatter plots: Get ready for exploring two-variable quantitative data", "Estimating with trend lines: Get ready for exploring two-variable quantitative data", "Logarithms: Get ready for exploring two-variable quantitative data", "Unit 4: Get ready for probability", "Fractions, decimals, and percentages: Get ready for probability", "Comparing decimals and fractions: Get ready for probability", "Arithmetic with fractions: Get ready for probability", "Probability introduction: Get ready for probability", "Experimental probability: Get ready for probability", "Unit 5: Get ready for random variables and probability distributions", "Predictions with probability: Get ready for random variables and probability distributions", "The counting principle: Get ready for random variables and probability distributions", "Probability distributions introduction: Get ready for random variables and probability distributions", "Start Course challenge"]}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Early math review8 units \u00b7 121 skills": ["Unit 1Counting", "Unit 2Addition and subtraction intro", "Unit 3Place value (tens and hundreds)", "Unit 4Addition and subtraction within 20", "Unit 5Addition and subtraction within 100", "Unit 6Addition and subtraction within 1000", "Unit 7Measurement and data", "Unit 8Geometry", "Start Course challenge", "Unit 1Unit 1: Counting", "Counting: Unit test", "Unit 2Unit 2: Addition and subtraction intro", "Addition and subtraction intro: Unit test", "Unit 3Unit 3: Place value (tens and hundreds)", "Place value (tens and hundreds): Unit test", "Unit 4Unit 4: Addition and subtraction within 20", "Addition and subtraction within 20: Unit test", "Unit 5Unit 5: Addition and subtraction within 100", "Addition and subtraction within 100: Unit test", "Unit 6Unit 6: Addition and subtraction within 1000", "Addition and subtraction within 1000: Unit test", "Unit 7Unit 7: Measurement and data", "Measurement and data: Unit test", "Unit 8Unit 8: Geometry", "Geometry: Unit test", "Start Course challenge", "Unit 1: Counting", "Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting", "Unit 2: Addition and subtraction intro", "What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro", "Unit 3: Place value (tens and hundreds)", "Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)", "Unit 4: Addition and subtraction within 20", "Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20", "Unit 5: Addition and subtraction within 100", "Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100", "Unit 6: Addition and subtraction within 1000", "Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000", "Unit 7: Measurement and data", "Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data", "Unit 8: Geometry", "Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"2nd grade8 units \u00b7 75 skills": ["Unit 1Add and subtract within 20", "Unit 2Place value", "Unit 3Add and subtract within 100", "Unit 4Add and subtract within 1,000", "Unit 5Money and time", "Unit 6Measurement", "Unit 7Data", "Unit 8Geometry", "Start Course challenge", "Unit 1Unit 1: Add and subtract within 20", "Add and subtract within 20: Unit test", "Unit 2Unit 2: Place value", "Place value: Unit test", "Unit 3Unit 3: Add and subtract within 100", "Add and subtract within 100: Unit test", "Unit 4Unit 4: Add and subtract within 1,000", "Add and subtract within 1,000: Unit test", "Unit 5Unit 5: Money and time", "Money and time: Unit test", "Unit 6Unit 6: Measurement", "Measurement: Unit test", "Unit 7Unit 7: Data", "Data: Unit test", "Unit 8Unit 8: Geometry", "Geometry: Unit test", "Start Course challenge", "Unit 1: Add and subtract within 20", "Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20", "Unit 2: Place value", "Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value", "Unit 3: Add and subtract within 100", "Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100", "Unit 4: Add and subtract within 1,000", "Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000", "Unit 5: Money and time", "Time: Money and time", "Unit 6: Measurement", "Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement", "Unit 7: Data", "Bar graphs: Data", "Line plots: Data", "Unit 8: Geometry", "Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Unit 1Counting": [], "Unit 2Addition and subtraction intro": [], "Unit 3Place value (tens and hundreds)": [], "Unit 4Addition and subtraction within 20": [], "Unit 5Addition and subtraction within 100": [], "Unit 6Addition and subtraction within 1000": [], "Unit 7Measurement and data": [], "Unit 8Geometry": ["Start Course challenge"], "Unit 1Unit 1: Counting": [], "Counting: Unit test": [], "Unit 2Unit 2: Addition and subtraction intro": [], "Addition and subtraction intro: Unit test": [], "Unit 3Unit 3: Place value (tens and hundreds)": [], "Place value (tens and hundreds): Unit test": [], "Unit 4Unit 4: Addition and subtraction within 20": [], "Addition and subtraction within 20: Unit test": [], "Unit 5Unit 5: Addition and subtraction within 100": [], "Addition and subtraction within 100: Unit test": [], "Unit 6Unit 6: Addition and subtraction within 1000": [], "Addition and subtraction within 1000: Unit test": [], "Unit 7Unit 7: Measurement and data": [], "Measurement and data: Unit test": [], "Unit 8Unit 8: Geometry": [], "Geometry: Unit test": ["Start Course challenge"], "Unit 1: Counting": ["Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting"], "Unit 2: Addition and subtraction intro": ["What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro"], "Unit 3: Place value (tens and hundreds)": ["Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)"], "Unit 4: Addition and subtraction within 20": ["Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20"], "Unit 5: Addition and subtraction within 100": ["Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100"], "Unit 6: Addition and subtraction within 1000": ["Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000"], "Unit 7: Measurement and data": ["Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data"], "Unit 8: Geometry": ["Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Add and subtract within 20": [], "Unit 2Place value": [], "Unit 3Add and subtract within 100": [], "Unit 4Add and subtract within 1,000": [], "Unit 5Money and time": [], "Unit 6Measurement": [], "Unit 7Data": [], "Unit 8Geometry": ["Start Course challenge"], "Unit 1Unit 1: Add and subtract within 20": [], "Add and subtract within 20: Unit test": [], "Unit 2Unit 2: Place value": [], "Place value: Unit test": [], "Unit 3Unit 3: Add and subtract within 100": [], "Add and subtract within 100: Unit test": [], "Unit 4Unit 4: Add and subtract within 1,000": [], "Add and subtract within 1,000: Unit test": [], "Unit 5Unit 5: Money and time": [], "Money and time: Unit test": [], "Unit 6Unit 6: Measurement": [], "Measurement: Unit test": [], "Unit 7Unit 7: Data": [], "Data: Unit test": [], "Unit 8Unit 8: Geometry": [], "Geometry: Unit test": ["Start Course challenge"], "Unit 1: Add and subtract within 20": ["Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20"], "Unit 2: Place value": ["Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value"], "Unit 3: Add and subtract within 100": ["Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100"], "Unit 4: Add and subtract within 1,000": ["Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000"], "Unit 5: Money and time": ["Time: Money and time"], "Unit 6: Measurement": ["Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement"], "Unit 7: Data": ["Bar graphs: Data", "Line plots: Data"], "Unit 8: Geometry": ["Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Intro to multiplication": [], "Unit 21-digit multiplication": [], "Unit 3Addition, subtraction, and estimation": [], "Unit 4Intro to division": [], "Unit 5Understand fractions": [], "Unit 6Equivalent fractions and comparing fractions": [], "Unit 7More with multiplication and division": [], "Unit 8Arithmetic patterns and problem solving": [], "Unit 9Quadrilaterals": [], "Unit 10Area": [], "Unit 11Perimeter": [], "Unit 12Time": [], "Unit 13Measurement": [], "Unit 14Represent and interpret data": ["Start Course challenge"], "Unit 1Unit 1: Intro to multiplication": [], "Intro to multiplication: Unit test": [], "Unit 2Unit 2: 1-digit multiplication": [], "1-digit multiplication: Unit test": [], "Unit 3Unit 3: Addition, subtraction, and estimation": [], "Addition, subtraction, and estimation: Unit test": [], "Unit 4Unit 4: Intro to division": [], "Intro to division: Unit test": [], "Unit 5Unit 5: Understand fractions": [], "Understand fractions: Unit test": [], "Unit 6Unit 6: Equivalent fractions and comparing fractions": [], "Equivalent fractions and comparing fractions: Unit test": [], "Unit 7Unit 7: More with multiplication and division": [], "More with multiplication and division: Unit test": [], "Unit 8Unit 8: Arithmetic patterns and problem solving": [], "Arithmetic patterns and problem solving: Unit test": [], "Unit 9Unit 9: Quadrilaterals": [], "Quadrilaterals: Unit test": [], "Unit 10Unit 10: Area": [], "Area: Unit test": [], "Unit 11Unit 11: Perimeter": [], "Perimeter: Unit test": [], "Unit 12Unit 12: Time": [], "Time: Unit test": [], "Unit 13Unit 13: Measurement": [], "Measurement: Unit test": [], "Unit 14Unit 14: Represent and interpret data": [], "Represent and interpret data: Unit test": ["Start Course challenge"], "Unit 1: Intro to multiplication": ["Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication"], "Unit 2: 1-digit multiplication": ["Distributive property: 1-digit multiplication"], "Unit 3: Addition, subtraction, and estimation": ["Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation"], "Unit 4: Intro to division": ["Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division"], "Unit 5: Understand fractions": ["Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions"], "Unit 6: Equivalent fractions and comparing fractions": ["Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions"], "Unit 7: More with multiplication and division": ["Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division"], "Unit 8: Arithmetic patterns and problem solving": ["2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving"], "Unit 9: Quadrilaterals": ["Quadrilaterals : Quadrilaterals"], "Unit 10: Area": [], "Count unit squares to find area: Area": ["Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area"], "Unit 11: Perimeter": ["Perimeter: Perimeter", "Perimeter word problems: Perimeter"], "Unit 12: Time": ["Time on number line: Time", "Telling time: Time", "Elapsed time: Time"], "Unit 13: Measurement": ["Mass: Measurement", "Volume: Measurement"], "Unit 14: Represent and interpret data": ["Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Place value": [], "Unit 2Addition, subtraction, and estimation": [], "Unit 3Multiply by 1-digit numbers": [], "Unit 4Multiply by 2-digit numbers": [], "Unit 5Division": [], "Unit 6Factors, multiples and patterns": [], "Unit 7Equivalent fractions and comparing fractions": [], "Unit 8Add and subtract fractions": [], "Unit 9Multiply fractions": [], "Unit 10Understand decimals": [], "Unit 11Plane figures": [], "Unit 12Measuring angles": [], "Unit 13Area and perimeter": [], "Unit 14Units of measurement": ["Start Course challenge"], "Unit 1Unit 1: Place value": [], "Place value: Unit test": [], "Unit 2Unit 2: Addition, subtraction, and estimation": [], "Addition, subtraction, and estimation: Unit test": [], "Unit 3Unit 3: Multiply by 1-digit numbers": [], "Multiply by 1-digit numbers: Unit test": [], "Unit 4Unit 4: Multiply by 2-digit numbers": [], "Multiply by 2-digit numbers: Unit test": [], "Unit 5Unit 5: Division": [], "Division: Unit test": [], "Unit 6Unit 6: Factors, multiples and patterns": [], "Factors, multiples and patterns: Unit test": [], "Unit 7Unit 7: Equivalent fractions and comparing fractions": [], "Equivalent fractions and comparing fractions: Unit test": [], "Unit 8Unit 8: Add and subtract fractions": [], "Add and subtract fractions: Unit test": [], "Unit 9Unit 9: Multiply fractions": [], "Multiply fractions: Unit test": [], "Unit 10Unit 10: Understand decimals": [], "Understand decimals: Unit test": [], "Unit 11Unit 11: Plane figures": [], "Plane figures: Unit test": [], "Unit 12Unit 12: Measuring angles": [], "Measuring angles: Unit test": [], "Unit 13Unit 13: Area and perimeter": [], "Area and perimeter: Unit test": [], "Unit 14Unit 14: Units of measurement": [], "Units of measurement: Unit test": ["Start Course challenge"], "Unit 1: Place value": ["Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value"], "Unit 2: Addition, subtraction, and estimation": ["Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation"], "Unit 3: Multiply by 1-digit numbers": ["Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers"], "Unit 4: Multiply by 2-digit numbers": ["Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers"], "Unit 5: Division": ["Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division"], "Unit 6: Factors, multiples and patterns": ["Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns"], "Unit 7: Equivalent fractions and comparing fractions": ["Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions"], "Unit 8: Add and subtract fractions": ["Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions"], "Unit 9: Multiply fractions": ["Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions"], "Unit 10: Understand decimals": ["Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals"], "Unit 11: Plane figures": ["Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures"], "Unit 12: Measuring angles": ["Measuring angles: Measuring angles", "Decomposing angles: Measuring angles"], "Unit 13: Area and perimeter": ["Area and perimeter: Area and perimeter"], "Unit 14: Units of measurement": [], "Estimating volume: Units of measurement": [], "Estimating length: Units of measurement": [], "Time: Units of measurement": [], "Converting units of mass: Units of measurement": [], "Converting units of volume: Units of measurement": [], "Converting units of length: Units of measurement": [], "Converting units of time: Units of measurement": [], "Money word problems: Units of measurement": [], "Conversion word problems: Units of measurement": ["Start Course challenge"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Decimal place value": [], "Unit 2Add decimals": [], "Unit 3Subtract decimals": [], "Unit 4Add and subtract fractions": [], "Unit 5Multi-digit multiplication and division": [], "Unit 6Multiply fractions": [], "Unit 7Divide fractions": [], "Unit 8Multiply decimals": [], "Unit 9Divide decimals": [], "Unit 10Powers of ten": [], "Unit 11Volume": [], "Unit 12Coordinate plane": [], "Unit 13Algebraic thinking": [], "Unit 14Converting units of measure": [], "Unit 15Line plots": [], "Unit 16Properties of shapes": ["Start Course challenge"], "Unit 1Unit 1: Decimal place value": [], "Decimal place value: Unit test": [], "Unit 2Unit 2: Add decimals": [], "Add decimals: Unit test": [], "Unit 3Unit 3: Subtract decimals": [], "Subtract decimals: Unit test": [], "Unit 4Unit 4: Add and subtract fractions": [], "Add and subtract fractions: Unit test": [], "Unit 5Unit 5: Multi-digit multiplication and division": [], "Multi-digit multiplication and division: Unit test": [], "Unit 6Unit 6: Multiply fractions": [], "Multiply fractions: Unit test": [], "Unit 7Unit 7: Divide fractions": [], "Divide fractions: Unit test": [], "Unit 8Unit 8: Multiply decimals": [], "Multiply decimals: Unit test": [], "Unit 9Unit 9: Divide decimals": [], "Divide decimals: Unit test": [], "Unit 10Unit 10: Powers of ten": [], "Powers of ten: Unit test": [], "Unit 11Unit 11: Volume": [], "Volume: Unit test": [], "Unit 12Unit 12: Coordinate plane": [], "Coordinate plane: Unit test": [], "Unit 13Unit 13: Algebraic thinking": [], "Algebraic thinking: Unit test": [], "Unit 14Unit 14: Converting units of measure": [], "Converting units of measure: Unit test": [], "Unit 15Unit 15: Line plots": [], "Line plots: Unit test": [], "Unit 16Unit 16: Properties of shapes": [], "Properties of shapes: Unit test": ["Start Course challenge"], "Unit 1: Decimal place value": ["Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value"], "Unit 2: Add decimals": ["Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals"], "Unit 3: Subtract decimals": ["Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals"], "Unit 4: Add and subtract fractions": ["Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions"], "Unit 5: Multi-digit multiplication and division": ["Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division"], "Unit 6: Multiply fractions": ["Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions"], "Unit 7: Divide fractions": ["Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions"], "Dividing unit fractions by whole numbers: Divide fractions": [], "Dividing whole numbers by unit fractions: Divide fractions": ["Dividing fractions and whole numbers word problems: Divide fractions"], "Unit 8: Multiply decimals": ["Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals"], "Unit 9: Divide decimals": ["Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals"], "Unit 10: Powers of ten": ["Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten"], "Unit 11: Volume": [], "Volume with unit cubes: Volume": ["Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume"], "Unit 12: Coordinate plane": ["Intro to the coordinate plane : Coordinate plane"], "Unit 13: Algebraic thinking": ["Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking"], "Unit 14: Converting units of measure": [], "Converting units of time: Converting units of measure": [], "Converting metric units: Converting units of measure": [], "Converting metric units word problems: Converting units of measure": [], "Converting US Customary units: Converting units of measure": [], "Converting US Customary units word problems: Converting units of measure": [], "Unit 15: Line plots": ["Graph data on line plots: Line plots", "Interpret data on line plots: Line plots"], "Unit 16: Properties of shapes": ["Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Ratios": [], "Unit 2Arithmetic with rational numbers": [], "Unit 3Rates and percentages": [], "Unit 4Exponents and order of operations": [], "Unit 5Negative numbers": [], "Unit 6Variables & expressions": [], "Unit 7Equations & inequalities": [], "Unit 8Plane figures": [], "Unit 9Coordinate plane": [], "Unit 103D figures": [], "Unit 11Data and statistics": ["Start Course challenge"], "Unit 1Unit 1: Ratios": [], "Ratios: Unit test": [], "Unit 2Unit 2: Arithmetic with rational numbers": [], "Arithmetic with rational numbers: Unit test": [], "Unit 3Unit 3: Rates and percentages": [], "Rates and percentages: Unit test": [], "Unit 4Unit 4: Exponents and order of operations": [], "Exponents and order of operations: Unit test": [], "Unit 5Unit 5: Negative numbers": [], "Negative numbers: Unit test": [], "Unit 6Unit 6: Variables & expressions": [], "Variables & expressions: Unit test": [], "Unit 7Unit 7: Equations & inequalities": [], "Equations & inequalities: Unit test": [], "Unit 8Unit 8: Plane figures": [], "Plane figures: Unit test": [], "Unit 9Unit 9: Coordinate plane": [], "Coordinate plane: Unit test": [], "Unit 10Unit 10: 3D figures": [], "3D figures: Unit test": [], "Unit 11Unit 11: Data and statistics": [], "Data and statistics: Unit test": ["Start Course challenge"], "Unit 1: Ratios": ["Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios"], "Unit 2: Arithmetic with rational numbers": ["Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers"], "Unit 3: Rates and percentages": ["Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 4: Exponents and order of operations": ["Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations"], "Unit 5: Negative numbers": ["Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers"], "Unit 6: Variables & expressions": ["Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions"], "Unit 7: Equations & inequalities": ["Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities"], "Unit 8: Plane figures": ["Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures"], "Unit 9: Coordinate plane": ["Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane"], "Unit 10: 3D figures": ["Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures"], "Unit 11: Data and statistics": ["Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Proportional relationships": [], "Unit 2Rates and percentages": [], "Unit 3Integers: addition and subtraction": [], "Unit 4Rational numbers: addition and subtraction": [], "Unit 5Negative numbers: multiplication and division": [], "Unit 6Expressions, equations, & inequalities": [], "Unit 7Statistics and probability": [], "Unit 8Scale copies": [], "Unit 9Geometry": ["Start Course challenge"], "Unit 1Unit 1: Proportional relationships": [], "Proportional relationships: Unit test": [], "Unit 2Unit 2: Rates and percentages": [], "Rates and percentages: Unit test": [], "Unit 3Unit 3: Integers: addition and subtraction": [], "Integers: addition and subtraction: Unit test": [], "Unit 4Unit 4: Rational numbers: addition and subtraction": [], "Rational numbers: addition and subtraction: Unit test": [], "Unit 5Unit 5: Negative numbers: multiplication and division": [], "Negative numbers: multiplication and division: Unit test": [], "Unit 6Unit 6: Expressions, equations, & inequalities": [], "Expressions, equations, & inequalities: Unit test": [], "Unit 7Unit 7: Statistics and probability": [], "Statistics and probability: Unit test": [], "Unit 8Unit 8: Scale copies": [], "Scale copies: Unit test": [], "Unit 9Unit 9: Geometry": [], "Geometry: Unit test": ["Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles"], "Unit 1: Proportional relationships": ["Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships"], "Unit 2: Rates and percentages": ["Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 3: Integers: addition and subtraction": ["Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction"], "Unit 4: Rational numbers: addition and subtraction": ["Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction"], "Unit 5: Negative numbers: multiplication and division": ["Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division"], "Unit 6: Expressions, equations, & inequalities": ["The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities"], "Unit 7: Statistics and probability": ["Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability"], "Unit 8: Scale copies": ["Scale copies: Scale copies", "Scale drawings: Scale copies"], "Unit 9: Geometry": ["Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Numbers and operations": [], "Unit 2Solving equations with one unknown": [], "Unit 3Linear equations and functions": [], "Unit 4Systems of equations": [], "Unit 5Geometry": [], "Unit 6Geometric transformations": [], "Unit 7Data and modeling": ["Start Course challenge"], "Unit 1Unit 1: Numbers and operations": [], "Numbers and operations: Unit test": [], "Unit 2Unit 2: Solving equations with one unknown": [], "Solving equations with one unknown: Unit test": [], "Unit 3Unit 3: Linear equations and functions": [], "Linear equations and functions: Unit test": [], "Unit 4Unit 4: Systems of equations": [], "Systems of equations: Unit test": [], "Unit 5Unit 5: Geometry": [], "Geometry: Unit test": [], "Unit 6Unit 6: Geometric transformations": [], "Geometric transformations: Unit test": [], "Unit 7Unit 7: Data and modeling": [], "Data and modeling: Unit test": ["Start Course challenge"], "Unit 1: Numbers and operations": ["Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations"], "Unit 2: Solving equations with one unknown": ["Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown"], "Unit 3: Linear equations and functions": ["Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions"], "Unit 4: Systems of equations": ["Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 5: Geometry": ["Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry"], "Unit 6: Geometric transformations": ["Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations"], "Unit 7: Data and modeling": ["Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for addition and subtraction": [], "Unit 2Get ready for multiplication and division": [], "Unit 3Get ready for fractions": [], "Unit 4Get ready for patterns and problem solving": [], "Unit 5Get ready for area and perimeter": [], "Unit 6Get ready for telling time": [], "Unit 7Get ready for data": ["Start Course challenge"], "Unit 1Unit 1: Get ready for addition and subtraction": [], "Get ready for addition and subtraction: Unit test": [], "Unit 2Unit 2: Get ready for multiplication and division": [], "Get ready for multiplication and division: Unit test": [], "Unit 3Unit 3: Get ready for fractions": [], "Get ready for fractions: Unit test": [], "Unit 4Unit 4: Get ready for patterns and problem solving": [], "Get ready for patterns and problem solving: Unit test": [], "Unit 5Unit 5: Get ready for area and perimeter": [], "Get ready for area and perimeter: Unit test": [], "Unit 6Unit 6: Get ready for telling time": [], "Get ready for telling time: Unit test": [], "Unit 7Unit 7: Get ready for data": [], "Get ready for data: Unit test": ["Start Course challenge"], "Unit 1: Get ready for addition and subtraction": ["Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction"], "Unit 2: Get ready for multiplication and division": ["Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division"], "Unit 3: Get ready for fractions": ["Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions"], "Unit 4: Get ready for patterns and problem solving": ["Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving"], "Unit 5: Get ready for area and perimeter": [], "Units of length: Get ready for area and perimeter": ["Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter"], "Unit 6: Get ready for telling time": ["Telling time: Get ready for telling time"], "Unit 7: Get ready for data": ["Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for place value": [], "Unit 2Get ready for addition, subtraction, and estimation": [], "Unit 3Get ready for multiplication": [], "Unit 4Get ready for division": [], "Unit 5Get ready for fractions": [], "Unit 6Get ready for plane figures": [], "Unit 7Get ready for area and perimeter": ["Start Course challenge"], "Unit 1Unit 1: Get ready for place value": [], "Get ready for place value: Unit test": [], "Unit 2Unit 2: Get ready for addition, subtraction, and estimation": [], "Get ready for addition, subtraction, and estimation: Unit test": [], "Unit 3Unit 3: Get ready for multiplication": [], "Get ready for multiplication: Unit test": [], "Unit 4Unit 4: Get ready for division": [], "Get ready for division: Unit test": [], "Unit 5Unit 5: Get ready for fractions": [], "Get ready for fractions: Unit test": [], "Unit 6Unit 6: Get ready for plane figures": [], "Get ready for plane figures : Unit test": [], "Unit 7Unit 7: Get ready for area and perimeter": [], "Get ready for area and perimeter: Unit test": ["Start Course challenge"], "Unit 1: Get ready for place value": ["Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value"], "Unit 2: Get ready for addition, subtraction, and estimation": ["Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation"], "Unit 3: Get ready for multiplication": ["Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication"], "Unit 4: Get ready for division": ["Division intro: Get ready for division", "Relate multiplication and division: Get ready for division"], "Unit 5: Get ready for fractions": ["Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions"], "Unit 6: Get ready for plane figures": ["Quadrilaterals: Get ready for plane figures"], "Unit 7: Get ready for area and perimeter": ["Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for decimal place value": [], "Unit 2Get ready for adding and subtracting decimals": [], "Unit 3Get ready for adding and subtracting fractions": [], "Unit 4Get ready for multiplication and division with whole numbers and decimals": [], "Unit 5Get ready for multiplying and dividing fractions": [], "Unit 6Get ready for powers of 10": [], "Unit 7Get ready for volume": [], "Unit 8Get ready for properties of shapes": ["Start Course challenge"], "Unit 1Unit 1: Get ready for decimal place value": [], "Get ready for decimal place value: Unit test": [], "Unit 2Unit 2: Get ready for adding and subtracting decimals": [], "Get ready for adding and subtracting decimals: Unit test": [], "Unit 3Unit 3: Get ready for adding and subtracting fractions": [], "Get ready for adding and subtracting fractions: Unit test": [], "Unit 4Unit 4: Get ready for multiplication and division with whole numbers and decimals": [], "Get ready for multiplication and division with whole numbers and decimals: Unit test": [], "Unit 5Unit 5: Get ready for multiplying and dividing fractions": [], "Get ready for multiplying and dividing fractions: Unit test": [], "Unit 6Unit 6: Get ready for powers of 10": [], "Get ready for powers of 10: Unit test": [], "Unit 7Unit 7: Get ready for volume": [], "Get ready for volume: Unit test": [], "Unit 8Unit 8: Get ready for properties of shapes": [], "Get ready for properties of shapes: Unit test": ["Start Course challenge"], "Unit 1: Get ready for decimal place value": ["Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value"], "Unit 2: Get ready for adding and subtracting decimals": ["Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals"], "Unit 3: Get ready for adding and subtracting fractions": ["Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions"], "Unit 4: Get ready for multiplication and division with whole numbers and decimals": ["Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals"], "Unit 5: Get ready for multiplying and dividing fractions": ["Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions"], "Unit 6: Get ready for powers of 10": ["How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10"], "Unit 7: Get ready for volume": ["Introduction to area: Get ready for volume"], "Unit 8: Get ready for properties of shapes": ["Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for ratios, rates, and percentages": [], "Unit 2Get ready for arithmetic operations": [], "Unit 3Get ready for negative numbers": [], "Unit 4Get ready for equations, expressions, and inequalities": [], "Unit 5Get ready for geometry": ["Start Course challenge"], "Unit 1Unit 1: Get ready for ratios, rates, and percentages": [], "Get ready for ratios, rates, and percentages: Unit test": [], "Unit 2Unit 2: Get ready for arithmetic operations": [], "Get ready for arithmetic operations: Unit test": [], "Unit 3Unit 3: Get ready for negative numbers": [], "Get ready for negative numbers: Unit test": [], "Unit 4Unit 4: Get ready for equations, expressions, and inequalities": [], "Get ready for equations, expressions, and inequalities: Unit test": [], "Unit 5Unit 5: Get ready for geometry": [], "Get ready for geometry: Unit test": ["Start Course challenge"], "Unit 1: Get ready for ratios, rates, and percentages": ["Multiplication and division word problems: Get ready for ratios, rates, and percentages"], "Convert units of measure: Get ready for ratios, rates, and percentages": ["Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages"], "Unit 2: Get ready for arithmetic operations": [], "Divide whole numbers by unit fractions: Get ready for arithmetic operations": [], "Divide unit fractions by whole numbers: Get ready for arithmetic operations": ["Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations"], "Unit 3: Get ready for negative numbers": ["Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers"], "Unit 4: Get ready for equations, expressions, and inequalities": ["Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities"], "Unit 5: Get ready for geometry": ["Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for negative number operations": [], "Unit 2Get ready for fractions, decimals, & percentages": [], "Unit 3Get ready for rates & proportional relationships": [], "Unit 4Get ready for expressions, equations, & inequalities": [], "Unit 5Get ready for geometry": [], "Unit 6Get ready for statistics & probability": ["Start Course challenge"], "Unit 1Unit 1: Get ready for negative number operations": [], "Get ready for negative number operations: Unit test": [], "Unit 2Unit 2: Get ready for fractions, decimals, & percentages": [], "Get ready for fractions, decimals, & percentages: Unit test": [], "Unit 3Unit 3: Get ready for rates & proportional relationships": [], "Get ready for rates & proportional relationships: Unit test": [], "Unit 4Unit 4: Get ready for expressions, equations, & inequalities": [], "Get ready for expressions, equations, & inequalities: Unit test": [], "Unit 5Unit 5: Get ready for geometry": [], "Get ready for geometry: Unit test": [], "Unit 6Unit 6: Get ready for statistics & probability": [], "Get ready for statistics & probability: Unit test": ["Start Course challenge"], "Unit 1: Get ready for negative number operations": ["Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations"], "Unit 2: Get ready for fractions, decimals, & percentages": ["Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages"], "Unit 3: Get ready for rates & proportional relationships": ["Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships"], "Unit 4: Get ready for expressions, equations, & inequalities": ["Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities"], "Unit 5: Get ready for geometry": ["Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry"], "Unit 6: Get ready for statistics & probability": ["Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for numbers and operations": [], "Unit 2Get ready for solving equations and systems of equations": [], "Unit 3Get ready for linear equations and functions": [], "Unit 4Get ready for geometry": ["Start Course challenge"], "Unit 1Unit 1: Get ready for numbers and operations": [], "Get ready for numbers and operations: Unit test": [], "Unit 2Unit 2: Get ready for solving equations and systems of equations": [], "Get ready for solving equations and systems of equations: Unit test": [], "Unit 3Unit 3: Get ready for linear equations and functions": [], "Get ready for linear equations and functions: Unit test": [], "Unit 4Unit 4: Get ready for geometry": [], "Get ready for geometry: Unit test": ["Start Course challenge"], "Unit 1: Get ready for numbers and operations": ["Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations"], "Unit 2: Get ready for solving equations and systems of equations": ["Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations"], "Unit 3: Get ready for linear equations and functions": ["Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions"], "Unit 4: Get ready for geometry": ["Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for equations & inequalities": [], "Unit 2Get ready for working with units": [], "Unit 3Get ready for linear relationships": [], "Unit 4Get ready for functions & sequences": [], "Unit 5Get ready for exponents, radicals, & irrational numbers": [], "Unit 6Get ready for quadratics": ["Start Course challenge"], "Unit 1Unit 1: Get ready for equations & inequalities": [], "Get ready for equations & inequalities: Unit test": [], "Unit 2Unit 2: Get ready for working with units": [], "Get ready for working with units: Unit test": [], "Unit 3Unit 3: Get ready for linear relationships": [], "Get ready for linear relationships: Unit test": [], "Unit 4Unit 4: Get ready for functions & sequences": [], "Get ready for functions & sequences: Unit test": [], "Unit 5Unit 5: Get ready for exponents, radicals, & irrational numbers": [], "Get ready for exponents, radicals, & irrational numbers: Unit test": [], "Unit 6Unit 6: Get ready for quadratics": [], "Get ready for quadratics: Unit test": ["Start Course challenge"], "Unit 1: Get ready for equations & inequalities": ["Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities"], "Unit 2: Get ready for working with units": [], "Intro to ratios: Get ready for working with units": [], "Equivalent ratios: Get ready for working with units": [], "Ratio application: Get ready for working with units": [], "Intro to rates: Get ready for working with units": [], "Rate problems: Get ready for working with units": [], "Unit 3: Get ready for linear relationships": ["Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships"], "Unit 4: Get ready for functions & sequences": ["Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences"], "Unit 5: Get ready for exponents, radicals, & irrational numbers": ["Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers"], "Unit 6: Get ready for quadratics": ["Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for congruence, similarity, and triangle trigonometry": [], "Unit 2Get ready for analytic geometry": [], "Unit 3Get ready for conic sections": [], "Unit 4Get ready for circles and solid geometry": ["Start Course challenge"], "Unit 1Unit 1: Get ready for congruence, similarity, and triangle trigonometry": [], "Get ready for congruence, similarity, and triangle trigonometry: Unit test": [], "Unit 2Unit 2: Get ready for analytic geometry": [], "Get ready for analytic geometry: Unit test": [], "Unit 3Unit 3: Get ready for conic sections": [], "Get ready for conic sections: Unit test": [], "Unit 4Unit 4: Get ready for circles and solid geometry": [], "Get ready for circles and solid geometry: Unit test": ["Start Course challenge"], "Unit 1: Get ready for congruence, similarity, and triangle trigonometry": ["Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry"], "Unit 2: Get ready for analytic geometry": ["Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry"], "Unit 3: Get ready for conic sections": ["Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections"], "Unit 4: Get ready for circles and solid geometry": ["Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for polynomial operations and complex numbers": [], "Unit 2Get ready for equations": [], "Unit 3Get ready for transformations of functions and modeling with functions": [], "Unit 4Get ready for exponential and logarithmic relationships": [], "Unit 5Get ready for trigonometry": [], "Unit 6Get ready for rational functions": ["Start Course challenge"], "Unit 1Unit 1: Get ready for polynomial operations and complex numbers": [], "Get ready for polynomial operations and complex numbers: Unit test": [], "Unit 2Unit 2: Get ready for equations": [], "Get ready for equations: Unit test": [], "Unit 3Unit 3: Get ready for transformations of functions and modeling with functions": [], "Get ready for transformations of functions and modeling with functions: Unit test": [], "Unit 4Unit 4: Get ready for exponential and logarithmic relationships": [], "Get ready for exponential and logarithmic relationships: Unit test": [], "Unit 5Unit 5: Get ready for trigonometry": [], "Get ready for trigonometry: Unit test": [], "Unit 6Unit 6: Get ready for rational functions": [], "Get ready for rational functions: Unit test": ["Start Course challenge"], "Unit 1: Get ready for polynomial operations and complex numbers": ["Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers"], "Unit 2: Get ready for equations": ["Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations"], "Unit 3: Get ready for transformations of functions and modeling with functions": ["Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions"], "Unit 4: Get ready for exponential and logarithmic relationships": ["Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships"], "Unit 5: Get ready for trigonometry": ["Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry"], "Unit 6: Get ready for rational functions": ["Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Get ready for Precalculus", "course_url": "/math/get-ready-for-precalculus", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for complex numbers": [], "Unit 2Get ready for polynomials": [], "Unit 3Get ready for composite and inverse functions": [], "Unit 4Get ready for trigonometry": [], "Unit 5Get ready for vectors and matrices": [], "Unit 6Get ready for series": [], "Unit 7Get ready for conic sections": [], "Unit 8Get ready for probability and combinatorics": ["Start Course challenge"], "Unit 1Unit 1: Get ready for complex numbers": [], "Get ready for complex numbers: Unit test": [], "Unit 2Unit 2: Get ready for polynomials": [], "Get ready for polynomials: Unit test": [], "Unit 3Unit 3: Get ready for composite and inverse functions": [], "Get ready for composite and inverse functions: Unit test": [], "Unit 4Unit 4: Get ready for trigonometry": [], "Get ready for trigonometry: Unit test": [], "Unit 5Unit 5: Get ready for vectors and matrices": [], "Get ready for vectors and matrices: Unit test": [], "Unit 6Unit 6: Get ready for series": [], "Get ready for series: Unit test": [], "Unit 7Unit 7: Get ready for conic sections": [], "Get ready for conic sections: Unit test": [], "Unit 8Unit 8: Get ready for probability and combinatorics": [], "Get ready for probability and combinatorics: Unit test": ["Start Course challenge"], "Unit 1: Get ready for complex numbers": [], "The imaginary unit i: Get ready for complex numbers": ["Complex numbers introduction: Get ready for complex numbers", "The complex plane: Get ready for complex numbers", "Adding and subtracting complex numbers: Get ready for complex numbers", "Quadratic equations with complex solutions: Get ready for complex numbers"], "Unit 2: Get ready for polynomials": ["Adding and subtracting polynomials: Get ready for polynomials", "Multiplying binomials by polynomials: Get ready for polynomials", "Special products of polynomials: Get ready for polynomials", "Factoring higher degree polynomials: Get ready for polynomials", "Factoring using structure: Get ready for polynomials", "Zeros of polynomials: Get ready for polynomials", "Dividing polynomials by x: Get ready for polynomials", "Dividing quadratics by linear factors: Get ready for polynomials", "Dividing polynomials by linear factors: Get ready for polynomials"], "Unit 3: Get ready for composite and inverse functions": ["Shifting functions: Get ready for composite and inverse functions", "Reflecting functions: Get ready for composite and inverse functions", "Scaling functions: Get ready for composite and inverse functions", "Identifying function transformations: Get ready for composite and inverse functions", "Intro to domain and range of a function: Get ready for composite and inverse functions", "Intro to inverse functions: Get ready for composite and inverse functions"], "Unit 4: Get ready for trigonometry": [], "Unit circle introduction: Get ready for trigonometry": ["Radians: Get ready for trigonometry", "The Pythagorean identity: Get ready for trigonometry", "Trigonometric values of special angles: Get ready for trigonometry", "Graphing sinusoidal functions: Get ready for trigonometry", "Sinusoidal models: Get ready for trigonometry"], "Unit 5: Get ready for vectors and matrices": ["Equivalent systems of equations and the elimination method: Get ready for vectors and matrices", "Dilations: Get ready for vectors and matrices", "Solving triangles using the trigonometric ratios: Get ready for vectors and matrices"], "Unit circle introduction: Get ready for vectors and matrices": ["Distance formula: Get ready for vectors and matrices"], "Unit 6: Get ready for series": ["Intro to sequences: Get ready for series", "Constructing arithmetic sequences: Get ready for series", "Constructing geometric sequences: Get ready for series", "Modeling with sequences: Get ready for series", "General sequences: Get ready for series", "Geometric series: Get ready for series"], "Unit 7: Get ready for conic sections": ["Graphs of circles intro: Get ready for conic sections", "Standard equation of a circle: Get ready for conic sections", "Expanded equation of a circle: Get ready for conic sections", "Focus and directrix of a parabola: Get ready for conic sections"], "Unit 8: Get ready for probability and combinatorics": ["Basic theoretical probability: Get ready for probability and combinatorics", "Probability using sample spaces: Get ready for probability and combinatorics", "Basic set operations: Get ready for probability and combinatorics", "Experimental probability: Get ready for probability and combinatorics", "Randomness, probability, and simulation: Get ready for probability and combinatorics", "Addition rule: Get ready for probability and combinatorics", "Start Course challenge"]}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Unit 1Counting": [], "Unit 2Addition and subtraction intro": [], "Unit 3Place value (tens and hundreds)": [], "Unit 4Addition and subtraction within 20": [], "Unit 5Addition and subtraction within 100": [], "Unit 6Addition and subtraction within 1000": [], "Unit 7Measurement and data": [], "Unit 8Geometry": ["Start Course challenge"], "Unit 1Unit 1: Counting": [], "Counting: Unit test": [], "Unit 2Unit 2: Addition and subtraction intro": [], "Addition and subtraction intro: Unit test": [], "Unit 3Unit 3: Place value (tens and hundreds)": [], "Place value (tens and hundreds): Unit test": [], "Unit 4Unit 4: Addition and subtraction within 20": [], "Addition and subtraction within 20: Unit test": [], "Unit 5Unit 5: Addition and subtraction within 100": [], "Addition and subtraction within 100: Unit test": [], "Unit 6Unit 6: Addition and subtraction within 1000": [], "Addition and subtraction within 1000: Unit test": [], "Unit 7Unit 7: Measurement and data": [], "Measurement and data: Unit test": [], "Unit 8Unit 8: Geometry": [], "Geometry: Unit test": ["Start Course challenge"], "Unit 1: Counting": ["Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting"], "Unit 2: Addition and subtraction intro": ["What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro"], "Unit 3: Place value (tens and hundreds)": ["Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)"], "Unit 4: Addition and subtraction within 20": ["Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20"], "Unit 5: Addition and subtraction within 100": ["Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100"], "Unit 6: Addition and subtraction within 1000": ["Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000"], "Unit 7: Measurement and data": ["Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data"], "Unit 8: Geometry": ["Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Add and subtract within 20": [], "Unit 2Place value": [], "Unit 3Add and subtract within 100": [], "Unit 4Add and subtract within 1,000": [], "Unit 5Money and time": [], "Unit 6Measurement": [], "Unit 7Data": [], "Unit 8Geometry": ["Start Course challenge"], "Unit 1Unit 1: Add and subtract within 20": [], "Add and subtract within 20: Unit test": [], "Unit 2Unit 2: Place value": [], "Place value: Unit test": [], "Unit 3Unit 3: Add and subtract within 100": [], "Add and subtract within 100: Unit test": [], "Unit 4Unit 4: Add and subtract within 1,000": [], "Add and subtract within 1,000: Unit test": [], "Unit 5Unit 5: Money and time": [], "Money and time: Unit test": [], "Unit 6Unit 6: Measurement": [], "Measurement: Unit test": [], "Unit 7Unit 7: Data": [], "Data: Unit test": [], "Unit 8Unit 8: Geometry": [], "Geometry: Unit test": ["Start Course challenge"], "Unit 1: Add and subtract within 20": ["Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20"], "Unit 2: Place value": ["Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value"], "Unit 3: Add and subtract within 100": ["Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100"], "Unit 4: Add and subtract within 1,000": ["Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000"], "Unit 5: Money and time": ["Time: Money and time"], "Unit 6: Measurement": ["Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement"], "Unit 7: Data": ["Bar graphs: Data", "Line plots: Data"], "Unit 8: Geometry": ["Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Intro to multiplication": [], "Unit 21-digit multiplication": [], "Unit 3Addition, subtraction, and estimation": [], "Unit 4Intro to division": [], "Unit 5Understand fractions": [], "Unit 6Equivalent fractions and comparing fractions": [], "Unit 7More with multiplication and division": [], "Unit 8Arithmetic patterns and problem solving": [], "Unit 9Quadrilaterals": [], "Unit 10Area": [], "Unit 11Perimeter": [], "Unit 12Time": [], "Unit 13Measurement": [], "Unit 14Represent and interpret data": ["Start Course challenge"], "Unit 1Unit 1: Intro to multiplication": [], "Intro to multiplication: Unit test": [], "Unit 2Unit 2: 1-digit multiplication": [], "1-digit multiplication: Unit test": [], "Unit 3Unit 3: Addition, subtraction, and estimation": [], "Addition, subtraction, and estimation: Unit test": [], "Unit 4Unit 4: Intro to division": [], "Intro to division: Unit test": [], "Unit 5Unit 5: Understand fractions": [], "Understand fractions: Unit test": [], "Unit 6Unit 6: Equivalent fractions and comparing fractions": [], "Equivalent fractions and comparing fractions: Unit test": [], "Unit 7Unit 7: More with multiplication and division": [], "More with multiplication and division: Unit test": [], "Unit 8Unit 8: Arithmetic patterns and problem solving": [], "Arithmetic patterns and problem solving: Unit test": [], "Unit 9Unit 9: Quadrilaterals": [], "Quadrilaterals: Unit test": [], "Unit 10Unit 10: Area": [], "Area: Unit test": [], "Unit 11Unit 11: Perimeter": [], "Perimeter: Unit test": [], "Unit 12Unit 12: Time": [], "Time: Unit test": [], "Unit 13Unit 13: Measurement": [], "Measurement: Unit test": [], "Unit 14Unit 14: Represent and interpret data": [], "Represent and interpret data: Unit test": ["Start Course challenge"], "Unit 1: Intro to multiplication": ["Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication"], "Unit 2: 1-digit multiplication": ["Distributive property: 1-digit multiplication"], "Unit 3: Addition, subtraction, and estimation": ["Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation"], "Unit 4: Intro to division": ["Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division"], "Unit 5: Understand fractions": ["Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions"], "Unit 6: Equivalent fractions and comparing fractions": ["Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions"], "Unit 7: More with multiplication and division": ["Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division"], "Unit 8: Arithmetic patterns and problem solving": ["2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving"], "Unit 9: Quadrilaterals": ["Quadrilaterals : Quadrilaterals"], "Unit 10: Area": [], "Count unit squares to find area: Area": ["Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area"], "Unit 11: Perimeter": ["Perimeter: Perimeter", "Perimeter word problems: Perimeter"], "Unit 12: Time": ["Time on number line: Time", "Telling time: Time", "Elapsed time: Time"], "Unit 13: Measurement": ["Mass: Measurement", "Volume: Measurement"], "Unit 14: Represent and interpret data": ["Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Place value": [], "Unit 2Addition, subtraction, and estimation": [], "Unit 3Multiply by 1-digit numbers": [], "Unit 4Multiply by 2-digit numbers": [], "Unit 5Division": [], "Unit 6Factors, multiples and patterns": [], "Unit 7Equivalent fractions and comparing fractions": [], "Unit 8Add and subtract fractions": [], "Unit 9Multiply fractions": [], "Unit 10Understand decimals": [], "Unit 11Plane figures": [], "Unit 12Measuring angles": [], "Unit 13Area and perimeter": [], "Unit 14Units of measurement": ["Start Course challenge"], "Unit 1Unit 1: Place value": [], "Place value: Unit test": [], "Unit 2Unit 2: Addition, subtraction, and estimation": [], "Addition, subtraction, and estimation: Unit test": [], "Unit 3Unit 3: Multiply by 1-digit numbers": [], "Multiply by 1-digit numbers: Unit test": [], "Unit 4Unit 4: Multiply by 2-digit numbers": [], "Multiply by 2-digit numbers: Unit test": [], "Unit 5Unit 5: Division": [], "Division: Unit test": [], "Unit 6Unit 6: Factors, multiples and patterns": [], "Factors, multiples and patterns: Unit test": [], "Unit 7Unit 7: Equivalent fractions and comparing fractions": [], "Equivalent fractions and comparing fractions: Unit test": [], "Unit 8Unit 8: Add and subtract fractions": [], "Add and subtract fractions: Unit test": [], "Unit 9Unit 9: Multiply fractions": [], "Multiply fractions: Unit test": [], "Unit 10Unit 10: Understand decimals": [], "Understand decimals: Unit test": [], "Unit 11Unit 11: Plane figures": [], "Plane figures: Unit test": [], "Unit 12Unit 12: Measuring angles": [], "Measuring angles: Unit test": [], "Unit 13Unit 13: Area and perimeter": [], "Area and perimeter: Unit test": [], "Unit 14Unit 14: Units of measurement": [], "Units of measurement: Unit test": ["Start Course challenge"], "Unit 1: Place value": ["Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value"], "Unit 2: Addition, subtraction, and estimation": ["Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation"], "Unit 3: Multiply by 1-digit numbers": ["Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers"], "Unit 4: Multiply by 2-digit numbers": ["Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers"], "Unit 5: Division": ["Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division"], "Unit 6: Factors, multiples and patterns": ["Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns"], "Unit 7: Equivalent fractions and comparing fractions": ["Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions"], "Unit 8: Add and subtract fractions": ["Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions"], "Unit 9: Multiply fractions": ["Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions"], "Unit 10: Understand decimals": ["Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals"], "Unit 11: Plane figures": ["Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures"], "Unit 12: Measuring angles": ["Measuring angles: Measuring angles", "Decomposing angles: Measuring angles"], "Unit 13: Area and perimeter": ["Area and perimeter: Area and perimeter"], "Unit 14: Units of measurement": [], "Estimating volume: Units of measurement": [], "Estimating length: Units of measurement": [], "Time: Units of measurement": [], "Converting units of mass: Units of measurement": [], "Converting units of volume: Units of measurement": [], "Converting units of length: Units of measurement": [], "Converting units of time: Units of measurement": [], "Money word problems: Units of measurement": [], "Conversion word problems: Units of measurement": ["Start Course challenge"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Decimal place value": [], "Unit 2Add decimals": [], "Unit 3Subtract decimals": [], "Unit 4Add and subtract fractions": [], "Unit 5Multi-digit multiplication and division": [], "Unit 6Multiply fractions": [], "Unit 7Divide fractions": [], "Unit 8Multiply decimals": [], "Unit 9Divide decimals": [], "Unit 10Powers of ten": [], "Unit 11Volume": [], "Unit 12Coordinate plane": [], "Unit 13Algebraic thinking": [], "Unit 14Converting units of measure": [], "Unit 15Line plots": [], "Unit 16Properties of shapes": ["Start Course challenge"], "Unit 1Unit 1: Decimal place value": [], "Decimal place value: Unit test": [], "Unit 2Unit 2: Add decimals": [], "Add decimals: Unit test": [], "Unit 3Unit 3: Subtract decimals": [], "Subtract decimals: Unit test": [], "Unit 4Unit 4: Add and subtract fractions": [], "Add and subtract fractions: Unit test": [], "Unit 5Unit 5: Multi-digit multiplication and division": [], "Multi-digit multiplication and division: Unit test": [], "Unit 6Unit 6: Multiply fractions": [], "Multiply fractions: Unit test": [], "Unit 7Unit 7: Divide fractions": [], "Divide fractions: Unit test": [], "Unit 8Unit 8: Multiply decimals": [], "Multiply decimals: Unit test": [], "Unit 9Unit 9: Divide decimals": [], "Divide decimals: Unit test": [], "Unit 10Unit 10: Powers of ten": [], "Powers of ten: Unit test": [], "Unit 11Unit 11: Volume": [], "Volume: Unit test": [], "Unit 12Unit 12: Coordinate plane": [], "Coordinate plane: Unit test": [], "Unit 13Unit 13: Algebraic thinking": [], "Algebraic thinking: Unit test": [], "Unit 14Unit 14: Converting units of measure": [], "Converting units of measure: Unit test": [], "Unit 15Unit 15: Line plots": [], "Line plots: Unit test": [], "Unit 16Unit 16: Properties of shapes": [], "Properties of shapes: Unit test": ["Start Course challenge"], "Unit 1: Decimal place value": ["Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value"], "Unit 2: Add decimals": ["Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals"], "Unit 3: Subtract decimals": ["Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals"], "Unit 4: Add and subtract fractions": ["Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions"], "Unit 5: Multi-digit multiplication and division": ["Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division"], "Unit 6: Multiply fractions": ["Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions"], "Unit 7: Divide fractions": ["Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions"], "Dividing unit fractions by whole numbers: Divide fractions": [], "Dividing whole numbers by unit fractions: Divide fractions": ["Dividing fractions and whole numbers word problems: Divide fractions"], "Unit 8: Multiply decimals": ["Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals"], "Unit 9: Divide decimals": ["Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals"], "Unit 10: Powers of ten": ["Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten"], "Unit 11: Volume": [], "Volume with unit cubes: Volume": ["Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume"], "Unit 12: Coordinate plane": ["Intro to the coordinate plane : Coordinate plane"], "Unit 13: Algebraic thinking": ["Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking"], "Unit 14: Converting units of measure": [], "Converting units of time: Converting units of measure": [], "Converting metric units: Converting units of measure": [], "Converting metric units word problems: Converting units of measure": [], "Converting US Customary units: Converting units of measure": [], "Converting US Customary units word problems: Converting units of measure": [], "Unit 15: Line plots": ["Graph data on line plots: Line plots", "Interpret data on line plots: Line plots"], "Unit 16: Properties of shapes": ["Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Ratios": [], "Unit 2Arithmetic with rational numbers": [], "Unit 3Rates and percentages": [], "Unit 4Exponents and order of operations": [], "Unit 5Negative numbers": [], "Unit 6Variables & expressions": [], "Unit 7Equations & inequalities": [], "Unit 8Plane figures": [], "Unit 9Coordinate plane": [], "Unit 103D figures": [], "Unit 11Data and statistics": ["Start Course challenge"], "Unit 1Unit 1: Ratios": [], "Ratios: Unit test": [], "Unit 2Unit 2: Arithmetic with rational numbers": [], "Arithmetic with rational numbers: Unit test": [], "Unit 3Unit 3: Rates and percentages": [], "Rates and percentages: Unit test": [], "Unit 4Unit 4: Exponents and order of operations": [], "Exponents and order of operations: Unit test": [], "Unit 5Unit 5: Negative numbers": [], "Negative numbers: Unit test": [], "Unit 6Unit 6: Variables & expressions": [], "Variables & expressions: Unit test": [], "Unit 7Unit 7: Equations & inequalities": [], "Equations & inequalities: Unit test": [], "Unit 8Unit 8: Plane figures": [], "Plane figures: Unit test": [], "Unit 9Unit 9: Coordinate plane": [], "Coordinate plane: Unit test": [], "Unit 10Unit 10: 3D figures": [], "3D figures: Unit test": [], "Unit 11Unit 11: Data and statistics": [], "Data and statistics: Unit test": ["Start Course challenge"], "Unit 1: Ratios": ["Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios"], "Unit 2: Arithmetic with rational numbers": ["Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers"], "Unit 3: Rates and percentages": ["Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 4: Exponents and order of operations": ["Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations"], "Unit 5: Negative numbers": ["Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers"], "Unit 6: Variables & expressions": ["Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions"], "Unit 7: Equations & inequalities": ["Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities"], "Unit 8: Plane figures": ["Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures"], "Unit 9: Coordinate plane": ["Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane"], "Unit 10: 3D figures": ["Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures"], "Unit 11: Data and statistics": ["Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Proportional relationships": [], "Unit 2Rates and percentages": [], "Unit 3Integers: addition and subtraction": [], "Unit 4Rational numbers: addition and subtraction": [], "Unit 5Negative numbers: multiplication and division": [], "Unit 6Expressions, equations, & inequalities": [], "Unit 7Statistics and probability": [], "Unit 8Scale copies": [], "Unit 9Geometry": ["Start Course challenge"], "Unit 1Unit 1: Proportional relationships": [], "Proportional relationships: Unit test": [], "Unit 2Unit 2: Rates and percentages": [], "Rates and percentages: Unit test": [], "Unit 3Unit 3: Integers: addition and subtraction": [], "Integers: addition and subtraction: Unit test": [], "Unit 4Unit 4: Rational numbers: addition and subtraction": [], "Rational numbers: addition and subtraction: Unit test": [], "Unit 5Unit 5: Negative numbers: multiplication and division": [], "Negative numbers: multiplication and division: Unit test": [], "Unit 6Unit 6: Expressions, equations, & inequalities": [], "Expressions, equations, & inequalities: Unit test": [], "Unit 7Unit 7: Statistics and probability": [], "Statistics and probability: Unit test": [], "Unit 8Unit 8: Scale copies": [], "Scale copies: Unit test": [], "Unit 9Unit 9: Geometry": [], "Geometry: Unit test": ["Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles"], "Unit 1: Proportional relationships": ["Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships"], "Unit 2: Rates and percentages": ["Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 3: Integers: addition and subtraction": ["Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction"], "Unit 4: Rational numbers: addition and subtraction": ["Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction"], "Unit 5: Negative numbers: multiplication and division": ["Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division"], "Unit 6: Expressions, equations, & inequalities": ["The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities"], "Unit 7: Statistics and probability": ["Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability"], "Unit 8: Scale copies": ["Scale copies: Scale copies", "Scale drawings: Scale copies"], "Unit 9: Geometry": ["Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1Numbers and operations": [], "Unit 2Solving equations with one unknown": [], "Unit 3Linear equations and functions": [], "Unit 4Systems of equations": [], "Unit 5Geometry": [], "Unit 6Geometric transformations": [], "Unit 7Data and modeling": ["Start Course challenge"], "Unit 1Unit 1: Numbers and operations": [], "Numbers and operations: Unit test": [], "Unit 2Unit 2: Solving equations with one unknown": [], "Solving equations with one unknown: Unit test": [], "Unit 3Unit 3: Linear equations and functions": [], "Linear equations and functions: Unit test": [], "Unit 4Unit 4: Systems of equations": [], "Systems of equations: Unit test": [], "Unit 5Unit 5: Geometry": [], "Geometry: Unit test": [], "Unit 6Unit 6: Geometric transformations": [], "Geometric transformations: Unit test": [], "Unit 7Unit 7: Data and modeling": [], "Data and modeling: Unit test": ["Start Course challenge"], "Unit 1: Numbers and operations": ["Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations"], "Unit 2: Solving equations with one unknown": ["Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown"], "Unit 3: Linear equations and functions": ["Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions"], "Unit 4: Systems of equations": ["Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 5: Geometry": ["Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry"], "Unit 6: Geometric transformations": ["Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations"], "Unit 7: Data and modeling": ["Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for addition and subtraction": [], "Unit 2Get ready for multiplication and division": [], "Unit 3Get ready for fractions": [], "Unit 4Get ready for patterns and problem solving": [], "Unit 5Get ready for area and perimeter": [], "Unit 6Get ready for telling time": [], "Unit 7Get ready for data": ["Start Course challenge"], "Unit 1Unit 1: Get ready for addition and subtraction": [], "Get ready for addition and subtraction: Unit test": [], "Unit 2Unit 2: Get ready for multiplication and division": [], "Get ready for multiplication and division: Unit test": [], "Unit 3Unit 3: Get ready for fractions": [], "Get ready for fractions: Unit test": [], "Unit 4Unit 4: Get ready for patterns and problem solving": [], "Get ready for patterns and problem solving: Unit test": [], "Unit 5Unit 5: Get ready for area and perimeter": [], "Get ready for area and perimeter: Unit test": [], "Unit 6Unit 6: Get ready for telling time": [], "Get ready for telling time: Unit test": [], "Unit 7Unit 7: Get ready for data": [], "Get ready for data: Unit test": ["Start Course challenge"], "Unit 1: Get ready for addition and subtraction": ["Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction"], "Unit 2: Get ready for multiplication and division": ["Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division"], "Unit 3: Get ready for fractions": ["Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions"], "Unit 4: Get ready for patterns and problem solving": ["Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving"], "Unit 5: Get ready for area and perimeter": [], "Units of length: Get ready for area and perimeter": ["Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter"], "Unit 6: Get ready for telling time": ["Telling time: Get ready for telling time"], "Unit 7: Get ready for data": ["Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for place value": [], "Unit 2Get ready for addition, subtraction, and estimation": [], "Unit 3Get ready for multiplication": [], "Unit 4Get ready for division": [], "Unit 5Get ready for fractions": [], "Unit 6Get ready for plane figures": [], "Unit 7Get ready for area and perimeter": ["Start Course challenge"], "Unit 1Unit 1: Get ready for place value": [], "Get ready for place value: Unit test": [], "Unit 2Unit 2: Get ready for addition, subtraction, and estimation": [], "Get ready for addition, subtraction, and estimation: Unit test": [], "Unit 3Unit 3: Get ready for multiplication": [], "Get ready for multiplication: Unit test": [], "Unit 4Unit 4: Get ready for division": [], "Get ready for division: Unit test": [], "Unit 5Unit 5: Get ready for fractions": [], "Get ready for fractions: Unit test": [], "Unit 6Unit 6: Get ready for plane figures": [], "Get ready for plane figures : Unit test": [], "Unit 7Unit 7: Get ready for area and perimeter": [], "Get ready for area and perimeter: Unit test": ["Start Course challenge"], "Unit 1: Get ready for place value": ["Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value"], "Unit 2: Get ready for addition, subtraction, and estimation": ["Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation"], "Unit 3: Get ready for multiplication": ["Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication"], "Unit 4: Get ready for division": ["Division intro: Get ready for division", "Relate multiplication and division: Get ready for division"], "Unit 5: Get ready for fractions": ["Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions"], "Unit 6: Get ready for plane figures": ["Quadrilaterals: Get ready for plane figures"], "Unit 7: Get ready for area and perimeter": ["Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for decimal place value": [], "Unit 2Get ready for adding and subtracting decimals": [], "Unit 3Get ready for adding and subtracting fractions": [], "Unit 4Get ready for multiplication and division with whole numbers and decimals": [], "Unit 5Get ready for multiplying and dividing fractions": [], "Unit 6Get ready for powers of 10": [], "Unit 7Get ready for volume": [], "Unit 8Get ready for properties of shapes": ["Start Course challenge"], "Unit 1Unit 1: Get ready for decimal place value": [], "Get ready for decimal place value: Unit test": [], "Unit 2Unit 2: Get ready for adding and subtracting decimals": [], "Get ready for adding and subtracting decimals: Unit test": [], "Unit 3Unit 3: Get ready for adding and subtracting fractions": [], "Get ready for adding and subtracting fractions: Unit test": [], "Unit 4Unit 4: Get ready for multiplication and division with whole numbers and decimals": [], "Get ready for multiplication and division with whole numbers and decimals: Unit test": [], "Unit 5Unit 5: Get ready for multiplying and dividing fractions": [], "Get ready for multiplying and dividing fractions: Unit test": [], "Unit 6Unit 6: Get ready for powers of 10": [], "Get ready for powers of 10: Unit test": [], "Unit 7Unit 7: Get ready for volume": [], "Get ready for volume: Unit test": [], "Unit 8Unit 8: Get ready for properties of shapes": [], "Get ready for properties of shapes: Unit test": ["Start Course challenge"], "Unit 1: Get ready for decimal place value": ["Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value"], "Unit 2: Get ready for adding and subtracting decimals": ["Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals"], "Unit 3: Get ready for adding and subtracting fractions": ["Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions"], "Unit 4: Get ready for multiplication and division with whole numbers and decimals": ["Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals"], "Unit 5: Get ready for multiplying and dividing fractions": ["Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions"], "Unit 6: Get ready for powers of 10": ["How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10"], "Unit 7: Get ready for volume": ["Introduction to area: Get ready for volume"], "Unit 8: Get ready for properties of shapes": ["Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for ratios, rates, and percentages": [], "Unit 2Get ready for arithmetic operations": [], "Unit 3Get ready for negative numbers": [], "Unit 4Get ready for equations, expressions, and inequalities": [], "Unit 5Get ready for geometry": ["Start Course challenge"], "Unit 1Unit 1: Get ready for ratios, rates, and percentages": [], "Get ready for ratios, rates, and percentages: Unit test": [], "Unit 2Unit 2: Get ready for arithmetic operations": [], "Get ready for arithmetic operations: Unit test": [], "Unit 3Unit 3: Get ready for negative numbers": [], "Get ready for negative numbers: Unit test": [], "Unit 4Unit 4: Get ready for equations, expressions, and inequalities": [], "Get ready for equations, expressions, and inequalities: Unit test": [], "Unit 5Unit 5: Get ready for geometry": [], "Get ready for geometry: Unit test": ["Start Course challenge"], "Unit 1: Get ready for ratios, rates, and percentages": ["Multiplication and division word problems: Get ready for ratios, rates, and percentages"], "Convert units of measure: Get ready for ratios, rates, and percentages": ["Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages"], "Unit 2: Get ready for arithmetic operations": [], "Divide whole numbers by unit fractions: Get ready for arithmetic operations": [], "Divide unit fractions by whole numbers: Get ready for arithmetic operations": ["Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations"], "Unit 3: Get ready for negative numbers": ["Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers"], "Unit 4: Get ready for equations, expressions, and inequalities": ["Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities"], "Unit 5: Get ready for geometry": ["Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for negative number operations": [], "Unit 2Get ready for fractions, decimals, & percentages": [], "Unit 3Get ready for rates & proportional relationships": [], "Unit 4Get ready for expressions, equations, & inequalities": [], "Unit 5Get ready for geometry": [], "Unit 6Get ready for statistics & probability": ["Start Course challenge"], "Unit 1Unit 1: Get ready for negative number operations": [], "Get ready for negative number operations: Unit test": [], "Unit 2Unit 2: Get ready for fractions, decimals, & percentages": [], "Get ready for fractions, decimals, & percentages: Unit test": [], "Unit 3Unit 3: Get ready for rates & proportional relationships": [], "Get ready for rates & proportional relationships: Unit test": [], "Unit 4Unit 4: Get ready for expressions, equations, & inequalities": [], "Get ready for expressions, equations, & inequalities: Unit test": [], "Unit 5Unit 5: Get ready for geometry": [], "Get ready for geometry: Unit test": [], "Unit 6Unit 6: Get ready for statistics & probability": [], "Get ready for statistics & probability: Unit test": ["Start Course challenge"], "Unit 1: Get ready for negative number operations": ["Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations"], "Unit 2: Get ready for fractions, decimals, & percentages": ["Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages"], "Unit 3: Get ready for rates & proportional relationships": ["Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships"], "Unit 4: Get ready for expressions, equations, & inequalities": ["Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities"], "Unit 5: Get ready for geometry": ["Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry"], "Unit 6: Get ready for statistics & probability": ["Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for numbers and operations": [], "Unit 2Get ready for solving equations and systems of equations": [], "Unit 3Get ready for linear equations and functions": [], "Unit 4Get ready for geometry": ["Start Course challenge"], "Unit 1Unit 1: Get ready for numbers and operations": [], "Get ready for numbers and operations: Unit test": [], "Unit 2Unit 2: Get ready for solving equations and systems of equations": [], "Get ready for solving equations and systems of equations: Unit test": [], "Unit 3Unit 3: Get ready for linear equations and functions": [], "Get ready for linear equations and functions: Unit test": [], "Unit 4Unit 4: Get ready for geometry": [], "Get ready for geometry: Unit test": ["Start Course challenge"], "Unit 1: Get ready for numbers and operations": ["Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations"], "Unit 2: Get ready for solving equations and systems of equations": ["Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations"], "Unit 3: Get ready for linear equations and functions": ["Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions"], "Unit 4: Get ready for geometry": ["Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for equations & inequalities": [], "Unit 2Get ready for working with units": [], "Unit 3Get ready for linear relationships": [], "Unit 4Get ready for functions & sequences": [], "Unit 5Get ready for exponents, radicals, & irrational numbers": [], "Unit 6Get ready for quadratics": ["Start Course challenge"], "Unit 1Unit 1: Get ready for equations & inequalities": [], "Get ready for equations & inequalities: Unit test": [], "Unit 2Unit 2: Get ready for working with units": [], "Get ready for working with units: Unit test": [], "Unit 3Unit 3: Get ready for linear relationships": [], "Get ready for linear relationships: Unit test": [], "Unit 4Unit 4: Get ready for functions & sequences": [], "Get ready for functions & sequences: Unit test": [], "Unit 5Unit 5: Get ready for exponents, radicals, & irrational numbers": [], "Get ready for exponents, radicals, & irrational numbers: Unit test": [], "Unit 6Unit 6: Get ready for quadratics": [], "Get ready for quadratics: Unit test": ["Start Course challenge"], "Unit 1: Get ready for equations & inequalities": ["Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities"], "Unit 2: Get ready for working with units": [], "Intro to ratios: Get ready for working with units": [], "Equivalent ratios: Get ready for working with units": [], "Ratio application: Get ready for working with units": [], "Intro to rates: Get ready for working with units": [], "Rate problems: Get ready for working with units": [], "Unit 3: Get ready for linear relationships": ["Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships"], "Unit 4: Get ready for functions & sequences": ["Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences"], "Unit 5: Get ready for exponents, radicals, & irrational numbers": ["Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers"], "Unit 6: Get ready for quadratics": ["Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for congruence, similarity, and triangle trigonometry": [], "Unit 2Get ready for analytic geometry": [], "Unit 3Get ready for conic sections": [], "Unit 4Get ready for circles and solid geometry": ["Start Course challenge"], "Unit 1Unit 1: Get ready for congruence, similarity, and triangle trigonometry": [], "Get ready for congruence, similarity, and triangle trigonometry: Unit test": [], "Unit 2Unit 2: Get ready for analytic geometry": [], "Get ready for analytic geometry: Unit test": [], "Unit 3Unit 3: Get ready for conic sections": [], "Get ready for conic sections: Unit test": [], "Unit 4Unit 4: Get ready for circles and solid geometry": [], "Get ready for circles and solid geometry: Unit test": ["Start Course challenge"], "Unit 1: Get ready for congruence, similarity, and triangle trigonometry": ["Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry"], "Unit 2: Get ready for analytic geometry": ["Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry"], "Unit 3: Get ready for conic sections": ["Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections"], "Unit 4: Get ready for circles and solid geometry": ["Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for polynomial operations and complex numbers": [], "Unit 2Get ready for equations": [], "Unit 3Get ready for transformations of functions and modeling with functions": [], "Unit 4Get ready for exponential and logarithmic relationships": [], "Unit 5Get ready for trigonometry": [], "Unit 6Get ready for rational functions": ["Start Course challenge"], "Unit 1Unit 1: Get ready for polynomial operations and complex numbers": [], "Get ready for polynomial operations and complex numbers: Unit test": [], "Unit 2Unit 2: Get ready for equations": [], "Get ready for equations: Unit test": [], "Unit 3Unit 3: Get ready for transformations of functions and modeling with functions": [], "Get ready for transformations of functions and modeling with functions: Unit test": [], "Unit 4Unit 4: Get ready for exponential and logarithmic relationships": [], "Get ready for exponential and logarithmic relationships: Unit test": [], "Unit 5Unit 5: Get ready for trigonometry": [], "Get ready for trigonometry: Unit test": [], "Unit 6Unit 6: Get ready for rational functions": [], "Get ready for rational functions: Unit test": ["Start Course challenge"], "Unit 1: Get ready for polynomial operations and complex numbers": ["Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers"], "Unit 2: Get ready for equations": ["Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations"], "Unit 3: Get ready for transformations of functions and modeling with functions": ["Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions"], "Unit 4: Get ready for exponential and logarithmic relationships": ["Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships"], "Unit 5: Get ready for trigonometry": ["Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry"], "Unit 6: Get ready for rational functions": ["Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Get ready for Precalculus", "course_url": "/math/get-ready-for-precalculus", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for complex numbers": [], "Unit 2Get ready for polynomials": [], "Unit 3Get ready for composite and inverse functions": [], "Unit 4Get ready for trigonometry": [], "Unit 5Get ready for vectors and matrices": [], "Unit 6Get ready for series": [], "Unit 7Get ready for conic sections": [], "Unit 8Get ready for probability and combinatorics": ["Start Course challenge"], "Unit 1Unit 1: Get ready for complex numbers": [], "Get ready for complex numbers: Unit test": [], "Unit 2Unit 2: Get ready for polynomials": [], "Get ready for polynomials: Unit test": [], "Unit 3Unit 3: Get ready for composite and inverse functions": [], "Get ready for composite and inverse functions: Unit test": [], "Unit 4Unit 4: Get ready for trigonometry": [], "Get ready for trigonometry: Unit test": [], "Unit 5Unit 5: Get ready for vectors and matrices": [], "Get ready for vectors and matrices: Unit test": [], "Unit 6Unit 6: Get ready for series": [], "Get ready for series: Unit test": [], "Unit 7Unit 7: Get ready for conic sections": [], "Get ready for conic sections: Unit test": [], "Unit 8Unit 8: Get ready for probability and combinatorics": [], "Get ready for probability and combinatorics: Unit test": ["Start Course challenge"], "Unit 1: Get ready for complex numbers": [], "The imaginary unit i: Get ready for complex numbers": ["Complex numbers introduction: Get ready for complex numbers", "The complex plane: Get ready for complex numbers", "Adding and subtracting complex numbers: Get ready for complex numbers", "Quadratic equations with complex solutions: Get ready for complex numbers"], "Unit 2: Get ready for polynomials": ["Adding and subtracting polynomials: Get ready for polynomials", "Multiplying binomials by polynomials: Get ready for polynomials", "Special products of polynomials: Get ready for polynomials", "Factoring higher degree polynomials: Get ready for polynomials", "Factoring using structure: Get ready for polynomials", "Zeros of polynomials: Get ready for polynomials", "Dividing polynomials by x: Get ready for polynomials", "Dividing quadratics by linear factors: Get ready for polynomials", "Dividing polynomials by linear factors: Get ready for polynomials"], "Unit 3: Get ready for composite and inverse functions": ["Shifting functions: Get ready for composite and inverse functions", "Reflecting functions: Get ready for composite and inverse functions", "Scaling functions: Get ready for composite and inverse functions", "Identifying function transformations: Get ready for composite and inverse functions", "Intro to domain and range of a function: Get ready for composite and inverse functions", "Intro to inverse functions: Get ready for composite and inverse functions"], "Unit 4: Get ready for trigonometry": [], "Unit circle introduction: Get ready for trigonometry": ["Radians: Get ready for trigonometry", "The Pythagorean identity: Get ready for trigonometry", "Trigonometric values of special angles: Get ready for trigonometry", "Graphing sinusoidal functions: Get ready for trigonometry", "Sinusoidal models: Get ready for trigonometry"], "Unit 5: Get ready for vectors and matrices": ["Equivalent systems of equations and the elimination method: Get ready for vectors and matrices", "Dilations: Get ready for vectors and matrices", "Solving triangles using the trigonometric ratios: Get ready for vectors and matrices"], "Unit circle introduction: Get ready for vectors and matrices": ["Distance formula: Get ready for vectors and matrices"], "Unit 6: Get ready for series": ["Intro to sequences: Get ready for series", "Constructing arithmetic sequences: Get ready for series", "Constructing geometric sequences: Get ready for series", "Modeling with sequences: Get ready for series", "General sequences: Get ready for series", "Geometric series: Get ready for series"], "Unit 7: Get ready for conic sections": ["Graphs of circles intro: Get ready for conic sections", "Standard equation of a circle: Get ready for conic sections", "Expanded equation of a circle: Get ready for conic sections", "Focus and directrix of a parabola: Get ready for conic sections"], "Unit 8: Get ready for probability and combinatorics": ["Basic theoretical probability: Get ready for probability and combinatorics", "Probability using sample spaces: Get ready for probability and combinatorics", "Basic set operations: Get ready for probability and combinatorics", "Experimental probability: Get ready for probability and combinatorics", "Randomness, probability, and simulation: Get ready for probability and combinatorics", "Addition rule: Get ready for probability and combinatorics", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Calculus", "course_url": "/math/get-ready-for-ap-calc", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for limits and continuity": [], "Unit 2Get ready for differentiation: definition and basic derivative rules": [], "Unit 3Get ready for differentiation: composite, implicit, and inverse functions": [], "Unit 4Get ready for contextual applications of differentiation": [], "Unit 5Get ready for applying derivatives to analyze functions": [], "Unit 6Get ready for integration and accumulation of change": [], "Unit 7Get ready for applications of integration": [], "Unit 8Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)": [], "Unit 9Get ready for infinite sequences and series (BC only)": ["Start Course challenge"], "Unit 1Unit 1: Get ready for limits and continuity": [], "Get ready for limits and continuity: Unit test": [], "Unit 2Unit 2: Get ready for differentiation: definition and basic derivative rules": [], "Get ready for differentiation: definition and basic derivative rules: Unit test": [], "Unit 3Unit 3: Get ready for differentiation: composite, implicit, and inverse functions": [], "Get ready for differentiation: composite, implicit, and inverse functions: Unit test": [], "Unit 4Unit 4: Get ready for contextual applications of differentiation": [], "Get ready for contextual applications of differentiation: Unit test": [], "Unit 5Unit 5: Get ready for applying derivatives to analyze functions": [], "Get ready for applying derivatives to analyze functions : Unit test": [], "Unit 6Unit 6: Get ready for integration and accumulation of change": [], "Get ready for integration and accumulation of change: Unit test": [], "Unit 7Unit 7: Get ready for applications of integration": [], "Get ready for applications of integration: Unit test": [], "Unit 8Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)": [], "Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only): Unit test": [], "Unit 9Unit 9: Get ready for infinite sequences and series (BC only)": [], "Get ready for infinite sequences and series (BC only): Unit test": ["Start Course challenge"], "Unit 1: Get ready for limits and continuity": ["Evaluating functions: Get ready for limits and continuity", "Inputs and outputs of a function: Get ready for limits and continuity", "Composing functions: Get ready for limits and continuity", "Piecewise functions: Get ready for limits and continuity", "Introduction to factoring: Get ready for limits and continuity", "Factoring quadratics intro: Get ready for limits and continuity", "Factoring quadratics by grouping: Get ready for limits and continuity", "Factoring quadratics with difference of squares: Get ready for limits and continuity", "Factoring quadratics with perfect squares: Get ready for limits and continuity", "Factoring higher degree polynomials: Get ready for limits and continuity", "Introduction to the trigonometric ratios: Get ready for limits and continuity"], "Unit circle introduction: Get ready for limits and continuity": ["Radians: Get ready for limits and continuity", "The Pythagorean identity: Get ready for limits and continuity", "Special trigonometric values in the first quadrant: Get ready for limits and continuity"], "Trigonometric identities on the unit circle: Get ready for limits and continuity": ["Angle addition identities: Get ready for limits and continuity", "Reducing rational expressions to lowest terms: Get ready for limits and continuity", "End behavior of rational functions: Get ready for limits and continuity", "Discontinuities of rational functions: Get ready for limits and continuity", "Multiplying and dividing rational expressions: Get ready for limits and continuity"], "Unit 2: Get ready for differentiation: definition and basic derivative rules": ["Intro to slope-intercept form: Get ready for differentiation: definition and basic derivative rules", "Writing slope-intercept equations: Get ready for differentiation: definition and basic derivative rules", "Point-slope form: Get ready for differentiation: definition and basic derivative rules", "Average rate of change: Get ready for differentiation: definition and basic derivative rules", "Rational exponents: Get ready for differentiation: definition and basic derivative rules", "Properties of exponents: Get ready for differentiation: definition and basic derivative rules", "Introduction to logarithms: Get ready for differentiation: definition and basic derivative rules"], "Unit 3: Get ready for differentiation: composite, implicit, and inverse functions": ["Composing functions: Get ready for differentiation: composite, implicit, and inverse functions", "Linear equations with unknown coefficients: Get ready for differentiation: composite, implicit, and inverse functions", "Intro to inverse functions: Get ready for differentiation: composite, implicit, and inverse functions", "Invertible functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse trigonometric functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse functions in graphs and tables: Get ready for differentiation: composite, implicit, and inverse functions", "Verifying inverse functions by composition: Get ready for differentiation: composite, implicit, and inverse functions"], "Unit 4: Get ready for contextual applications of differentiation": [], "Word problems with multiple units: Get ready for contextual applications of differentiation": ["Linear equations word problems: Get ready for contextual applications of differentiation", "Interpreting function notation: Get ready for contextual applications of differentiation", "Average rate of change word problems: Get ready for contextual applications of differentiation", "Modeling with composite functions: Get ready for contextual applications of differentiation", "Modeling with right triangles: Get ready for contextual applications of differentiation", "Volume and surface area: Get ready for contextual applications of differentiation"], "Unit 5: Get ready for applying derivatives to analyze functions": ["Maximum and minimum points: Get ready for applying derivatives to analyze functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for applying derivatives to analyze functions", "Interpreting features of graphs: Get ready for applying derivatives to analyze functions", "Distance formula: Get ready for applying derivatives to analyze functions", "Square-root equations: Get ready for applying derivatives to analyze functions", "Zeros of polynomials: Get ready for applying derivatives to analyze functions", "Positive and negative intervals of polynomials: Get ready for applying derivatives to analyze functions"], "Unit 6: Get ready for integration and accumulation of change": ["Completing the square: Get ready for integration and accumulation of change", "Dividing quadratics by linear factors: Get ready for integration and accumulation of change", "Dividing polynomials by linear factors: Get ready for integration and accumulation of change", "Partial fraction expansion: Get ready for integration and accumulation of change", "Summation notation: Get ready for integration and accumulation of change"], "Unit 7: Get ready for applications of integration": ["Rational equations: Get ready for applications of integration", "Square-root equations: Get ready for applications of integration", "Extraneous solutions: Get ready for applications of integration", "Sinusoidal equations: Get ready for applications of integration", "Manipulating formulas: Get ready for applications of integration", "Solving equations by graphing: Get ready for applications of integration"], "Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)": ["Sectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vectors introduction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Magnitude of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Scalar multiplication: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Direction of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components from magnitude & direction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)"], "Unit 9: Get ready for infinite sequences and series (BC only)": ["Arithmetic sequences: Get ready for infinite sequences and series (BC only)", "Geometric sequences: Get ready for infinite sequences and series (BC only)", "Summation notation: Get ready for infinite sequences and series (BC only)", "Arithmetic series: Get ready for infinite sequences and series (BC only)", "Geometric series: Get ready for infinite sequences and series (BC only)", "End behavior of rational functions: Get ready for infinite sequences and series (BC only)", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Statistics", "course_url": "/math/get-ready-for-ap-statistics", "page_contents": {"syllabus": {"topics": {"Unit 1Get ready for exploring categorical data": [], "Unit 2Get ready for exploring one-variable quantitative data": [], "Unit 3Get ready for exploring two-variable quantitative data": [], "Unit 4Get ready for probability": [], "Unit 5Get ready for random variables and probability distributions": ["Start Course challenge"], "Unit 1Unit 1: Get ready for exploring categorical data": [], "Get ready for exploring categorical data: Unit test": [], "Unit 2Unit 2: Get ready for exploring one-variable quantitative data": [], "Get ready for exploring one-variable quantitative data: Unit test": [], "Unit 3Unit 3: Get ready for exploring two-variable quantitative data": [], "Get ready for exploring two-variable quantitative data: Unit test": [], "Unit 4Unit 4: Get ready for probability": [], "Get ready for probability: Unit test": [], "Unit 5Unit 5: Get ready for random variables and probability distributions": [], "Get ready for random variables and probability distributions: Unit test": ["Start Course challenge"], "Unit 1: Get ready for exploring categorical data": ["Frequency tables: Get ready for exploring categorical data", "Bar graphs: Get ready for exploring categorical data", "Fractions, decimals, and percentages: Get ready for exploring categorical data"], "Unit 2: Get ready for exploring one-variable quantitative data": ["Frequency tables and dot plots: Get ready for exploring one-variable quantitative data", "Box and whisker plots: Get ready for exploring one-variable quantitative data", "Comparing data displays: Get ready for exploring one-variable quantitative data", "Mean, median, and mode: Get ready for exploring one-variable quantitative data", "Mean absolute deviation: Get ready for exploring one-variable quantitative data", "Linear equations with variables on both sides: Get ready for exploring one-variable quantitative data", "Linear equations with unknown coefficients: Get ready for exploring one-variable quantitative data"], "Unit 3: Get ready for exploring two-variable quantitative data": ["Introduction to scatter plots: Get ready for exploring two-variable quantitative data", "Estimating with trend lines: Get ready for exploring two-variable quantitative data", "Logarithms: Get ready for exploring two-variable quantitative data"], "Unit 4: Get ready for probability": ["Fractions, decimals, and percentages: Get ready for probability", "Comparing decimals and fractions: Get ready for probability", "Arithmetic with fractions: Get ready for probability", "Probability introduction: Get ready for probability", "Experimental probability: Get ready for probability"], "Unit 5: Get ready for random variables and probability distributions": ["Predictions with probability: Get ready for random variables and probability distributions", "The counting principle: Get ready for random variables and probability distributions", "Probability distributions introduction: Get ready for random variables and probability distributions", "Start Course challenge"]}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Unit 8Geometry": ["Start Course challenge"], "Geometry: Unit test": ["Start Course challenge"], "Unit 1: Counting": ["Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting"], "Unit 2: Addition and subtraction intro": ["What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro"], "Unit 3: Place value (tens and hundreds)": ["Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)"], "Unit 4: Addition and subtraction within 20": ["Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20"], "Unit 5: Addition and subtraction within 100": ["Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100"], "Unit 6: Addition and subtraction within 1000": ["Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000"], "Unit 7: Measurement and data": ["Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data"], "Unit 8: Geometry": ["Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 8Geometry": ["Start Course challenge"], "Geometry: Unit test": ["Start Course challenge"], "Unit 1: Add and subtract within 20": ["Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20"], "Unit 2: Place value": ["Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value"], "Unit 3: Add and subtract within 100": ["Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100"], "Unit 4: Add and subtract within 1,000": ["Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000"], "Unit 5: Money and time": ["Time: Money and time"], "Unit 6: Measurement": ["Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement"], "Unit 7: Data": ["Bar graphs: Data", "Line plots: Data"], "Unit 8: Geometry": ["Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 14Represent and interpret data": ["Start Course challenge"], "Represent and interpret data: Unit test": ["Start Course challenge"], "Unit 1: Intro to multiplication": ["Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication"], "Unit 2: 1-digit multiplication": ["Distributive property: 1-digit multiplication"], "Unit 3: Addition, subtraction, and estimation": ["Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation"], "Unit 4: Intro to division": ["Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division"], "Unit 5: Understand fractions": ["Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions"], "Unit 6: Equivalent fractions and comparing fractions": ["Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions"], "Unit 7: More with multiplication and division": ["Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division"], "Unit 8: Arithmetic patterns and problem solving": ["2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving"], "Unit 9: Quadrilaterals": ["Quadrilaterals : Quadrilaterals"], "Count unit squares to find area: Area": ["Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area"], "Unit 11: Perimeter": ["Perimeter: Perimeter", "Perimeter word problems: Perimeter"], "Unit 12: Time": ["Time on number line: Time", "Telling time: Time", "Elapsed time: Time"], "Unit 13: Measurement": ["Mass: Measurement", "Volume: Measurement"], "Unit 14: Represent and interpret data": ["Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 14Units of measurement": ["Start Course challenge"], "Units of measurement: Unit test": ["Start Course challenge"], "Unit 1: Place value": ["Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value"], "Unit 2: Addition, subtraction, and estimation": ["Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation"], "Unit 3: Multiply by 1-digit numbers": ["Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers"], "Unit 4: Multiply by 2-digit numbers": ["Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers"], "Unit 5: Division": ["Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division"], "Unit 6: Factors, multiples and patterns": ["Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns"], "Unit 7: Equivalent fractions and comparing fractions": ["Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions"], "Unit 8: Add and subtract fractions": ["Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions"], "Unit 9: Multiply fractions": ["Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions"], "Unit 10: Understand decimals": ["Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals"], "Unit 11: Plane figures": ["Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures"], "Unit 12: Measuring angles": ["Measuring angles: Measuring angles", "Decomposing angles: Measuring angles"], "Unit 13: Area and perimeter": ["Area and perimeter: Area and perimeter"], "Conversion word problems: Units of measurement": ["Start Course challenge"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 16Properties of shapes": ["Start Course challenge"], "Properties of shapes: Unit test": ["Start Course challenge"], "Unit 1: Decimal place value": ["Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value"], "Unit 2: Add decimals": ["Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals"], "Unit 3: Subtract decimals": ["Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals"], "Unit 4: Add and subtract fractions": ["Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions"], "Unit 5: Multi-digit multiplication and division": ["Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division"], "Unit 6: Multiply fractions": ["Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions"], "Unit 7: Divide fractions": ["Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions"], "Dividing whole numbers by unit fractions: Divide fractions": ["Dividing fractions and whole numbers word problems: Divide fractions"], "Unit 8: Multiply decimals": ["Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals"], "Unit 9: Divide decimals": ["Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals"], "Unit 10: Powers of ten": ["Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten"], "Volume with unit cubes: Volume": ["Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume"], "Unit 12: Coordinate plane": ["Intro to the coordinate plane : Coordinate plane"], "Unit 13: Algebraic thinking": ["Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking"], "Unit 15: Line plots": ["Graph data on line plots: Line plots", "Interpret data on line plots: Line plots"], "Unit 16: Properties of shapes": ["Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 11Data and statistics": ["Start Course challenge"], "Data and statistics: Unit test": ["Start Course challenge"], "Unit 1: Ratios": ["Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios"], "Unit 2: Arithmetic with rational numbers": ["Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers"], "Unit 3: Rates and percentages": ["Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 4: Exponents and order of operations": ["Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations"], "Unit 5: Negative numbers": ["Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers"], "Unit 6: Variables & expressions": ["Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions"], "Unit 7: Equations & inequalities": ["Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities"], "Unit 8: Plane figures": ["Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures"], "Unit 9: Coordinate plane": ["Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane"], "Unit 10: 3D figures": ["Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures"], "Unit 11: Data and statistics": ["Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 9Geometry": ["Start Course challenge"], "Geometry: Unit test": ["Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles"], "Unit 1: Proportional relationships": ["Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships"], "Unit 2: Rates and percentages": ["Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 3: Integers: addition and subtraction": ["Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction"], "Unit 4: Rational numbers: addition and subtraction": ["Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction"], "Unit 5: Negative numbers: multiplication and division": ["Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division"], "Unit 6: Expressions, equations, & inequalities": ["The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities"], "Unit 7: Statistics and probability": ["Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability"], "Unit 8: Scale copies": ["Scale copies: Scale copies", "Scale drawings: Scale copies"], "Unit 9: Geometry": ["Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 7Data and modeling": ["Start Course challenge"], "Data and modeling: Unit test": ["Start Course challenge"], "Unit 1: Numbers and operations": ["Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations"], "Unit 2: Solving equations with one unknown": ["Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown"], "Unit 3: Linear equations and functions": ["Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions"], "Unit 4: Systems of equations": ["Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 5: Geometry": ["Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry"], "Unit 6: Geometric transformations": ["Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations"], "Unit 7: Data and modeling": ["Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Unit 7Get ready for data": ["Start Course challenge"], "Get ready for data: Unit test": ["Start Course challenge"], "Unit 1: Get ready for addition and subtraction": ["Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction"], "Unit 2: Get ready for multiplication and division": ["Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division"], "Unit 3: Get ready for fractions": ["Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions"], "Unit 4: Get ready for patterns and problem solving": ["Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving"], "Units of length: Get ready for area and perimeter": ["Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter"], "Unit 6: Get ready for telling time": ["Telling time: Get ready for telling time"], "Unit 7: Get ready for data": ["Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Unit 7Get ready for area and perimeter": ["Start Course challenge"], "Get ready for area and perimeter: Unit test": ["Start Course challenge"], "Unit 1: Get ready for place value": ["Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value"], "Unit 2: Get ready for addition, subtraction, and estimation": ["Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation"], "Unit 3: Get ready for multiplication": ["Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication"], "Unit 4: Get ready for division": ["Division intro: Get ready for division", "Relate multiplication and division: Get ready for division"], "Unit 5: Get ready for fractions": ["Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions"], "Unit 6: Get ready for plane figures": ["Quadrilaterals: Get ready for plane figures"], "Unit 7: Get ready for area and perimeter": ["Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Unit 8Get ready for properties of shapes": ["Start Course challenge"], "Get ready for properties of shapes: Unit test": ["Start Course challenge"], "Unit 1: Get ready for decimal place value": ["Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value"], "Unit 2: Get ready for adding and subtracting decimals": ["Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals"], "Unit 3: Get ready for adding and subtracting fractions": ["Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions"], "Unit 4: Get ready for multiplication and division with whole numbers and decimals": ["Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals"], "Unit 5: Get ready for multiplying and dividing fractions": ["Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions"], "Unit 6: Get ready for powers of 10": ["How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10"], "Unit 7: Get ready for volume": ["Introduction to area: Get ready for volume"], "Unit 8: Get ready for properties of shapes": ["Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Unit 5Get ready for geometry": ["Start Course challenge"], "Get ready for geometry: Unit test": ["Start Course challenge"], "Unit 1: Get ready for ratios, rates, and percentages": ["Multiplication and division word problems: Get ready for ratios, rates, and percentages"], "Convert units of measure: Get ready for ratios, rates, and percentages": ["Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages"], "Divide unit fractions by whole numbers: Get ready for arithmetic operations": ["Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations"], "Unit 3: Get ready for negative numbers": ["Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers"], "Unit 4: Get ready for equations, expressions, and inequalities": ["Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities"], "Unit 5: Get ready for geometry": ["Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Unit 6Get ready for statistics & probability": ["Start Course challenge"], "Get ready for statistics & probability: Unit test": ["Start Course challenge"], "Unit 1: Get ready for negative number operations": ["Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations"], "Unit 2: Get ready for fractions, decimals, & percentages": ["Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages"], "Unit 3: Get ready for rates & proportional relationships": ["Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships"], "Unit 4: Get ready for expressions, equations, & inequalities": ["Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities"], "Unit 5: Get ready for geometry": ["Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry"], "Unit 6: Get ready for statistics & probability": ["Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Unit 4Get ready for geometry": ["Start Course challenge"], "Get ready for geometry: Unit test": ["Start Course challenge"], "Unit 1: Get ready for numbers and operations": ["Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations"], "Unit 2: Get ready for solving equations and systems of equations": ["Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations"], "Unit 3: Get ready for linear equations and functions": ["Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions"], "Unit 4: Get ready for geometry": ["Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Unit 6Get ready for quadratics": ["Start Course challenge"], "Get ready for quadratics: Unit test": ["Start Course challenge"], "Unit 1: Get ready for equations & inequalities": ["Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities"], "Unit 3: Get ready for linear relationships": ["Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships"], "Unit 4: Get ready for functions & sequences": ["Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences"], "Unit 5: Get ready for exponents, radicals, & irrational numbers": ["Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers"], "Unit 6: Get ready for quadratics": ["Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Unit 4Get ready for circles and solid geometry": ["Start Course challenge"], "Get ready for circles and solid geometry: Unit test": ["Start Course challenge"], "Unit 1: Get ready for congruence, similarity, and triangle trigonometry": ["Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry"], "Unit 2: Get ready for analytic geometry": ["Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry"], "Unit 3: Get ready for conic sections": ["Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections"], "Unit 4: Get ready for circles and solid geometry": ["Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Unit 6Get ready for rational functions": ["Start Course challenge"], "Get ready for rational functions: Unit test": ["Start Course challenge"], "Unit 1: Get ready for polynomial operations and complex numbers": ["Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers"], "Unit 2: Get ready for equations": ["Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations"], "Unit 3: Get ready for transformations of functions and modeling with functions": ["Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions"], "Unit 4: Get ready for exponential and logarithmic relationships": ["Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships"], "Unit 5: Get ready for trigonometry": ["Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry"], "Unit 6: Get ready for rational functions": ["Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Get ready for Precalculus", "course_url": "/math/get-ready-for-precalculus", "page_contents": {"syllabus": {"topics": {"Unit 8Get ready for probability and combinatorics": ["Start Course challenge"], "Get ready for probability and combinatorics: Unit test": ["Start Course challenge"], "The imaginary unit i: Get ready for complex numbers": ["Complex numbers introduction: Get ready for complex numbers", "The complex plane: Get ready for complex numbers", "Adding and subtracting complex numbers: Get ready for complex numbers", "Quadratic equations with complex solutions: Get ready for complex numbers"], "Unit 2: Get ready for polynomials": ["Adding and subtracting polynomials: Get ready for polynomials", "Multiplying binomials by polynomials: Get ready for polynomials", "Special products of polynomials: Get ready for polynomials", "Factoring higher degree polynomials: Get ready for polynomials", "Factoring using structure: Get ready for polynomials", "Zeros of polynomials: Get ready for polynomials", "Dividing polynomials by x: Get ready for polynomials", "Dividing quadratics by linear factors: Get ready for polynomials", "Dividing polynomials by linear factors: Get ready for polynomials"], "Unit 3: Get ready for composite and inverse functions": ["Shifting functions: Get ready for composite and inverse functions", "Reflecting functions: Get ready for composite and inverse functions", "Scaling functions: Get ready for composite and inverse functions", "Identifying function transformations: Get ready for composite and inverse functions", "Intro to domain and range of a function: Get ready for composite and inverse functions", "Intro to inverse functions: Get ready for composite and inverse functions"], "Unit circle introduction: Get ready for trigonometry": ["Radians: Get ready for trigonometry", "The Pythagorean identity: Get ready for trigonometry", "Trigonometric values of special angles: Get ready for trigonometry", "Graphing sinusoidal functions: Get ready for trigonometry", "Sinusoidal models: Get ready for trigonometry"], "Unit 5: Get ready for vectors and matrices": ["Equivalent systems of equations and the elimination method: Get ready for vectors and matrices", "Dilations: Get ready for vectors and matrices", "Solving triangles using the trigonometric ratios: Get ready for vectors and matrices"], "Unit circle introduction: Get ready for vectors and matrices": ["Distance formula: Get ready for vectors and matrices"], "Unit 6: Get ready for series": ["Intro to sequences: Get ready for series", "Constructing arithmetic sequences: Get ready for series", "Constructing geometric sequences: Get ready for series", "Modeling with sequences: Get ready for series", "General sequences: Get ready for series", "Geometric series: Get ready for series"], "Unit 7: Get ready for conic sections": ["Graphs of circles intro: Get ready for conic sections", "Standard equation of a circle: Get ready for conic sections", "Expanded equation of a circle: Get ready for conic sections", "Focus and directrix of a parabola: Get ready for conic sections"], "Unit 8: Get ready for probability and combinatorics": ["Basic theoretical probability: Get ready for probability and combinatorics", "Probability using sample spaces: Get ready for probability and combinatorics", "Basic set operations: Get ready for probability and combinatorics", "Experimental probability: Get ready for probability and combinatorics", "Randomness, probability, and simulation: Get ready for probability and combinatorics", "Addition rule: Get ready for probability and combinatorics", "Start Course challenge"]}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Pre-K through grade 2 (Khan Kids)", "course_url": "/kids", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Counting": ["Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting"], "Unit 2: Addition and subtraction intro": ["What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro"], "Unit 3: Place value (tens and hundreds)": ["Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)"], "Unit 4: Addition and subtraction within 20": ["Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20"], "Unit 5: Addition and subtraction within 100": ["Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100"], "Unit 6: Addition and subtraction within 1000": ["Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000"], "Unit 7: Measurement and data": ["Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data"], "Unit 8: Geometry": ["Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Add and subtract within 20": ["Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20"], "Unit 2: Place value": ["Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value"], "Unit 3: Add and subtract within 100": ["Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100"], "Unit 4: Add and subtract within 1,000": ["Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000"], "Unit 6: Measurement": ["Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement"], "Unit 7: Data": ["Bar graphs: Data", "Line plots: Data"], "Unit 8: Geometry": ["Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Intro to multiplication": ["Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication"], "Unit 3: Addition, subtraction, and estimation": ["Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation"], "Unit 4: Intro to division": ["Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division"], "Unit 5: Understand fractions": ["Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions"], "Unit 6: Equivalent fractions and comparing fractions": ["Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions"], "Unit 7: More with multiplication and division": ["Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division"], "Unit 8: Arithmetic patterns and problem solving": ["2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving"], "Count unit squares to find area: Area": ["Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area"], "Unit 11: Perimeter": ["Perimeter: Perimeter", "Perimeter word problems: Perimeter"], "Unit 12: Time": ["Time on number line: Time", "Telling time: Time", "Elapsed time: Time"], "Unit 13: Measurement": ["Mass: Measurement", "Volume: Measurement"], "Unit 14: Represent and interpret data": ["Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Place value": ["Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value"], "Unit 2: Addition, subtraction, and estimation": ["Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation"], "Unit 3: Multiply by 1-digit numbers": ["Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers"], "Unit 4: Multiply by 2-digit numbers": ["Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers"], "Unit 5: Division": ["Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division"], "Unit 6: Factors, multiples and patterns": ["Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns"], "Unit 7: Equivalent fractions and comparing fractions": ["Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions"], "Unit 8: Add and subtract fractions": ["Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions"], "Unit 9: Multiply fractions": ["Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions"], "Unit 10: Understand decimals": ["Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals"], "Unit 11: Plane figures": ["Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures"], "Unit 12: Measuring angles": ["Measuring angles: Measuring angles", "Decomposing angles: Measuring angles"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Decimal place value": ["Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value"], "Unit 2: Add decimals": ["Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals"], "Unit 3: Subtract decimals": ["Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals"], "Unit 4: Add and subtract fractions": ["Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions"], "Unit 5: Multi-digit multiplication and division": ["Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division"], "Unit 6: Multiply fractions": ["Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions"], "Unit 7: Divide fractions": ["Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions"], "Unit 8: Multiply decimals": ["Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals"], "Unit 9: Divide decimals": ["Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals"], "Unit 10: Powers of ten": ["Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten"], "Volume with unit cubes: Volume": ["Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume"], "Unit 13: Algebraic thinking": ["Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking"], "Unit 15: Line plots": ["Graph data on line plots: Line plots", "Interpret data on line plots: Line plots"], "Unit 16: Properties of shapes": ["Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Ratios": ["Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios"], "Unit 2: Arithmetic with rational numbers": ["Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers"], "Unit 3: Rates and percentages": ["Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 4: Exponents and order of operations": ["Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations"], "Unit 5: Negative numbers": ["Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers"], "Unit 6: Variables & expressions": ["Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions"], "Unit 7: Equations & inequalities": ["Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities"], "Unit 8: Plane figures": ["Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures"], "Unit 9: Coordinate plane": ["Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane"], "Unit 10: 3D figures": ["Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures"], "Unit 11: Data and statistics": ["Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"Geometry: Unit test": ["Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles"], "Unit 1: Proportional relationships": ["Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships"], "Unit 2: Rates and percentages": ["Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 3: Integers: addition and subtraction": ["Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction"], "Unit 4: Rational numbers: addition and subtraction": ["Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction"], "Unit 5: Negative numbers: multiplication and division": ["Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division"], "Unit 6: Expressions, equations, & inequalities": ["The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities"], "Unit 7: Statistics and probability": ["Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability"], "Unit 8: Scale copies": ["Scale copies: Scale copies", "Scale drawings: Scale copies"], "Unit 9: Geometry": ["Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Numbers and operations": ["Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations"], "Unit 2: Solving equations with one unknown": ["Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown"], "Unit 3: Linear equations and functions": ["Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions"], "Unit 4: Systems of equations": ["Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 5: Geometry": ["Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry"], "Unit 6: Geometric transformations": ["Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations"], "Unit 7: Data and modeling": ["Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for addition and subtraction": ["Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction"], "Unit 2: Get ready for multiplication and division": ["Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division"], "Unit 3: Get ready for fractions": ["Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions"], "Unit 4: Get ready for patterns and problem solving": ["Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving"], "Units of length: Get ready for area and perimeter": ["Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter"], "Unit 7: Get ready for data": ["Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for place value": ["Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value"], "Unit 2: Get ready for addition, subtraction, and estimation": ["Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation"], "Unit 3: Get ready for multiplication": ["Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication"], "Unit 4: Get ready for division": ["Division intro: Get ready for division", "Relate multiplication and division: Get ready for division"], "Unit 5: Get ready for fractions": ["Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions"], "Unit 7: Get ready for area and perimeter": ["Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for decimal place value": ["Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value"], "Unit 2: Get ready for adding and subtracting decimals": ["Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals"], "Unit 3: Get ready for adding and subtracting fractions": ["Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions"], "Unit 4: Get ready for multiplication and division with whole numbers and decimals": ["Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals"], "Unit 5: Get ready for multiplying and dividing fractions": ["Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions"], "Unit 6: Get ready for powers of 10": ["How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10"], "Unit 8: Get ready for properties of shapes": ["Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Convert units of measure: Get ready for ratios, rates, and percentages": ["Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages"], "Divide unit fractions by whole numbers: Get ready for arithmetic operations": ["Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations"], "Unit 3: Get ready for negative numbers": ["Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers"], "Unit 4: Get ready for equations, expressions, and inequalities": ["Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities"], "Unit 5: Get ready for geometry": ["Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for negative number operations": ["Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations"], "Unit 2: Get ready for fractions, decimals, & percentages": ["Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages"], "Unit 3: Get ready for rates & proportional relationships": ["Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships"], "Unit 4: Get ready for expressions, equations, & inequalities": ["Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities"], "Unit 5: Get ready for geometry": ["Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry"], "Unit 6: Get ready for statistics & probability": ["Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for numbers and operations": ["Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations"], "Unit 2: Get ready for solving equations and systems of equations": ["Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations"], "Unit 3: Get ready for linear equations and functions": ["Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions"], "Unit 4: Get ready for geometry": ["Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for equations & inequalities": ["Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities"], "Unit 3: Get ready for linear relationships": ["Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships"], "Unit 4: Get ready for functions & sequences": ["Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences"], "Unit 5: Get ready for exponents, radicals, & irrational numbers": ["Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers"], "Unit 6: Get ready for quadratics": ["Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for congruence, similarity, and triangle trigonometry": ["Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry"], "Unit 2: Get ready for analytic geometry": ["Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry"], "Unit 3: Get ready for conic sections": ["Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections"], "Unit 4: Get ready for circles and solid geometry": ["Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for polynomial operations and complex numbers": ["Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers"], "Unit 2: Get ready for equations": ["Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations"], "Unit 3: Get ready for transformations of functions and modeling with functions": ["Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions"], "Unit 4: Get ready for exponential and logarithmic relationships": ["Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships"], "Unit 5: Get ready for trigonometry": ["Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry"], "Unit 6: Get ready for rational functions": ["Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Get ready for Precalculus", "course_url": "/math/get-ready-for-precalculus", "page_contents": {"syllabus": {"topics": {"The imaginary unit i: Get ready for complex numbers": ["Complex numbers introduction: Get ready for complex numbers", "The complex plane: Get ready for complex numbers", "Adding and subtracting complex numbers: Get ready for complex numbers", "Quadratic equations with complex solutions: Get ready for complex numbers"], "Unit 2: Get ready for polynomials": ["Adding and subtracting polynomials: Get ready for polynomials", "Multiplying binomials by polynomials: Get ready for polynomials", "Special products of polynomials: Get ready for polynomials", "Factoring higher degree polynomials: Get ready for polynomials", "Factoring using structure: Get ready for polynomials", "Zeros of polynomials: Get ready for polynomials", "Dividing polynomials by x: Get ready for polynomials", "Dividing quadratics by linear factors: Get ready for polynomials", "Dividing polynomials by linear factors: Get ready for polynomials"], "Unit 3: Get ready for composite and inverse functions": ["Shifting functions: Get ready for composite and inverse functions", "Reflecting functions: Get ready for composite and inverse functions", "Scaling functions: Get ready for composite and inverse functions", "Identifying function transformations: Get ready for composite and inverse functions", "Intro to domain and range of a function: Get ready for composite and inverse functions", "Intro to inverse functions: Get ready for composite and inverse functions"], "Unit circle introduction: Get ready for trigonometry": ["Radians: Get ready for trigonometry", "The Pythagorean identity: Get ready for trigonometry", "Trigonometric values of special angles: Get ready for trigonometry", "Graphing sinusoidal functions: Get ready for trigonometry", "Sinusoidal models: Get ready for trigonometry"], "Unit 5: Get ready for vectors and matrices": ["Equivalent systems of equations and the elimination method: Get ready for vectors and matrices", "Dilations: Get ready for vectors and matrices", "Solving triangles using the trigonometric ratios: Get ready for vectors and matrices"], "Unit 6: Get ready for series": ["Intro to sequences: Get ready for series", "Constructing arithmetic sequences: Get ready for series", "Constructing geometric sequences: Get ready for series", "Modeling with sequences: Get ready for series", "General sequences: Get ready for series", "Geometric series: Get ready for series"], "Unit 7: Get ready for conic sections": ["Graphs of circles intro: Get ready for conic sections", "Standard equation of a circle: Get ready for conic sections", "Expanded equation of a circle: Get ready for conic sections", "Focus and directrix of a parabola: Get ready for conic sections"], "Unit 8: Get ready for probability and combinatorics": ["Basic theoretical probability: Get ready for probability and combinatorics", "Probability using sample spaces: Get ready for probability and combinatorics", "Basic set operations: Get ready for probability and combinatorics", "Experimental probability: Get ready for probability and combinatorics", "Randomness, probability, and simulation: Get ready for probability and combinatorics", "Addition rule: Get ready for probability and combinatorics", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Calculus", "course_url": "/math/get-ready-for-ap-calc", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for limits and continuity": ["Evaluating functions: Get ready for limits and continuity", "Inputs and outputs of a function: Get ready for limits and continuity", "Composing functions: Get ready for limits and continuity", "Piecewise functions: Get ready for limits and continuity", "Introduction to factoring: Get ready for limits and continuity", "Factoring quadratics intro: Get ready for limits and continuity", "Factoring quadratics by grouping: Get ready for limits and continuity", "Factoring quadratics with difference of squares: Get ready for limits and continuity", "Factoring quadratics with perfect squares: Get ready for limits and continuity", "Factoring higher degree polynomials: Get ready for limits and continuity", "Introduction to the trigonometric ratios: Get ready for limits and continuity"], "Unit circle introduction: Get ready for limits and continuity": ["Radians: Get ready for limits and continuity", "The Pythagorean identity: Get ready for limits and continuity", "Special trigonometric values in the first quadrant: Get ready for limits and continuity"], "Trigonometric identities on the unit circle: Get ready for limits and continuity": ["Angle addition identities: Get ready for limits and continuity", "Reducing rational expressions to lowest terms: Get ready for limits and continuity", "End behavior of rational functions: Get ready for limits and continuity", "Discontinuities of rational functions: Get ready for limits and continuity", "Multiplying and dividing rational expressions: Get ready for limits and continuity"], "Unit 2: Get ready for differentiation: definition and basic derivative rules": ["Intro to slope-intercept form: Get ready for differentiation: definition and basic derivative rules", "Writing slope-intercept equations: Get ready for differentiation: definition and basic derivative rules", "Point-slope form: Get ready for differentiation: definition and basic derivative rules", "Average rate of change: Get ready for differentiation: definition and basic derivative rules", "Rational exponents: Get ready for differentiation: definition and basic derivative rules", "Properties of exponents: Get ready for differentiation: definition and basic derivative rules", "Introduction to logarithms: Get ready for differentiation: definition and basic derivative rules"], "Unit 3: Get ready for differentiation: composite, implicit, and inverse functions": ["Composing functions: Get ready for differentiation: composite, implicit, and inverse functions", "Linear equations with unknown coefficients: Get ready for differentiation: composite, implicit, and inverse functions", "Intro to inverse functions: Get ready for differentiation: composite, implicit, and inverse functions", "Invertible functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse trigonometric functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse functions in graphs and tables: Get ready for differentiation: composite, implicit, and inverse functions", "Verifying inverse functions by composition: Get ready for differentiation: composite, implicit, and inverse functions"], "Word problems with multiple units: Get ready for contextual applications of differentiation": ["Linear equations word problems: Get ready for contextual applications of differentiation", "Interpreting function notation: Get ready for contextual applications of differentiation", "Average rate of change word problems: Get ready for contextual applications of differentiation", "Modeling with composite functions: Get ready for contextual applications of differentiation", "Modeling with right triangles: Get ready for contextual applications of differentiation", "Volume and surface area: Get ready for contextual applications of differentiation"], "Unit 5: Get ready for applying derivatives to analyze functions": ["Maximum and minimum points: Get ready for applying derivatives to analyze functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for applying derivatives to analyze functions", "Interpreting features of graphs: Get ready for applying derivatives to analyze functions", "Distance formula: Get ready for applying derivatives to analyze functions", "Square-root equations: Get ready for applying derivatives to analyze functions", "Zeros of polynomials: Get ready for applying derivatives to analyze functions", "Positive and negative intervals of polynomials: Get ready for applying derivatives to analyze functions"], "Unit 6: Get ready for integration and accumulation of change": ["Completing the square: Get ready for integration and accumulation of change", "Dividing quadratics by linear factors: Get ready for integration and accumulation of change", "Dividing polynomials by linear factors: Get ready for integration and accumulation of change", "Partial fraction expansion: Get ready for integration and accumulation of change", "Summation notation: Get ready for integration and accumulation of change"], "Unit 7: Get ready for applications of integration": ["Rational equations: Get ready for applications of integration", "Square-root equations: Get ready for applications of integration", "Extraneous solutions: Get ready for applications of integration", "Sinusoidal equations: Get ready for applications of integration", "Manipulating formulas: Get ready for applications of integration", "Solving equations by graphing: Get ready for applications of integration"], "Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)": ["Sectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vectors introduction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Magnitude of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Scalar multiplication: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Direction of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components from magnitude & direction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)"], "Unit 9: Get ready for infinite sequences and series (BC only)": ["Arithmetic sequences: Get ready for infinite sequences and series (BC only)", "Geometric sequences: Get ready for infinite sequences and series (BC only)", "Summation notation: Get ready for infinite sequences and series (BC only)", "Arithmetic series: Get ready for infinite sequences and series (BC only)", "Geometric series: Get ready for infinite sequences and series (BC only)", "End behavior of rational functions: Get ready for infinite sequences and series (BC only)", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Statistics", "course_url": "/math/get-ready-for-ap-statistics", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for exploring categorical data": ["Frequency tables: Get ready for exploring categorical data", "Bar graphs: Get ready for exploring categorical data", "Fractions, decimals, and percentages: Get ready for exploring categorical data"], "Unit 2: Get ready for exploring one-variable quantitative data": ["Frequency tables and dot plots: Get ready for exploring one-variable quantitative data", "Box and whisker plots: Get ready for exploring one-variable quantitative data", "Comparing data displays: Get ready for exploring one-variable quantitative data", "Mean, median, and mode: Get ready for exploring one-variable quantitative data", "Mean absolute deviation: Get ready for exploring one-variable quantitative data", "Linear equations with variables on both sides: Get ready for exploring one-variable quantitative data", "Linear equations with unknown coefficients: Get ready for exploring one-variable quantitative data"], "Unit 3: Get ready for exploring two-variable quantitative data": ["Introduction to scatter plots: Get ready for exploring two-variable quantitative data", "Estimating with trend lines: Get ready for exploring two-variable quantitative data", "Logarithms: Get ready for exploring two-variable quantitative data"], "Unit 4: Get ready for probability": ["Fractions, decimals, and percentages: Get ready for probability", "Comparing decimals and fractions: Get ready for probability", "Arithmetic with fractions: Get ready for probability", "Probability introduction: Get ready for probability", "Experimental probability: Get ready for probability"], "Unit 5: Get ready for random variables and probability distributions": ["Predictions with probability: Get ready for random variables and probability distributions", "The counting principle: Get ready for random variables and probability distributions", "Probability distributions introduction: Get ready for random variables and probability distributions", "Start Course challenge"]}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Counting": ["Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting"], "Unit 2: Addition and subtraction intro": ["What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro"], "Unit 3: Place value (tens and hundreds)": ["Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)"], "Unit 4: Addition and subtraction within 20": ["Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20"], "Unit 5: Addition and subtraction within 100": ["Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100"], "Unit 6: Addition and subtraction within 1000": ["Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000"], "Unit 7: Measurement and data": ["Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data"], "Unit 8: Geometry": ["Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Add and subtract within 20": ["Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20"], "Unit 2: Place value": ["Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value"], "Unit 3: Add and subtract within 100": ["Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100"], "Unit 4: Add and subtract within 1,000": ["Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000"], "Unit 6: Measurement": ["Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement"], "Unit 7: Data": ["Bar graphs: Data", "Line plots: Data"], "Unit 8: Geometry": ["Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Intro to multiplication": ["Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication"], "Unit 3: Addition, subtraction, and estimation": ["Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation"], "Unit 4: Intro to division": ["Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division"], "Unit 5: Understand fractions": ["Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions"], "Unit 6: Equivalent fractions and comparing fractions": ["Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions"], "Unit 7: More with multiplication and division": ["Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division"], "Unit 8: Arithmetic patterns and problem solving": ["2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving"], "Count unit squares to find area: Area": ["Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area"], "Unit 11: Perimeter": ["Perimeter: Perimeter", "Perimeter word problems: Perimeter"], "Unit 12: Time": ["Time on number line: Time", "Telling time: Time", "Elapsed time: Time"], "Unit 13: Measurement": ["Mass: Measurement", "Volume: Measurement"], "Unit 14: Represent and interpret data": ["Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Place value": ["Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value"], "Unit 2: Addition, subtraction, and estimation": ["Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation"], "Unit 3: Multiply by 1-digit numbers": ["Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers"], "Unit 4: Multiply by 2-digit numbers": ["Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers"], "Unit 5: Division": ["Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division"], "Unit 6: Factors, multiples and patterns": ["Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns"], "Unit 7: Equivalent fractions and comparing fractions": ["Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions"], "Unit 8: Add and subtract fractions": ["Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions"], "Unit 9: Multiply fractions": ["Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions"], "Unit 10: Understand decimals": ["Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals"], "Unit 11: Plane figures": ["Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures"], "Unit 12: Measuring angles": ["Measuring angles: Measuring angles", "Decomposing angles: Measuring angles"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Decimal place value": ["Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value"], "Unit 2: Add decimals": ["Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals"], "Unit 3: Subtract decimals": ["Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals"], "Unit 4: Add and subtract fractions": ["Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions"], "Unit 5: Multi-digit multiplication and division": ["Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division"], "Unit 6: Multiply fractions": ["Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions"], "Unit 7: Divide fractions": ["Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions"], "Unit 8: Multiply decimals": ["Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals"], "Unit 9: Divide decimals": ["Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals"], "Unit 10: Powers of ten": ["Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten"], "Volume with unit cubes: Volume": ["Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume"], "Unit 13: Algebraic thinking": ["Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking"], "Unit 15: Line plots": ["Graph data on line plots: Line plots", "Interpret data on line plots: Line plots"], "Unit 16: Properties of shapes": ["Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Ratios": ["Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios"], "Unit 2: Arithmetic with rational numbers": ["Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers"], "Unit 3: Rates and percentages": ["Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 4: Exponents and order of operations": ["Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations"], "Unit 5: Negative numbers": ["Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers"], "Unit 6: Variables & expressions": ["Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions"], "Unit 7: Equations & inequalities": ["Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities"], "Unit 8: Plane figures": ["Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures"], "Unit 9: Coordinate plane": ["Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane"], "Unit 10: 3D figures": ["Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures"], "Unit 11: Data and statistics": ["Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"Geometry: Unit test": ["Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles"], "Unit 1: Proportional relationships": ["Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships"], "Unit 2: Rates and percentages": ["Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 3: Integers: addition and subtraction": ["Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction"], "Unit 4: Rational numbers: addition and subtraction": ["Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction"], "Unit 5: Negative numbers: multiplication and division": ["Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division"], "Unit 6: Expressions, equations, & inequalities": ["The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities"], "Unit 7: Statistics and probability": ["Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability"], "Unit 8: Scale copies": ["Scale copies: Scale copies", "Scale drawings: Scale copies"], "Unit 9: Geometry": ["Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Numbers and operations": ["Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations"], "Unit 2: Solving equations with one unknown": ["Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown"], "Unit 3: Linear equations and functions": ["Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions"], "Unit 4: Systems of equations": ["Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 5: Geometry": ["Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry"], "Unit 6: Geometric transformations": ["Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations"], "Unit 7: Data and modeling": ["Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for addition and subtraction": ["Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction"], "Unit 2: Get ready for multiplication and division": ["Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division"], "Unit 3: Get ready for fractions": ["Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions"], "Unit 4: Get ready for patterns and problem solving": ["Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving"], "Units of length: Get ready for area and perimeter": ["Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter"], "Unit 7: Get ready for data": ["Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for place value": ["Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value"], "Unit 2: Get ready for addition, subtraction, and estimation": ["Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation"], "Unit 3: Get ready for multiplication": ["Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication"], "Unit 4: Get ready for division": ["Division intro: Get ready for division", "Relate multiplication and division: Get ready for division"], "Unit 5: Get ready for fractions": ["Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions"], "Unit 7: Get ready for area and perimeter": ["Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for decimal place value": ["Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value"], "Unit 2: Get ready for adding and subtracting decimals": ["Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals"], "Unit 3: Get ready for adding and subtracting fractions": ["Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions"], "Unit 4: Get ready for multiplication and division with whole numbers and decimals": ["Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals"], "Unit 5: Get ready for multiplying and dividing fractions": ["Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions"], "Unit 6: Get ready for powers of 10": ["How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10"], "Unit 8: Get ready for properties of shapes": ["Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Convert units of measure: Get ready for ratios, rates, and percentages": ["Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages"], "Divide unit fractions by whole numbers: Get ready for arithmetic operations": ["Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations"], "Unit 3: Get ready for negative numbers": ["Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers"], "Unit 4: Get ready for equations, expressions, and inequalities": ["Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities"], "Unit 5: Get ready for geometry": ["Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for negative number operations": ["Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations"], "Unit 2: Get ready for fractions, decimals, & percentages": ["Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages"], "Unit 3: Get ready for rates & proportional relationships": ["Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships"], "Unit 4: Get ready for expressions, equations, & inequalities": ["Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities"], "Unit 5: Get ready for geometry": ["Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry"], "Unit 6: Get ready for statistics & probability": ["Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for numbers and operations": ["Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations"], "Unit 2: Get ready for solving equations and systems of equations": ["Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations"], "Unit 3: Get ready for linear equations and functions": ["Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions"], "Unit 4: Get ready for geometry": ["Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for equations & inequalities": ["Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities"], "Unit 3: Get ready for linear relationships": ["Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships"], "Unit 4: Get ready for functions & sequences": ["Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences"], "Unit 5: Get ready for exponents, radicals, & irrational numbers": ["Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers"], "Unit 6: Get ready for quadratics": ["Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for congruence, similarity, and triangle trigonometry": ["Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry"], "Unit 2: Get ready for analytic geometry": ["Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry"], "Unit 3: Get ready for conic sections": ["Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections"], "Unit 4: Get ready for circles and solid geometry": ["Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for polynomial operations and complex numbers": ["Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers"], "Unit 2: Get ready for equations": ["Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations"], "Unit 3: Get ready for transformations of functions and modeling with functions": ["Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions"], "Unit 4: Get ready for exponential and logarithmic relationships": ["Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships"], "Unit 5: Get ready for trigonometry": ["Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry"], "Unit 6: Get ready for rational functions": ["Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Get ready for Precalculus", "course_url": "/math/get-ready-for-precalculus", "page_contents": {"syllabus": {"topics": {"The imaginary unit i: Get ready for complex numbers": ["Complex numbers introduction: Get ready for complex numbers", "The complex plane: Get ready for complex numbers", "Adding and subtracting complex numbers: Get ready for complex numbers", "Quadratic equations with complex solutions: Get ready for complex numbers"], "Unit 2: Get ready for polynomials": ["Adding and subtracting polynomials: Get ready for polynomials", "Multiplying binomials by polynomials: Get ready for polynomials", "Special products of polynomials: Get ready for polynomials", "Factoring higher degree polynomials: Get ready for polynomials", "Factoring using structure: Get ready for polynomials", "Zeros of polynomials: Get ready for polynomials", "Dividing polynomials by x: Get ready for polynomials", "Dividing quadratics by linear factors: Get ready for polynomials", "Dividing polynomials by linear factors: Get ready for polynomials"], "Unit 3: Get ready for composite and inverse functions": ["Shifting functions: Get ready for composite and inverse functions", "Reflecting functions: Get ready for composite and inverse functions", "Scaling functions: Get ready for composite and inverse functions", "Identifying function transformations: Get ready for composite and inverse functions", "Intro to domain and range of a function: Get ready for composite and inverse functions", "Intro to inverse functions: Get ready for composite and inverse functions"], "Unit circle introduction: Get ready for trigonometry": ["Radians: Get ready for trigonometry", "The Pythagorean identity: Get ready for trigonometry", "Trigonometric values of special angles: Get ready for trigonometry", "Graphing sinusoidal functions: Get ready for trigonometry", "Sinusoidal models: Get ready for trigonometry"], "Unit 5: Get ready for vectors and matrices": ["Equivalent systems of equations and the elimination method: Get ready for vectors and matrices", "Dilations: Get ready for vectors and matrices", "Solving triangles using the trigonometric ratios: Get ready for vectors and matrices"], "Unit 6: Get ready for series": ["Intro to sequences: Get ready for series", "Constructing arithmetic sequences: Get ready for series", "Constructing geometric sequences: Get ready for series", "Modeling with sequences: Get ready for series", "General sequences: Get ready for series", "Geometric series: Get ready for series"], "Unit 7: Get ready for conic sections": ["Graphs of circles intro: Get ready for conic sections", "Standard equation of a circle: Get ready for conic sections", "Expanded equation of a circle: Get ready for conic sections", "Focus and directrix of a parabola: Get ready for conic sections"], "Unit 8: Get ready for probability and combinatorics": ["Basic theoretical probability: Get ready for probability and combinatorics", "Probability using sample spaces: Get ready for probability and combinatorics", "Basic set operations: Get ready for probability and combinatorics", "Experimental probability: Get ready for probability and combinatorics", "Randomness, probability, and simulation: Get ready for probability and combinatorics", "Addition rule: Get ready for probability and combinatorics", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Calculus", "course_url": "/math/get-ready-for-ap-calc", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for limits and continuity": ["Evaluating functions: Get ready for limits and continuity", "Inputs and outputs of a function: Get ready for limits and continuity", "Composing functions: Get ready for limits and continuity", "Piecewise functions: Get ready for limits and continuity", "Introduction to factoring: Get ready for limits and continuity", "Factoring quadratics intro: Get ready for limits and continuity", "Factoring quadratics by grouping: Get ready for limits and continuity", "Factoring quadratics with difference of squares: Get ready for limits and continuity", "Factoring quadratics with perfect squares: Get ready for limits and continuity", "Factoring higher degree polynomials: Get ready for limits and continuity", "Introduction to the trigonometric ratios: Get ready for limits and continuity"], "Unit circle introduction: Get ready for limits and continuity": ["Radians: Get ready for limits and continuity", "The Pythagorean identity: Get ready for limits and continuity", "Special trigonometric values in the first quadrant: Get ready for limits and continuity"], "Trigonometric identities on the unit circle: Get ready for limits and continuity": ["Angle addition identities: Get ready for limits and continuity", "Reducing rational expressions to lowest terms: Get ready for limits and continuity", "End behavior of rational functions: Get ready for limits and continuity", "Discontinuities of rational functions: Get ready for limits and continuity", "Multiplying and dividing rational expressions: Get ready for limits and continuity"], "Unit 2: Get ready for differentiation: definition and basic derivative rules": ["Intro to slope-intercept form: Get ready for differentiation: definition and basic derivative rules", "Writing slope-intercept equations: Get ready for differentiation: definition and basic derivative rules", "Point-slope form: Get ready for differentiation: definition and basic derivative rules", "Average rate of change: Get ready for differentiation: definition and basic derivative rules", "Rational exponents: Get ready for differentiation: definition and basic derivative rules", "Properties of exponents: Get ready for differentiation: definition and basic derivative rules", "Introduction to logarithms: Get ready for differentiation: definition and basic derivative rules"], "Unit 3: Get ready for differentiation: composite, implicit, and inverse functions": ["Composing functions: Get ready for differentiation: composite, implicit, and inverse functions", "Linear equations with unknown coefficients: Get ready for differentiation: composite, implicit, and inverse functions", "Intro to inverse functions: Get ready for differentiation: composite, implicit, and inverse functions", "Invertible functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse trigonometric functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse functions in graphs and tables: Get ready for differentiation: composite, implicit, and inverse functions", "Verifying inverse functions by composition: Get ready for differentiation: composite, implicit, and inverse functions"], "Word problems with multiple units: Get ready for contextual applications of differentiation": ["Linear equations word problems: Get ready for contextual applications of differentiation", "Interpreting function notation: Get ready for contextual applications of differentiation", "Average rate of change word problems: Get ready for contextual applications of differentiation", "Modeling with composite functions: Get ready for contextual applications of differentiation", "Modeling with right triangles: Get ready for contextual applications of differentiation", "Volume and surface area: Get ready for contextual applications of differentiation"], "Unit 5: Get ready for applying derivatives to analyze functions": ["Maximum and minimum points: Get ready for applying derivatives to analyze functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for applying derivatives to analyze functions", "Interpreting features of graphs: Get ready for applying derivatives to analyze functions", "Distance formula: Get ready for applying derivatives to analyze functions", "Square-root equations: Get ready for applying derivatives to analyze functions", "Zeros of polynomials: Get ready for applying derivatives to analyze functions", "Positive and negative intervals of polynomials: Get ready for applying derivatives to analyze functions"], "Unit 6: Get ready for integration and accumulation of change": ["Completing the square: Get ready for integration and accumulation of change", "Dividing quadratics by linear factors: Get ready for integration and accumulation of change", "Dividing polynomials by linear factors: Get ready for integration and accumulation of change", "Partial fraction expansion: Get ready for integration and accumulation of change", "Summation notation: Get ready for integration and accumulation of change"], "Unit 7: Get ready for applications of integration": ["Rational equations: Get ready for applications of integration", "Square-root equations: Get ready for applications of integration", "Extraneous solutions: Get ready for applications of integration", "Sinusoidal equations: Get ready for applications of integration", "Manipulating formulas: Get ready for applications of integration", "Solving equations by graphing: Get ready for applications of integration"], "Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)": ["Sectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vectors introduction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Magnitude of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Scalar multiplication: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Direction of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components from magnitude & direction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)"], "Unit 9: Get ready for infinite sequences and series (BC only)": ["Arithmetic sequences: Get ready for infinite sequences and series (BC only)", "Geometric sequences: Get ready for infinite sequences and series (BC only)", "Summation notation: Get ready for infinite sequences and series (BC only)", "Arithmetic series: Get ready for infinite sequences and series (BC only)", "Geometric series: Get ready for infinite sequences and series (BC only)", "End behavior of rational functions: Get ready for infinite sequences and series (BC only)", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Statistics", "course_url": "/math/get-ready-for-ap-statistics", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for exploring categorical data": ["Frequency tables: Get ready for exploring categorical data", "Bar graphs: Get ready for exploring categorical data", "Fractions, decimals, and percentages: Get ready for exploring categorical data"], "Unit 2: Get ready for exploring one-variable quantitative data": ["Frequency tables and dot plots: Get ready for exploring one-variable quantitative data", "Box and whisker plots: Get ready for exploring one-variable quantitative data", "Comparing data displays: Get ready for exploring one-variable quantitative data", "Mean, median, and mode: Get ready for exploring one-variable quantitative data", "Mean absolute deviation: Get ready for exploring one-variable quantitative data", "Linear equations with variables on both sides: Get ready for exploring one-variable quantitative data", "Linear equations with unknown coefficients: Get ready for exploring one-variable quantitative data"], "Unit 3: Get ready for exploring two-variable quantitative data": ["Introduction to scatter plots: Get ready for exploring two-variable quantitative data", "Estimating with trend lines: Get ready for exploring two-variable quantitative data", "Logarithms: Get ready for exploring two-variable quantitative data"], "Unit 4: Get ready for probability": ["Fractions, decimals, and percentages: Get ready for probability", "Comparing decimals and fractions: Get ready for probability", "Arithmetic with fractions: Get ready for probability", "Probability introduction: Get ready for probability", "Experimental probability: Get ready for probability"], "Unit 5: Get ready for random variables and probability distributions": ["Predictions with probability: Get ready for random variables and probability distributions", "The counting principle: Get ready for random variables and probability distributions", "Probability distributions introduction: Get ready for random variables and probability distributions", "Start Course challenge"]}}}}
{"course_title": "Algebra 1", "course_url": "/math/algebra", "page_contents": {"syllabus": {"topics": {"Unit 1: Algebra foundations": ["Overview and history of algebra: Algebra foundations", "Introduction to variables: Algebra foundations", "Substitution and evaluating expressions: Algebra foundations", "Combining like terms: Algebra foundations", "Introduction to equivalent expressions: Algebra foundations", "Division by zero: Algebra foundations"], "Unit 2: Solving equations & inequalities": ["Linear equations with variables on both sides: Solving equations & inequalities", "Linear equations with parentheses: Solving equations & inequalities", "Analyzing the number of solutions to linear equations: Solving equations & inequalities", "Linear equations with unknown coefficients: Solving equations & inequalities", "Multi-step inequalities: Solving equations & inequalities", "Compound inequalities: Solving equations & inequalities"], "Unit 4: Linear equations & graphs": ["Two-variable linear equations intro: Linear equations & graphs", "Slope: Linear equations & graphs", "Horizontal & vertical lines: Linear equations & graphs", "x-intercepts and y-intercepts: Linear equations & graphs", "Applying intercepts and slope: Linear equations & graphs", "Modeling with linear equations and inequalities: Linear equations & graphs"], "Unit 5: Forms of linear equations": ["Intro to slope-intercept form: Forms of linear equations", "Graphing slope-intercept equations: Forms of linear equations", "Writing slope-intercept equations: Forms of linear equations", "Point-slope form: Forms of linear equations", "Standard form: Forms of linear equations", "Summary: Forms of two-variable linear equations: Forms of linear equations"], "Unit 6: Systems of equations": ["Introduction to systems of equations: Systems of equations", "Solving systems of equations with substitution: Systems of equations", "Solving systems of equations with elimination: Systems of equations", "Equivalent systems of equations: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 7: Inequalities (systems & graphs)": ["Checking solutions of two-variable inequalities: Inequalities (systems & graphs)", "Graphing two-variable inequalities: Inequalities (systems & graphs)", "Modeling with linear inequalities: Inequalities (systems & graphs)"], "Unit 8: Functions": ["Evaluating functions: Functions", "Inputs and outputs of a function: Functions", "Functions and equations: Functions", "Interpreting function notation: Functions", "Introduction to the domain and range of a function: Functions", "Determining the domain of a function: Functions", "Recognizing functions: Functions", "Maximum and minimum points: Functions", "Intervals where a function is positive, negative, increasing, or decreasing: Functions", "Interpreting features of graphs: Functions", "Average rate of change: Functions", "Average rate of change word problems: Functions", "Intro to inverse functions: Functions"], "Unit 9: Sequences": ["Introduction to arithmetic sequences: Sequences", "Constructing arithmetic sequences: Sequences", "Introduction to geometric sequences: Sequences", "Constructing geometric sequences: Sequences", "Modeling with sequences: Sequences", "General sequences: Sequences"], "Unit 10: Absolute value & piecewise functions": ["Graphs of absolute value functions: Absolute value & piecewise functions", "Piecewise functions: Absolute value & piecewise functions"], "Unit 11: Exponents & radicals": ["Exponent properties review: Exponents & radicals", "Radicals: Exponents & radicals", "Simplifying square roots: Exponents & radicals"], "Unit 12: Exponential growth & decay": ["Exponential vs. linear growth: Exponential growth & decay", "Exponential expressions: Exponential growth & decay", "Graphs of exponential growth: Exponential growth & decay", "Exponential vs. linear growth over time: Exponential growth & decay", "Exponential growth & decay: Exponential growth & decay", "Exponential functions from tables & graphs: Exponential growth & decay", "Exponential vs. linear models: Exponential growth & decay"], "Unit 13: Quadratics: Multiplying & factoring": ["Multiplying monomials by polynomials: Quadratics: Multiplying & factoring", "Multiplying binomials: Quadratics: Multiplying & factoring", "Special products of binomials: Quadratics: Multiplying & factoring", "Introduction to factoring: Quadratics: Multiplying & factoring", "Factoring quadratics intro: Quadratics: Multiplying & factoring", "Factoring quadratics by grouping: Quadratics: Multiplying & factoring", "Factoring quadratics with difference of squares: Quadratics: Multiplying & factoring", "Factoring quadratics with perfect squares: Quadratics: Multiplying & factoring", "Strategy in factoring quadratics: Quadratics: Multiplying & factoring"], "Unit 14: Quadratic functions & equations": ["Intro to parabolas: Quadratic functions & equations", "Solving and graphing with factored form: Quadratic functions & equations", "Solving by taking the square root: Quadratic functions & equations", "Vertex form: Quadratic functions & equations", "Solving quadratics by factoring: Quadratic functions & equations", "The quadratic formula: Quadratic functions & equations", "Completing the square intro: Quadratic functions & equations", "More on completing the square: Quadratic functions & equations", "Strategizing to solve quadratic equations: Quadratic functions & equations", "Quadratic standard form: Quadratic functions & equations", "Features & forms of quadratic functions: Quadratic functions & equations", "Comparing quadratic functions: Quadratic functions & equations", "Transforming quadratic functions: Quadratic functions & equations"], "Unit 15: Irrational numbers": ["Irrational numbers: Irrational numbers", "Sums and products of rational and irrational numbers: Irrational numbers", "Proofs concerning irrational numbers: Irrational numbers"], "Unit 16: Creativity in algebra": ["Creativity in algebra: Creativity in algebra", "Start Course challenge"]}}}}
{"course_title": "Geometry", "course_url": "/math/geometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Performing transformations": ["Introduction to rigid transformations: Performing transformations", "Translations: Performing transformations", "Rotations: Performing transformations", "Reflections: Performing transformations", "Dilations: Performing transformations"], "Unit 2: Transformation properties and proofs": ["Dilation preserved properties: Transformation properties and proofs", "Properties & definitions of transformations: Transformation properties and proofs", "Symmetry: Transformation properties and proofs", "Proofs with transformations: Transformation properties and proofs"], "Unit 3: Congruence": ["Triangle congruence from transformations: Congruence", "Congruent triangles: Congruence", "Working with triangles: Congruence", "Theorems concerning quadrilateral properties: Congruence", "Proofs of general theorems: Congruence", "Constructing lines & angles: Congruence"], "Unit 4: Similarity": ["Introduction to triangle similarity: Similarity", "Solving similar triangles: Similarity", "Angle bisector theorem: Similarity", "Solving problems with similar & congruent triangles: Similarity", "Proving relationships using similarity: Similarity", "Solving modeling problems with similar & congruent triangles: Similarity"], "Unit 5: Right triangles & trigonometry": ["Pythagorean theorem proofs: Right triangles & trigonometry", "Special right triangles: Right triangles & trigonometry", "Introduction to the trigonometric ratios: Right triangles & trigonometry", "Solving for a side in a right triangle using the trigonometric ratios: Right triangles & trigonometry", "Sine & cosine of complementary angles: Right triangles & trigonometry", "Modeling with right triangles: Right triangles & trigonometry"], "Unit 6: Analytic geometry": ["Dividing line segments: Analytic geometry", "Problem solving with distance on the coordinate plane: Analytic geometry", "Parallel & perpendicular lines on the coordinate plane: Analytic geometry", "Equations of parallel & perpendicular lines: Analytic geometry"], "Unit 7: Conic sections": ["Standard equation of a circle: Conic sections", "Expanded equation of a circle: Conic sections", "Focus and directrix of a parabola: Conic sections"], "Unit 8: Circles": ["Arc measure: Circles", "Arc length (from degrees): Circles", "Introduction to radians: Circles", "Arc length (from radians): Circles", "Sectors: Circles", "Inscribed angles: Circles", "Inscribed shapes problem solving: Circles", "Proofs with inscribed shapes: Circles", "Properties of tangents: Circles", "Constructing regular polygons inscribed in circles: Circles", "Constructing circumcircles & incircles: Circles", "Constructing a line tangent to a circle: Circles"], "Unit 9: Solid geometry": ["Volume and surface area: Solid geometry", "Density: Solid geometry", "Start Course challenge", "Modeling with right triangles", "Volume and surface area", "Special right triangles", "Introduction to triangle similarity"]}}}}
{"course_title": "Algebra 2", "course_url": "/math/algebra2", "page_contents": {"syllabus": {"topics": {"Unit 1: Polynomial arithmetic": ["Intro to polynomials: Polynomial arithmetic", "Average rate of change of polynomials: Polynomial arithmetic", "Adding and subtracting polynomials: Polynomial arithmetic", "Multiplying monomials by polynomials: Polynomial arithmetic", "Multiplying binomials by polynomials: Polynomial arithmetic", "Special products of polynomials: Polynomial arithmetic"], "The imaginary unit i: Complex numbers": ["Complex numbers introduction: Complex numbers", "The complex plane: Complex numbers", "Adding and subtracting complex numbers: Complex numbers", "Quadratic equations with complex solutions: Complex numbers"], "Unit 3: Polynomial factorization": ["Factoring monomials: Polynomial factorization", "Greatest common factor: Polynomial factorization", "Taking common factors: Polynomial factorization", "Factoring higher degree polynomials: Polynomial factorization", "Factoring using structure: Polynomial factorization", "Polynomial identities: Polynomial factorization", "Geometric series: Polynomial factorization"], "Unit 4: Polynomial division": ["Dividing polynomials by x: Polynomial division", "Dividing quadratics by linear factors: Polynomial division", "Dividing polynomials by linear factors: Polynomial division", "Polynomial Remainder Theorem: Polynomial division"], "Unit 5: Polynomial graphs": ["Zeros of polynomials: Polynomial graphs", "Positive and negative intervals of polynomials: Polynomial graphs", "End behavior of polynomials: Polynomial graphs"], "Unit 6: Rational exponents and radicals": ["Rational exponents: Rational exponents and radicals", "Properties of exponents (rational exponents): Rational exponents and radicals", "Evaluating exponents & radicals: Rational exponents and radicals", "Equivalent forms of exponential expressions: Rational exponents and radicals", "Solving exponential equations using properties of exponents: Rational exponents and radicals"], "Unit 7: Exponential models": ["Interpreting the rate of change of exponential models: Exponential models", "Constructing exponential models according to rate of change: Exponential models", "Advanced interpretation of exponential models: Exponential models"], "Unit 8: Logarithms": ["Introduction to logarithms: Logarithms", "The constant e and the natural logarithm: Logarithms", "Properties of logarithms: Logarithms", "The change of base formula for logarithms: Logarithms", "Solving exponential equations with logarithms: Logarithms", "Solving exponential models: Logarithms"], "Unit 9: Transformations of functions": ["Shifting functions: Transformations of functions", "Reflecting functions: Transformations of functions", "Symmetry of functions: Transformations of functions", "Scaling functions: Transformations of functions", "Putting it all together: Transformations of functions", "Graphs of square and cube root functions: Transformations of functions", "Graphs of exponential functions: Transformations of functions", "Graphs of logarithmic functions: Transformations of functions"], "Unit 10: Equations": ["Rational equations: Equations", "Square-root equations: Equations", "Extraneous solutions: Equations", "Cube-root equations: Equations", "Quadratic systems: Equations", "Solving equations by graphing: Equations"], "Unit circle introduction: Trigonometry": ["Radians: Trigonometry", "The Pythagorean identity: Trigonometry", "Trigonometric values of special angles: Trigonometry", "Graphs of sin(x), cos(x), and tan(x): Trigonometry", "Amplitude, midline and period: Trigonometry", "Transforming sinusoidal graphs: Trigonometry", "Graphing sinusoidal functions: Trigonometry", "Sinusoidal models: Trigonometry"], "Unit 12: Modeling": ["Modeling with function combination: Modeling", "Interpreting features of functions: Modeling", "Manipulating formulas: Modeling", "Modeling with two variables: Modeling", "Modeling with multiple variables: Modeling", "Start Course challenge"]}}}}
{"course_title": "Integrated math 1", "course_url": "/math/math1", "page_contents": {"syllabus": {"topics": {"Unit 1: Algebra foundations": ["Overview and history of algebra: Algebra foundations", "Introduction to variables: Algebra foundations", "Substitution and evaluating expressions: Algebra foundations", "Combining like terms: Algebra foundations", "Introduction to equivalent expressions: Algebra foundations", "Division by zero: Algebra foundations"], "Unit 2: Solving equations & inequalities": ["Linear equations with variables on both sides: Solving equations & inequalities", "Linear equations with parentheses: Solving equations & inequalities", "Analyzing the number of solutions to linear equations: Solving equations & inequalities", "Linear equations with unknown coefficients: Solving equations & inequalities", "Multi-step inequalities: Solving equations & inequalities", "Compound inequalities: Solving equations & inequalities"], "Unit 4: Linear equations & graphs": ["Two-variable linear equations intro: Linear equations & graphs", "Slope: Linear equations & graphs", "Horizontal & vertical lines: Linear equations & graphs", "x-intercepts and y-intercepts: Linear equations & graphs", "Applying intercepts and slope: Linear equations & graphs"], "Unit 5: Forms of linear equations": ["Intro to slope-intercept form: Forms of linear equations", "Graphing slope-intercept equations: Forms of linear equations", "Writing slope-intercept equations: Forms of linear equations", "Point-slope form: Forms of linear equations", "Standard form: Forms of linear equations", "Summary: Forms of two-variable linear equations: Forms of linear equations"], "Unit 6: Systems of equations": ["Introduction to systems of equations: Systems of equations", "Solving systems of equations with substitution: Systems of equations", "Equivalent systems of equations: Systems of equations", "Solving systems of equations with elimination: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 7: Inequalities (systems & graphs)": ["Checking solutions of two-variable inequalities: Inequalities (systems & graphs)", "Graphing two-variable inequalities: Inequalities (systems & graphs)", "Modeling with linear inequalities: Inequalities (systems & graphs)"], "Unit 8: Functions": ["Evaluating functions: Functions", "Inputs and outputs of a function: Functions", "Functions and equations: Functions", "Interpreting function notation: Functions", "Introduction to the domain and range of a function: Functions", "Determining the domain of a function: Functions", "Recognizing functions: Functions", "Maximum and minimum points: Functions", "Intervals where a function is positive, negative, increasing, or decreasing: Functions", "Interpreting features of graphs: Functions", "Average rate of change: Functions", "Average rate of change word problems: Functions", "Intro to inverse functions: Functions"], "Unit 9: Scatterplots": ["Creating and interpreting scatterplots: Scatterplots", "Estimating with trend lines: Scatterplots"], "Unit 10: Data distributions": ["Displays of distributions: Data distributions", "Summarizing center of distributions (central tendency): Data distributions", "Box and whisker plots: Data distributions", "Comparing distributions: Data distributions"], "Unit 12: Sequences": ["Introduction to arithmetic sequences: Sequences", "Constructing arithmetic sequences: Sequences", "Introduction to geometric sequences: Sequences", "Constructing geometric sequences: Sequences", "Modeling with sequences: Sequences", "General sequences: Sequences"], "Unit 13: Exponents & radicals": ["Exponent properties review: Exponents & radicals", "Radicals: Exponents & radicals", "Simplifying square roots: Exponents & radicals"], "Unit 14: Exponential growth & decay": ["Exponential vs. linear growth: Exponential growth & decay", "Exponential expressions: Exponential growth & decay", "Graphs of exponential growth: Exponential growth & decay", "Exponential vs. linear growth over time: Exponential growth & decay", "Exponential growth & decay: Exponential growth & decay", "Exponential functions from tables & graphs: Exponential growth & decay", "Exponential vs. linear models: Exponential growth & decay"], "Unit 15: Performing transformations": ["Translations: Performing transformations", "Rotations: Performing transformations", "Reflections: Performing transformations", "Dilations: Performing transformations"], "Unit 16: Transformation properties and proofs": ["Dilation preserved properties: Transformation properties and proofs", "Properties & definitions of transformations: Transformation properties and proofs", "Symmetry: Transformation properties and proofs", "Proofs with transformations: Transformation properties and proofs"], "Unit 17: Congruence": ["Triangle congruence from transformations: Congruence", "Congruent triangles: Congruence", "Working with triangles: Congruence", "Theorems concerning quadrilateral properties: Congruence", "Proofs of general theorems that use triangle congruence: Congruence", "Constructing lines & angles: Congruence"], "Unit 18: Analytic geometry": ["Dividing line segments: Analytic geometry", "Problem solving with distance on the coordinate plane: Analytic geometry", "Parallel & perpendicular lines on the coordinate plane: Analytic geometry", "Equations of parallel & perpendicular lines: Analytic geometry", "Start Course challenge"]}}}}
{"course_title": "Integrated math 2", "course_url": "/math/math2", "page_contents": {"syllabus": {"topics": {"Unit 1: Absolute value & piecewise functions": ["Graphs of absolute value functions: Absolute value & piecewise functions", "Piecewise functions: Absolute value & piecewise functions"], "Unit 2: Quadratics: Multiplying & factoring": ["Multiplying monomials by polynomials: Quadratics: Multiplying & factoring", "Multiplying binomials: Quadratics: Multiplying & factoring", "Special products of binomials: Quadratics: Multiplying & factoring", "Introduction to factoring: Quadratics: Multiplying & factoring", "Factoring quadratics intro: Quadratics: Multiplying & factoring", "Factoring quadratics by grouping: Quadratics: Multiplying & factoring", "Factoring quadratics with difference of squares: Quadratics: Multiplying & factoring", "Factoring quadratics with perfect squares: Quadratics: Multiplying & factoring", "Strategy in factoring quadratics: Quadratics: Multiplying & factoring"], "Unit 3: Quadratic functions & equations": ["Intro to parabolas: Quadratic functions & equations", "Solving and graphing with factored form: Quadratic functions & equations", "Solving by taking the square root: Quadratic functions & equations", "Vertex form: Quadratic functions & equations", "Solving quadratics by factoring: Quadratic functions & equations", "The quadratic formula: Quadratic functions & equations", "Completing the square: Quadratic functions & equations", "Strategizing to solve quadratic equations: Quadratic functions & equations", "Quadratics standard form: Quadratic functions & equations", "Features & forms of quadratic functions: Quadratic functions & equations", "Comparing quadratic functions: Quadratic functions & equations", "Transforming quadratic functions: Quadratic functions & equations"], "Unit 4: Irrational numbers": ["Irrational numbers: Irrational numbers", "Sums & products of rational/irrational numbers: Irrational numbers", "Proofs concerning irrational numbers: Irrational numbers"], "The imaginary unit i: Complex numbers": ["Complex numbers introduction: Complex numbers", "The complex plane: Complex numbers", "Adding & subtracting complex numbers: Complex numbers", "Quadratic equations with complex solutions: Complex numbers"], "Unit 6: Rational exponents and radicals": ["Rational exponents: Rational exponents and radicals", "Properties of exponents (rational exponents): Rational exponents and radicals", "Equivalent forms of exponential expressions: Rational exponents and radicals", "Evaluating exponents and radicals: Rational exponents and radicals", "Solving exponential expressions using properties of exponents: Rational exponents and radicals"], "Unit 7: Exponential models": ["Interpreting the rate of change of exponential models: Exponential models", "Constructing exponential models according to rate of change: Exponential models", "Advanced interpretation of exponential models: Exponential models"], "Unit 8: Similarity": ["Introduction to triangle similarity: Similarity", "Angle bisector theorem: Similarity", "Solving problems with similar & congruent triangles: Similarity", "Proving relationships using similarity: Similarity", "Solving modeling problems with similar & congruent triangles: Similarity"], "Unit 9: Right triangles & trigonometry": ["Pythagorean theorem proofs: Right triangles & trigonometry", "Special right triangles: Right triangles & trigonometry", "Introduction to the trigonometric ratios: Right triangles & trigonometry", "Sine & cosine of complementary angles: Right triangles & trigonometry", "Modeling with right triangles: Right triangles & trigonometry"], "Unit 10: Solid geometry": ["Volume and surface area: Solid geometry", "Density: Solid geometry"], "Unit 11: Circles": ["Arc measure: Circles", "Arc length (from degrees): Circles", "Introduction to radians: Circles", "Arc length (from radians): Circles", "Sectors: Circles", "Inscribed angles: Circles", "Inscribed shapes problem solving: Circles", "Proofs with inscribed shapes: Circles", "Properties of tangents: Circles", "Constructing regular polygons inscribed in circles: Circles", "Constructing circumcircles & incircles: Circles", "Constructing a line tangent to a circle: Circles"], "Unit 12: Conic sections": ["Features of a circle: Conic sections", "Standard equation of a circle: Conic sections", "Expanded equation of a circle: Conic sections", "Focus & directrix of a parabola: Conic sections"], "Unit 13: Probability": ["Probability basics: Probability", "Counting with combinations: Probability", "Probability with counting, permutations, combinations: Probability", "Multiplication rule for independent events: Probability", "Multiplication rule for dependent events: Probability", "Addition rule for probability: Probability", "Start Course challenge"]}}}}
{"course_title": "Integrated math 3", "course_url": "/math/math3", "page_contents": {"syllabus": {"topics": {"Unit 1: Polynomial arithmetic": ["Intro to polynomials: Polynomial arithmetic", "Average rate of change of polynomials: Polynomial arithmetic", "Adding and subtracting polynomials: Polynomial arithmetic", "Multiplying monomials by polynomials: Polynomial arithmetic", "Multiplying binomials by polynomials: Polynomial arithmetic", "Special products of polynomials: Polynomial arithmetic"], "Unit 2: Polynomial factorization": ["Factoring monomials: Polynomial factorization", "Greatest common factor: Polynomial factorization", "Taking common factors: Polynomial factorization", "Factoring higher degree polynomials: Polynomial factorization", "Factoring using structure: Polynomial factorization", "Polynomial identities: Polynomial factorization", "Geometric series: Polynomial factorization"], "Unit 3: Polynomial division": ["Dividing polynomials by x: Polynomial division", "Dividing quadratics by linear factors: Polynomial division", "Dividing polynomials by linear factors: Polynomial division", "Polynomial remainder theorem: Polynomial division"], "Unit 4: Polynomial graphs": ["Zeros of polynomials: Polynomial graphs", "Positive and negative intervals of polynomials: Polynomial graphs", "End behavior of polynomials: Polynomial graphs"], "Unit 5: Logarithms": ["Introduction to logarithms: Logarithms", "The constant e and the natural logarithm: Logarithms", "Properties of logarithms: Logarithms", "Change of base formula for logarithms: Logarithms", "Solving exponential equations with logarithms: Logarithms", "Solving exponential models: Logarithms"], "Unit 6: Transformations of functions": ["Shifting functions: Transformations of functions", "Reflecting functions: Transformations of functions", "Symmetry of functions: Transformations of functions", "Scaling functions: Transformations of functions", "Putting it all together: Transformations of functions", "Graphs of square and cube root functions: Transformations of functions", "Graphs of exponential functions: Transformations of functions", "Graphs of logarithmic functions: Transformations of functions"], "Unit 7: Equations": ["Rational equations: Equations", "Square-root equations: Equations", "Extraneous solutions: Equations", "Cube-root equations: Equations", "Quadratic systems: Equations", "Solving equations by graphing: Equations"], "Unit 8: Trigonometry": ["Law of sines: Trigonometry", "Law of cosines: Trigonometry", "Solving general triangles: Trigonometry"], "Unit circle introduction: Trigonometry": ["Radians: Trigonometry", "The Pythagorean identity: Trigonometry", "Trigonometric values of special angles: Trigonometry", "Graphs of sin(x), cos(x), and tan(x): Trigonometry", "Amplitude, midline, & period: Trigonometry", "Transforming sinusoidal graphs: Trigonometry", "Graphing sinusoidal functions: Trigonometry", "Sinusoidal models: Trigonometry"], "Unit 9: Modeling": ["Modeling with function combination: Modeling", "Interpreting features of functions: Modeling", "Manipulating formulas: Modeling", "Modeling with two variables: Modeling", "Modeling with multiple variables: Modeling"], "Unit 10: Study Design": ["Samples and surveys: Study Design", "Observational studies and experiments: Study Design"], "Unit 13: Rational functions": ["Cancelling common factors: Rational functions", "End behavior of rational functions: Rational functions", "Discontinuities of rational functions: Rational functions", "Graphs of rational functions: Rational functions", "Modeling with rational functions: Rational functions", "Multiplying & dividing rational expressions: Rational functions", "Adding subtracting rational expressions intro: Rational functions", "Adding subtracting rational expressions (factored): Rational functions", "Adding subtracting rational expressions (not factored): Rational functions", "Start Course challenge"]}}}}
{"course_title": "Algebra basics", "course_url": "/math/algebra-basics", "page_contents": {"syllabus": {"topics": {"Unit 1: Foundations": ["Absolute value: Foundations", "Exponents: Foundations", "Square roots: Foundations", "Order of operations: Foundations", "Fractions: Foundations", "Decimals, fractions and percentages: Foundations", "Operations with decimals: Foundations", "Area of triangles: Foundations", "Circumference and area of circles: Foundations"], "Unit 2: Algebraic expressions": ["Introduction to variables: Algebraic expressions", "Substitution & evaluating expressions: Algebraic expressions", "Writing algebraic expressions: Algebraic expressions", "Combining like terms: Algebraic expressions", "Distributive property: Algebraic expressions", "Equivalent algebraic expressions: Algebraic expressions", "Nested fractions: Algebraic expressions"], "Unit 3: Linear equations and inequalities": ["One-step equations: Linear equations and inequalities", "Two-steps equations: Linear equations and inequalities", "Multi-step equations: Linear equations and inequalities", "One-step inequalities: Linear equations and inequalities", "Two-step inequalities: Linear equations and inequalities", "Multi-step inequalities: Linear equations and inequalities", "Writing & solving proportions: Linear equations and inequalities"], "Unit 4: Graphing lines and slope": ["Coordinate plane: Graphing lines and slope", "Solutions to two-variable linear equations: Graphing lines and slope", "x-intercepts and y-intercepts: Graphing lines and slope", "Slope: Graphing lines and slope", "Horizontal & vertical lines: Graphing lines and slope", "Slope-intercept form intro: Graphing lines and slope", "Writing slope-intercept equations: Graphing lines and slope", "Graphing two-variable inequalities: Graphing lines and slope"], "Unit 5: Systems of equations": ["Systems of equations intro: Systems of equations", "Elimination method for systems of equations: Systems of equations", "Substitution method for systems of equations: Systems of equations", "Number of solutions to systems of equations: Systems of equations"], "Unit 6: Expressions with exponents": ["Exponent properties intro : Expressions with exponents", "Negative exponents: Expressions with exponents", "Exponent properties (integer exponents) : Expressions with exponents", "Scientific notation intro: Expressions with exponents", "Scientific notation word problems: Expressions with exponents"], "Unit 7: Quadratics and polynomials": ["Adding & subtracting polynomials: Quadratics and polynomials", "Multiplying binomials: Quadratics and polynomials", "Special products of binomials: Quadratics and polynomials", "Factoring polynomials by taking common factors: Quadratics and polynomials", "Factoring quadratics 1: Quadratics and polynomials", "Factoring quadratics 2: Quadratics and polynomials", "Factoring quadratics: Difference of squares: Quadratics and polynomials", "Factoring quadratics: Perfect squares: Quadratics and polynomials", "Solving quadratic equations by factoring: Quadratics and polynomials"], "Unit 8: Equations and geometry": ["Equations & geometry: Equations and geometry", "Triangle angles: Equations and geometry", "Pythagorean theorem: Equations and geometry", "Triangle similarity intro: Equations and geometry", "Start Course challenge"]}}}}
{"course_title": "Trigonometry", "course_url": "/math/trigonometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Right triangles & trigonometry": ["Introduction to the trigonometric ratios: Right triangles & trigonometry", "Solving for a side in a right triangle using the trigonometric ratios: Right triangles & trigonometry", "Sine and cosine of complementary angles: Right triangles & trigonometry", "Modeling with right triangles: Right triangles & trigonometry"], "Unit circle introduction: Trigonometric functions": ["Radians: Trigonometric functions", "The Pythagorean identity: Trigonometric functions", "Special trigonometric values in the first quadrant: Trigonometric functions"], "Trigonometric values on the unit circle: Trigonometric functions": ["Graphs of sin(x), cos(x), and tan(x): Trigonometric functions", "Amplitude, midline, and period: Trigonometric functions", "Transforming sinusoidal graphs: Trigonometric functions", "Graphing sinusoidal functions: Trigonometric functions", "Sinusoidal models: Trigonometric functions", "Long live Tau: Trigonometric functions"], "Unit 3: Non-right triangles & trigonometry": ["Law of sines: Non-right triangles & trigonometry", "Law of cosines: Non-right triangles & trigonometry", "Solving general triangles: Non-right triangles & trigonometry"], "Unit 4: Trigonometric equations and identities": ["Inverse trigonometric functions: Trigonometric equations and identities", "Sinusoidal equations: Trigonometric equations and identities", "Sinusoidal models: Trigonometric equations and identities", "Angle addition identities: Trigonometric equations and identities", "Using trigonometric identities: Trigonometric equations and identities", "Challenging trigonometry problems: Trigonometric equations and identities", "Start Course challenge", "The reciprocal trigonometric ratios"]}}}}
{"course_title": "Precalculus", "course_url": "/math/precalculus", "page_contents": {"syllabus": {"topics": {"Unit 1: Composite and inverse functions": ["Composing functions: Composite and inverse functions", "Modeling with composite functions: Composite and inverse functions", "Invertible functions: Composite and inverse functions", "Inverse functions in graphs and tables: Composite and inverse functions", "Verifying inverse functions by composition: Composite and inverse functions"], "Trigonometric identities on the unit circle: Trigonometry": ["Inverse trigonometric functions: Trigonometry", "Law of sines: Trigonometry", "Law of cosines: Trigonometry", "Solving general triangles: Trigonometry", "Sinusoidal equations: Trigonometry", "Sinusoidal models: Trigonometry", "Angle addition identities: Trigonometry", "Using trigonometric identities: Trigonometry"], "Unit 3: Complex numbers": ["The complex plane: Complex numbers", "Distance and midpoint of complex numbers: Complex numbers", "Complex conjugates and dividing complex numbers: Complex numbers", "Identities with complex numbers: Complex numbers", "Modulus (absolute value) and argument (angle) of complex numbers: Complex numbers", "Polar form of complex numbers: Complex numbers", "Graphically multiplying complex numbers: Complex numbers", "Multiplying and dividing complex numbers in polar form: Complex numbers", "The fundamental theorem of algebra: Complex numbers"], "Unit 4: Rational functions": ["End behavior of rational functions: Rational functions", "Discontinuities of rational functions: Rational functions", "Graphs of rational functions: Rational functions", "Modeling with rational functions: Rational functions", "Multiplying and dividing rational expressions: Rational functions"], "Unit 5: Conic sections": ["Introduction to conic sections: Conic sections", "Center and radii of an ellipse: Conic sections", "Foci of an ellipse: Conic sections", "Introduction to hyperbolas: Conic sections", "Foci of a hyperbola: Conic sections", "Hyperbolas not centered at the origin: Conic sections"], "Unit 6: Vectors": ["Vectors introduction: Vectors", "Vector components: Vectors", "Magnitude of vectors: Vectors", "Scalar multiplication: Vectors", "Vector addition and subtraction: Vectors", "Direction of vectors: Vectors", "Vector components from magnitude and direction: Vectors", "Adding vectors in magnitude and direction form: Vectors", "Vectors word problems: Vectors"], "Unit 7: Matrices": ["Introduction to matrices: Matrices", "Using matrices to represent data: Matrices", "Multiplying matrices by scalars: Matrices", "Adding and subtracting matrices: Matrices", "Using matrices to manipulate data: Matrices", "Matrices as transformations of the plane: Matrices", "Using matrices to transform the plane: Matrices", "Transforming 3D and 4D vectors with matrices: Matrices", "Multiplying matrices by matrices: Matrices", "Properties of matrix multiplication: Matrices", "Representing systems of equations with matrices: Matrices", "Introduction to matrix inverses: Matrices", "Finding inverses of 2x2 matrices: Matrices", "Solving linear systems with matrices: Matrices"], "Unit 8: Probability and combinatorics": ["Venn diagrams and the addition rule: Probability and combinatorics", "Multiplication rule for probabilities: Probability and combinatorics", "Permutations: Probability and combinatorics", "Combinations: Probability and combinatorics", "Probability using combinatorics: Probability and combinatorics", "Probability distributions introduction: Probability and combinatorics", "Theoretical & empirical probability distributions: Probability and combinatorics", "Decisions with probability: Probability and combinatorics", "Expected value: Probability and combinatorics"], "Unit 9: Series": ["Geometric series: Series", "Geometric series (with summation notation): Series", "The binomial theorem: Series", "Arithmetic series: Series"], "Unit 10: Limits and continuity": ["Defining limits and using limit notation: Limits and continuity", "Estimating limit values from graphs: Limits and continuity", "Estimating limit values from tables: Limits and continuity", "Determining limits using algebraic properties of limits: limit properties: Limits and continuity", "Determining limits using algebraic properties of limits: direct substitution: Limits and continuity", "Determining limits using algebraic manipulation: Limits and continuity", "Selecting procedures for determining limits: Limits and continuity", "Determining limits using the squeeze theorem: Limits and continuity", "Exploring types of discontinuities: Limits and continuity", "Defining continuity at a point: Limits and continuity", "Confirming continuity over an interval: Limits and continuity", "Removing discontinuities: Limits and continuity", "Connecting infinite limits and vertical asymptotes: Limits and continuity", "Connecting limits at infinity and horizontal asymptotes: Limits and continuity", "Working with the intermediate value theorem: Limits and continuity", "Start Course challenge"]}}}}
{"course_title": "High school statistics", "course_url": "/math/probability", "page_contents": {"syllabus": {"topics": {"Unit 1: Displaying a single quantitative variable": ["Frequency tables and dot plots: Displaying a single quantitative variable", "Histograms: Displaying a single quantitative variable", "Mean and median in data displays: Displaying a single quantitative variable", "Interquartile range: Displaying a single quantitative variable", "Box and whisker plots: Displaying a single quantitative variable"], "Unit 2: Analyzing a single quantitative variable": ["Standard deviation: Analyzing a single quantitative variable", "Comparing distributions: Analyzing a single quantitative variable", "Percentiles and z-scores: Analyzing a single quantitative variable", "Normal distributions and the empirical rule: Analyzing a single quantitative variable", "Normal distribution calculations: Analyzing a single quantitative variable"], "Unit 3: Two-way tables": ["Two-way tables introduction: Two-way tables", "Distributions in two-way tables: Two-way tables"], "Unit 4: Scatterplots": ["Fitting trend lines to scatterplots: Scatterplots", "Analyzing trend lines in scatterplots: Scatterplots", "Residuals: Scatterplots"], "Unit 5: Study design": ["Introduction to planning a study: Study design", "Potential problems with sampling: Study design", "Sampling methods: Study design", "Introduction to experimental design: Study design", "Inference and experiments: Study design"], "Unit 6: Probability": ["Venn diagrams and the addition rule: Probability", "Multiplication rule for probabilities: Probability", "Conditional probability: Probability", "Probability from simulations: Probability", "Permutations: Probability", "Combinations: Probability", "Probability using combinatorics: Probability"], "Unit 7: Probability distributions & expected value": ["Probability distributions introduction: Probability distributions & expected value", "Theoretical & empirical probability distributions: Probability distributions & expected value", "Decisions with probability: Probability distributions & expected value", "Expected value: Probability distributions & expected value", "Start Course challenge"]}}}}
{"course_title": "Statistics & probability", "course_url": "/math/statistics-probability", "page_contents": {"syllabus": {"topics": {"Unit 1: Analyzing categorical data": ["Analyzing one categorical variable: Analyzing categorical data", "Two-way tables: Analyzing categorical data", "Distributions in two-way tables: Analyzing categorical data"], "Unit 2: Displaying and comparing quantitative data": ["Displaying quantitative data with graphs: Displaying and comparing quantitative data", "Describing and comparing distributions: Displaying and comparing quantitative data", "More on data displays: Displaying and comparing quantitative data"], "Unit 3: Summarizing quantitative data": ["Measuring center in quantitative data: Summarizing quantitative data", "Interquartile range (IQR): Summarizing quantitative data", "Variance and standard deviation of a population: Summarizing quantitative data", "Variance and standard deviation of a sample: Summarizing quantitative data", "More on standard deviation: Summarizing quantitative data", "Box and whisker plots: Summarizing quantitative data", "Other measures of spread: Summarizing quantitative data"], "Unit 4: Modeling data distributions": ["Percentiles: Modeling data distributions", "Z-scores: Modeling data distributions", "Effects of linear transformations: Modeling data distributions", "Density curves: Modeling data distributions", "Normal distributions and the empirical rule: Modeling data distributions", "Normal distribution calculations: Modeling data distributions", "More on normal distributions: Modeling data distributions"], "Unit 5: Exploring bivariate numerical data": ["Introduction to scatterplots: Exploring bivariate numerical data", "Correlation coefficients: Exploring bivariate numerical data", "Introduction to trend lines: Exploring bivariate numerical data", "Least-squares regression equations: Exploring bivariate numerical data", "Assessing the fit in least-squares regression: Exploring bivariate numerical data", "More on regression: Exploring bivariate numerical data"], "Unit 6: Study design": ["Statistical questions: Study design", "Sampling and observational studies: Study design", "Sampling methods: Study design", "Types of studies (experimental vs. observational): Study design", "Experiments: Study design"], "Unit 7: Probability": ["Basic theoretical probability: Probability", "Probability using sample spaces: Probability", "Basic set operations: Probability", "Experimental probability: Probability", "Randomness, probability, and simulation: Probability", "Addition rule: Probability", "Multiplication rule for independent events: Probability", "Multiplication rule for dependent events: Probability", "Conditional probability and independence: Probability"], "Unit 8: Counting, permutations, and combinations": ["Counting principle and factorial: Counting, permutations, and combinations", "Permutations: Counting, permutations, and combinations", "Combinations: Counting, permutations, and combinations", "Combinatorics and probability: Counting, permutations, and combinations"], "Unit 9: Random variables": ["Discrete random variables: Random variables", "Continuous random variables: Random variables", "Transforming random variables: Random variables", "Combining random variables: Random variables", "Binomial random variables: Random variables", "Binomial mean and standard deviation formulas: Random variables", "Geometric random variables: Random variables", "More on expected value: Random variables", "Poisson distribution: Random variables"], "Unit 10: Sampling distributions": ["What is a sampling distribution?: Sampling distributions", "Sampling distribution of a sample proportion: Sampling distributions", "Sampling distribution of a sample mean: Sampling distributions"], "Unit 11: Confidence intervals": ["Introduction to confidence intervals: Confidence intervals", "Estimating a population proportion: Confidence intervals", "Estimating a population mean: Confidence intervals", "More confidence interval videos: Confidence intervals"], "Unit 12: Significance tests (hypothesis testing)": ["The idea of significance tests: Significance tests (hypothesis testing)", "Error probabilities and power: Significance tests (hypothesis testing)", "Tests about a population proportion: Significance tests (hypothesis testing)", "Tests about a population mean: Significance tests (hypothesis testing)", "More significance testing videos: Significance tests (hypothesis testing)"], "Unit 13: Two-sample inference for the difference between groups": ["Comparing two proportions: Two-sample inference for the difference between groups", "Comparing two means: Two-sample inference for the difference between groups"], "Unit 14: Inference for categorical data (chi-square tests)": ["Chi-square goodness-of-fit tests: Inference for categorical data (chi-square tests)", "Chi-square tests for relationships: Inference for categorical data (chi-square tests)"], "Unit 15: Advanced regression (inference and transforming)": ["Inference about slope: Advanced regression (inference and transforming)", "Nonlinear regression: Advanced regression (inference and transforming)"], "Unit 16: Analysis of variance (ANOVA)": ["Analysis of variance (ANOVA): Analysis of variance (ANOVA)", "Start Course challenge"]}}}}
{"course_title": "College algebraNEW", "course_url": "/math/college-algebra", "page_contents": {"syllabus": {"topics": {"Unit 1: Linear equations and inequalities": ["Solving equations with one unknown: Linear equations and inequalities", "Solutions to linear equations: Linear equations and inequalities", "Multi-step linear inequalities: Linear equations and inequalities", "Compound inequalities: Linear equations and inequalities", "Modeling with linear equations and inequalities: Linear equations and inequalities", "Absolute value equations: Linear equations and inequalities"], "Unit 2: Graphs and forms of linear equations": ["Intercepts: Graphs and forms of linear equations", "Graphing from slope: Graphs and forms of linear equations", "Horizontal and vertical lines: Graphs and forms of linear equations", "Slope-intercept form: Graphs and forms of linear equations", "Point-slope form: Graphs and forms of linear equations", "Writing linear equations in any form: Graphs and forms of linear equations", "Equations of parallel and perpendicular lines: Graphs and forms of linear equations"], "Unit 3: Functions": ["Evaluating functions: Functions", "Inputs and outputs of a function: Functions", "Domain and range of a function: Functions", "Recognizing functions: Functions", "Intervals where a function is positive, negative, increasing, or decreasing: Functions", "Intro to inverse functions: Functions"], "Unit 4: Quadratics: Multiplying and factoring": ["Multiplying binomials: Quadratics: Multiplying and factoring", "Special products of binomials: Quadratics: Multiplying and factoring", "Factoring quadratics intro: Quadratics: Multiplying and factoring", "Factoring quadratics by grouping: Quadratics: Multiplying and factoring", "Factoring quadratics with difference of squares: Quadratics: Multiplying and factoring", "Factoring quadratics with perfect squares: Quadratics: Multiplying and factoring"], "Unit 5: Quadratic functions and equations": ["Solving quadratics by taking the square root: Quadratic functions and equations", "Vertex form: Quadratic functions and equations", "Solving quadratics by factoring: Quadratic functions and equations", "The quadratic formula: Quadratic functions and equations", "Completing the square: Quadratic functions and equations", "Forms and features of quadratic functions: Quadratic functions and equations"], "The imaginary unit i: Complex numbers": ["Adding and subtracting complex numbers: Complex numbers", "Complex conjugates and dividing complex numbers: Complex numbers"], "Unit 7: Exponents and radicals": ["Exponent properties (integer exponents): Exponents and radicals", "Simplifying square roots: Exponents and radicals", "Exponential expressions: Exponents and radicals", "Graphing exponential growth and decay: Exponents and radicals"], "Unit 8: Rational expressions and equations": ["Rational equations: Rational expressions and equations", "Modeling with rational expressions: Rational expressions and equations", "Multiplying and dividing rational expressions: Rational expressions and equations"], "Unit 9: Relating algebra and geometry": ["Distance and midpoints: Relating algebra and geometry", "Standard equation of a circle: Relating algebra and geometry", "Expanded equation of a circle: Relating algebra and geometry"], "Unit 10: Polynomial arithmetic": ["Average rate of change of polynomials: Polynomial arithmetic", "Adding and subtracting polynomials: Polynomial arithmetic", "Taking common factors: Polynomial arithmetic", "Factoring higher degree polynomials: Polynomial arithmetic", "Factoring using structure: Polynomial arithmetic"], "Unit 11: Advanced function types": ["Graphs of absolute value functions: Advanced function types", "Piecewise functions: Advanced function types", "Composing functions: Advanced function types", "Verifying inverse functions by composition: Advanced function types"], "Unit 12: Transformations of functions": ["Shifting functions: Transformations of functions", "Reflecting functions: Transformations of functions", "Symmetry of functions: Transformations of functions", "Scaling functions: Transformations of functions"], "Unit 13: Rational exponents and radicals": ["Rational exponents: Rational exponents and radicals", "Properties of exponents (rational exponents): Rational exponents and radicals", "Evaluating exponents and radicals: Rational exponents and radicals", "Solving exponential equations using properties of exponents: Rational exponents and radicals", "Interpreting the rate of change of exponential models: Rational exponents and radicals", "Square-root equations: Rational exponents and radicals"], "Unit 14: Logarithms": ["Introduction to logarithms: Logarithms", "Properties of logarithms: Logarithms", "The change of base formula for logarithms: Logarithms", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Calculus AB", "course_url": "/math/ap-calculus-ab", "page_contents": {"syllabus": {"topics": {"Unit 10Unit 10: AP\u00ae\ufe0e Calculus AB Standards mappings": ["Start Course challenge", "Watch an introduction video3:263 minutes 26 seconds", "Learn more", "Learn more", "Watch an introduction video3:263 minutes 26 seconds"], "Unit 1: Limits and continuity": ["About the course: Limits and continuity", "Defining limits and using limit notation: Limits and continuity", "Estimating limit values from graphs: Limits and continuity", "Estimating limit values from tables: Limits and continuity", "Determining limits using algebraic properties of limits: limit properties: Limits and continuity", "Determining limits using algebraic properties of limits: direct substitution: Limits and continuity", "Determining limits using algebraic manipulation: Limits and continuity", "Selecting procedures for determining limits: Limits and continuity", "Determining limits using the squeeze theorem: Limits and continuity", "Exploring types of discontinuities: Limits and continuity", "Defining continuity at a point: Limits and continuity", "Confirming continuity over an interval: Limits and continuity", "Removing discontinuities: Limits and continuity", "Connecting infinite limits and vertical asymptotes: Limits and continuity", "Connecting limits at infinity and horizontal asymptotes: Limits and continuity", "Working with the intermediate value theorem: Limits and continuity", "Optional videos: Limits and continuity"], "Unit 2: Differentiation: definition and basic derivative rules": ["Defining average and instantaneous rates of change at a point: Differentiation: definition and basic derivative rules", "Defining the derivative of a function and using derivative notation: Differentiation: definition and basic derivative rules", "Estimating derivatives of a function at a point: Differentiation: definition and basic derivative rules", "Connecting differentiability and continuity: determining when derivatives do and do not exist: Differentiation: definition and basic derivative rules", "Applying the power rule: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: introduction: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule: Differentiation: definition and basic derivative rules", "Derivatives of cos(x), sin(x), \ud835\udc52\u02e3, and ln(x): Differentiation: definition and basic derivative rules", "The product rule: Differentiation: definition and basic derivative rules", "The quotient rule: Differentiation: definition and basic derivative rules", "Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions: Differentiation: definition and basic derivative rules", "Optional videos: Differentiation: definition and basic derivative rules"], "Unit 3: Differentiation: composite, implicit, and inverse functions": ["The chain rule: introduction: Differentiation: composite, implicit, and inverse functions", "The chain rule: further practice: Differentiation: composite, implicit, and inverse functions", "Implicit differentiation: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse functions: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse trigonometric functions: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: strategy: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: multiple rules: Differentiation: composite, implicit, and inverse functions", "Calculating higher-order derivatives: Differentiation: composite, implicit, and inverse functions", "Further practice connecting derivatives and limits: Differentiation: composite, implicit, and inverse functions", "Optional videos: Differentiation: composite, implicit, and inverse functions"], "Unit 4: Contextual applications of differentiation": ["Interpreting the meaning of the derivative in context: Contextual applications of differentiation", "Straight-line motion: connecting position, velocity, and acceleration: Contextual applications of differentiation", "Rates of change in other applied contexts (non-motion problems): Contextual applications of differentiation", "Introduction to related rates: Contextual applications of differentiation", "Approximating values of a function using local linearity and linearization: Contextual applications of differentiation", "Using L\u2019H\u00f4pital\u2019s rule for finding limits of indeterminate forms: Contextual applications of differentiation", "Optional videos: Contextual applications of differentiation"], "Unit 5: Applying derivatives to analyze functions": ["Using the mean value theorem: Applying derivatives to analyze functions", "Extreme value theorem, global versus local extrema, and critical points: Applying derivatives to analyze functions", "Determining intervals on which a function is increasing or decreasing: Applying derivatives to analyze functions", "Using the first derivative test to find relative (local) extrema: Applying derivatives to analyze functions", "Using the candidates test to find absolute (global) extrema: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: graphical: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: algebraic: Applying derivatives to analyze functions", "Using the second derivative test to find extrema: Applying derivatives to analyze functions", "Sketching curves of functions and their derivatives: Applying derivatives to analyze functions", "Connecting a function, its first derivative, and its second derivative: Applying derivatives to analyze functions", "Solving optimization problems: Applying derivatives to analyze functions", "Exploring behaviors of implicit relations: Applying derivatives to analyze functions"], "Unit 6: Integration and accumulation of change": ["Exploring accumulations of change: Integration and accumulation of change", "Approximating areas with Riemann sums: Integration and accumulation of change", "Riemann sums, summation notation, and definite integral notation: Integration and accumulation of change", "The fundamental theorem of calculus and accumulation functions: Integration and accumulation of change", "Interpreting the behavior of accumulation functions involving area: Integration and accumulation of change", "Applying properties of definite integrals: Integration and accumulation of change", "The fundamental theorem of calculus and definite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals: Integration and accumulation of change", "Integrating using substitution: Integration and accumulation of change", "Integrating functions using long division and completing the square: Integration and accumulation of change", "Optional videos: Integration and accumulation of change"], "Unit 7: Differential equations": ["Modeling situations with differential equations: Differential equations", "Verifying solutions for differential equations: Differential equations", "Sketching slope fields: Differential equations", "Reasoning using slope fields: Differential equations", "Finding general solutions using separation of variables: Differential equations", "Finding particular solutions using initial conditions and separation of variables: Differential equations", "Exponential models with differential equations: Differential equations"], "Unit 8: Applications of integration": ["Finding the average value of a function on an interval: Applications of integration", "Connecting position, velocity, and acceleration functions using integrals: Applications of integration", "Using accumulation functions and definite integrals in applied contexts: Applications of integration", "Finding the area between curves expressed as functions of x: Applications of integration", "Finding the area between curves expressed as functions of y: Applications of integration", "Volumes with cross sections: squares and rectangles: Applications of integration", "Volumes with cross sections: triangles and semicircles: Applications of integration", "Volume with disc method: revolving around x- or y-axis: Applications of integration", "Volume with disc method: revolving around other axes: Applications of integration", "Volume with washer method: revolving around x- or y-axis: Applications of integration", "Volume with washer method: revolving around other axes: Applications of integration"], "Unit 9: AP Calculus AB solved free response questions from past exams": ["AP Calculus AB 2017 free response: AP Calculus AB solved free response questions from past exams", "AP Calculus AB 2015 free response: AP Calculus AB solved free response questions from past exams", "AP Calculus AB 2011 free response: AP Calculus AB solved free response questions from past exams"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Calculus BC", "course_url": "/math/ap-calculus-bc", "page_contents": {"syllabus": {"topics": {"Unit 1: Limits and continuity": ["About the course: Limits and continuity", "Defining limits and using limit notation: Limits and continuity", "Estimating limit values from graphs: Limits and continuity", "Estimating limit values from tables: Limits and continuity", "Determining limits using algebraic properties of limits: limit properties: Limits and continuity", "Determining limits using algebraic properties of limits: direct substitution: Limits and continuity", "Determining limits using algebraic manipulation: Limits and continuity", "Selecting procedures for determining limits: Limits and continuity", "Determining limits using the squeeze theorem: Limits and continuity", "Exploring types of discontinuities: Limits and continuity", "Defining continuity at a point: Limits and continuity", "Confirming continuity over an interval: Limits and continuity", "Removing discontinuities: Limits and continuity", "Connecting infinite limits and vertical asymptotes: Limits and continuity", "Connecting limits at infinity and horizontal asymptotes: Limits and continuity", "Working with the intermediate value theorem: Limits and continuity", "Optional videos: Limits and continuity"], "Unit 2: Differentiation: definition and basic derivative rules": ["Defining average and instantaneous rates of change at a point: Differentiation: definition and basic derivative rules", "Defining the derivative of a function and using derivative notation: Differentiation: definition and basic derivative rules", "Estimating derivatives of a function at a point: Differentiation: definition and basic derivative rules", "Connecting differentiability and continuity: determining when derivatives do and do not exist: Differentiation: definition and basic derivative rules", "Applying the power rule: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: introduction: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule: Differentiation: definition and basic derivative rules", "Derivatives of cos(x), sin(x), \ud835\udc52\u02e3, and ln(x): Differentiation: definition and basic derivative rules", "The product rule: Differentiation: definition and basic derivative rules", "The quotient rule: Differentiation: definition and basic derivative rules", "Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions: Differentiation: definition and basic derivative rules", "Optional videos: Differentiation: definition and basic derivative rules"], "Unit 3: Differentiation: composite, implicit, and inverse functions": ["The chain rule: introduction: Differentiation: composite, implicit, and inverse functions", "The chain rule: further practice: Differentiation: composite, implicit, and inverse functions", "Implicit differentiation: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse functions: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse trigonometric functions: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: strategy: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: multiple rules: Differentiation: composite, implicit, and inverse functions", "Calculating higher-order derivatives: Differentiation: composite, implicit, and inverse functions", "Further practice connecting derivatives and limits: Differentiation: composite, implicit, and inverse functions", "Optional videos: Differentiation: composite, implicit, and inverse functions"], "Unit 4: Contextual applications of differentiation": ["Interpreting the meaning of the derivative in context: Contextual applications of differentiation", "Straight-line motion: connecting position, velocity, and acceleration: Contextual applications of differentiation", "Rates of change in other applied contexts (non-motion problems): Contextual applications of differentiation", "Introduction to related rates: Contextual applications of differentiation", "Approximating values of a function using local linearity and linearization: Contextual applications of differentiation", "Using L\u2019H\u00f4pital\u2019s rule for finding limits of indeterminate forms: Contextual applications of differentiation", "Optional videos: Contextual applications of differentiation"], "Unit 5: Applying derivatives to analyze functions": ["Using the mean value theorem: Applying derivatives to analyze functions", "Extreme value theorem, global versus local extrema, and critical points: Applying derivatives to analyze functions", "Determining intervals on which a function is increasing or decreasing: Applying derivatives to analyze functions", "Using the first derivative test to find relative (local) extrema: Applying derivatives to analyze functions", "Using the candidates test to find absolute (global) extrema: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: graphical: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: algebraic: Applying derivatives to analyze functions", "Using the second derivative test to find extrema: Applying derivatives to analyze functions", "Sketching curves of functions and their derivatives: Applying derivatives to analyze functions", "Connecting a function, its first derivative, and its second derivative: Applying derivatives to analyze functions", "Solving optimization problems: Applying derivatives to analyze functions", "Exploring behaviors of implicit relations: Applying derivatives to analyze functions"], "Unit 6: Integration and accumulation of change": ["Exploring accumulations of change: Integration and accumulation of change", "Approximating areas with Riemann sums: Integration and accumulation of change", "Riemann sums, summation notation, and definite integral notation: Integration and accumulation of change", "The fundamental theorem of calculus and accumulation functions: Integration and accumulation of change", "Interpreting the behavior of accumulation functions involving area: Integration and accumulation of change", "Applying properties of definite integrals: Integration and accumulation of change", "The fundamental theorem of calculus and definite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals: Integration and accumulation of change", "Integrating using substitution: Integration and accumulation of change", "Integrating functions using long division and completing the square: Integration and accumulation of change", "Using integration by parts: Integration and accumulation of change", "Integrating using linear partial fractions: Integration and accumulation of change", "Evaluating improper integrals: Integration and accumulation of change", "Optional videos: Integration and accumulation of change"], "Unit 7: Differential equations": ["Modeling situations with differential equations: Differential equations", "Verifying solutions for differential equations: Differential equations", "Sketching slope fields: Differential equations", "Reasoning using slope fields: Differential equations", "Approximating solutions using Euler\u2019s method: Differential equations", "Finding general solutions using separation of variables: Differential equations", "Finding particular solutions using initial conditions and separation of variables: Differential equations", "Exponential models with differential equations: Differential equations", "Logistic models with differential equations: Differential equations"], "Unit 8: Applications of integration": ["Finding the average value of a function on an interval: Applications of integration", "Connecting position, velocity, and acceleration functions using integrals: Applications of integration", "Using accumulation functions and definite integrals in applied contexts: Applications of integration", "Finding the area between curves expressed as functions of x: Applications of integration", "Finding the area between curves expressed as functions of y: Applications of integration", "Volumes with cross sections: squares and rectangles: Applications of integration", "Volumes with cross sections: triangles and semicircles: Applications of integration", "Volume with disc method: revolving around x- or y-axis: Applications of integration", "Volume with disc method: revolving around other axes: Applications of integration", "Volume with washer method: revolving around x- or y-axis: Applications of integration", "Volume with washer method: revolving around other axes: Applications of integration", "The arc length of a smooth, planar curve and distance traveled: Applications of integration"], "Unit 9: Parametric equations, polar coordinates, and vector-valued functions": ["Defining and differentiating parametric equations: Parametric equations, polar coordinates, and vector-valued functions", "Second derivatives of parametric equations: Parametric equations, polar coordinates, and vector-valued functions", "Finding arc lengths of curves given by parametric equations: Parametric equations, polar coordinates, and vector-valued functions", "Defining and differentiating vector-valued functions: Parametric equations, polar coordinates, and vector-valued functions", "Solving motion problems using parametric and vector-valued functions: Parametric equations, polar coordinates, and vector-valued functions", "Defining polar coordinates and differentiating in polar form: Parametric equations, polar coordinates, and vector-valued functions", "Finding the area of a polar region or the area bounded by a single polar curve: Parametric equations, polar coordinates, and vector-valued functions", "Finding the area of the region bounded by two polar curves: Parametric equations, polar coordinates, and vector-valued functions", "Calculator-active practice: Parametric equations, polar coordinates, and vector-valued functions"], "Unit 10: Infinite sequences and series": ["Defining convergent and divergent infinite series: Infinite sequences and series", "Working with geometric series: Infinite sequences and series", "The nth-term test for divergence: Infinite sequences and series", "Integral test for convergence: Infinite sequences and series", "Harmonic series and p-series: Infinite sequences and series", "Comparison tests for convergence: Infinite sequences and series", "Alternating series test for convergence: Infinite sequences and series", "Ratio test for convergence: Infinite sequences and series", "Determining absolute or conditional convergence: Infinite sequences and series", "Alternating series error bound: Infinite sequences and series", "Finding Taylor polynomial approximations of functions: Infinite sequences and series", "Lagrange error bound: Infinite sequences and series", "Radius and interval of convergence of power series: Infinite sequences and series", "Finding Taylor or Maclaurin series for a function: Infinite sequences and series", "Representing functions as power series: Infinite sequences and series", "Optional videos: Infinite sequences and series"], "Unit 11: AP Calculus BC solved exams": ["AP Calculus BC 2017: AP Calculus BC solved exams", "AP Calculus BC 2015: AP Calculus BC solved exams", "AP Calculus BC 2011: AP Calculus BC solved exams", "AP Calculus BC 2008: AP Calculus BC solved exams"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Statistics", "course_url": "/math/ap-statistics", "page_contents": {"syllabus": {"topics": {"Unit 1: Exploring categorical data": ["The language of variation: Variables: Exploring categorical data", "Representing a categorical variable with graphs: Exploring categorical data", "Representing two categorical variables: Exploring categorical data", "Statistics for two categorical variables: Exploring categorical data"], "Unit 2: Exploring one-variable quantitative data: Displaying and describing": ["Representing a quantitative variable with dot plots: Exploring one-variable quantitative data: Displaying and describing", "Representing a quantitative variable with histograms and stem plots: Exploring one-variable quantitative data: Displaying and describing", "Describing the distribution of a quantitative variable: Exploring one-variable quantitative data: Displaying and describing", "Comparing distributions of a quantitative variable: Exploring one-variable quantitative data: Displaying and describing"], "Unit 3: Exploring one-variable quantitative data: Summary statistics": ["Measuring center in quantitative data: Exploring one-variable quantitative data: Summary statistics", "Measuring variability in quantitative data: Exploring one-variable quantitative data: Summary statistics", "Effects of linear transformations: Exploring one-variable quantitative data: Summary statistics", "More on standard deviation (optional): Exploring one-variable quantitative data: Summary statistics", "Graphical representations of summary statistics: Exploring one-variable quantitative data: Summary statistics"], "Unit 4: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution": ["Percentiles: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Z-scores: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Density curves: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Normal distributions and the empirical rule: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Normal distribution calculations: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution"], "Unit 5: Exploring two-variable quantitative data": ["Representing the relationship between two quantitative variables: Exploring two-variable quantitative data", "Correlation: Exploring two-variable quantitative data", "Residuals: Exploring two-variable quantitative data", "Least-squares regression: Exploring two-variable quantitative data"], "Unit 6: Collecting data": ["Introduction to planning a study: Collecting data", "Potential problems with sampling: Collecting data", "Random sampling and data collection: Collecting data", "Introduction to experimental design: Collecting data", "Inference and experiments: Collecting data"], "Unit 7: Probability": ["Estimating probabilities using simulation: Probability", "Mutually exclusive events and unions of events: Probability", "Conditional probability: Probability", "Independent versus dependent events and the multiplication rule: Probability"], "Unit 8: Random variables and probability distributions": ["Introduction to random variables and probability distributions: Random variables and probability distributions", "Mean and standard deviation of random variables: Random variables and probability distributions", "Transforming random variables: Random variables and probability distributions", "Combining random variables: Random variables and probability distributions", "Introduction to the binomial distribution: Random variables and probability distributions", "Parameters for a binomial distribution: Random variables and probability distributions", "The geometric distribution: Random variables and probability distributions"], "Unit 9: Sampling distributions": ["The normal distribution, revisited: Sampling distributions", "The central limit theorem: Sampling distributions", "Biased and unbiased point estimates: Sampling distributions", "Sampling distributions for sample proportions: Sampling distributions", "Sampling distributions for differences in sample proportions: Sampling distributions", "Sampling distributions for sample means: Sampling distributions", "Sampling distributions for differences in sample means: Sampling distributions"], "Unit 10: Inference for categorical data: Proportions": ["Introduction to confidence intervals: Inference for categorical data: Proportions", "Confidence intervals for proportions: Inference for categorical data: Proportions", "The idea of significance tests: Inference for categorical data: Proportions", "Setting up a test for a population proportion: Inference for categorical data: Proportions", "Carrying out a test for a population proportion: Inference for categorical data: Proportions", "Concluding a test for a population proportion: Inference for categorical data: Proportions", "Potential errors when performing tests: Inference for categorical data: Proportions", "Confidence intervals for the difference of two proportions: Inference for categorical data: Proportions", "Testing for the difference of two population proportions: Inference for categorical data: Proportions"], "Unit 11: Inference for quantitative data: Means": ["Constructing a confidence interval for a population mean: Inference for quantitative data: Means", "Setting up a test for a population mean: Inference for quantitative data: Means", "Carrying out a test for a population mean: Inference for quantitative data: Means", "Confidence intervals for the difference of two means: Inference for quantitative data: Means", "Testing for the difference of two population means: Inference for quantitative data: Means"], "Unit 12: Inference for categorical data: Chi-square": ["Chi-square test for goodness of fit: Inference for categorical data: Chi-square", "Chi square tests for relationships (homogeneity or independence): Inference for categorical data: Chi-square"], "Unit 13: Inference for quantitative data: slopes": ["Confidence intervals for the slope of a regression model: Inference for quantitative data: slopes", "Testing for the slope of a regression model: Inference for quantitative data: slopes"], "Unit 14: Prepare for the 2022 AP\u00ae\ufe0e Statistics Exam": ["Prepare for the exam: Prepare for the 2022 AP\u00ae\ufe0e Statistics Exam", "Start Course challenge"]}}}}
{"course_title": "Multivariable calculus", "course_url": "/math/multivariable-calculus", "page_contents": {"syllabus": {"topics": {"Unit 1: Thinking about multivariable functions": ["Introduction to multivariable calculus: Thinking about multivariable functions", "Visualizing scalar-valued functions: Thinking about multivariable functions", "Visualizing vector-valued functions: Thinking about multivariable functions", "Transformations: Thinking about multivariable functions"], "Unit 2: Derivatives of multivariable functions": ["Partial derivatives: Derivatives of multivariable functions", "Gradient and directional derivatives: Derivatives of multivariable functions", "Differentiating parametric curves: Derivatives of multivariable functions", "Multivariable chain rule: Derivatives of multivariable functions", "Curvature: Derivatives of multivariable functions", "Partial derivatives of vector-valued functions: Derivatives of multivariable functions", "Divergence: Derivatives of multivariable functions", "Curl: Derivatives of multivariable functions", "Laplacian: Derivatives of multivariable functions", "Jacobian: Derivatives of multivariable functions"], "Unit 3: Applications of multivariable derivatives": ["Tangent planes and local linearization: Applications of multivariable derivatives", "Quadratic approximations: Applications of multivariable derivatives", "Optimizing multivariable functions: Applications of multivariable derivatives", "Lagrange multipliers and constrained optimization: Applications of multivariable derivatives"], "Unit 4: Integrating multivariable functions": ["Line integrals for scalar functions: Integrating multivariable functions", "Line integrals in vector fields: Integrating multivariable functions", "Double integrals: Integrating multivariable functions", "Triple integrals: Integrating multivariable functions", "Surface integral preliminaries: Integrating multivariable functions", "Surface integrals: Integrating multivariable functions", "Flux in 3D: Integrating multivariable functions"], "Unit 5: Green's, Stokes', and the divergence theorems": ["2D divergence theorem: Green's, Stokes', and the divergence theorems", "Stokes' theorem: Green's, Stokes', and the divergence theorems", "3D divergence theorem: Green's, Stokes', and the divergence theorems", "Proof of Stokes' theorem: Green's, Stokes', and the divergence theorems", "Types of regions in three dimensions: Green's, Stokes', and the divergence theorems", "Divergence theorem proof: Green's, Stokes', and the divergence theorems", "Start Course challenge"]}}}}
{"course_title": "Differential equations", "course_url": "/math/differential-equations", "page_contents": {"syllabus": {"topics": {"Unit 1: First order differential equations": ["Intro to differential equations: First order differential equations", "Slope fields: First order differential equations", "Euler's Method: First order differential equations", "Separable equations: First order differential equations", "Exponential models: First order differential equations", "Logistic models: First order differential equations", "Exact equations and integrating factors: First order differential equations", "Homogeneous equations: First order differential equations"], "Unit 2: Second order linear equations": ["Linear homogeneous equations: Second order linear equations", "Complex and repeated roots of characteristic equation: Second order linear equations", "Method of undetermined coefficients: Second order linear equations"], "Unit 3: Laplace transform": ["Laplace transform: Laplace transform", "Properties of the Laplace transform: Laplace transform", "Laplace transform to solve a differential equation: Laplace transform", "The convolution integral: Laplace transform"]}}}}
{"course_title": "Linear algebra", "course_url": "/math/linear-algebra", "page_contents": {"syllabus": {"topics": {"Unit 1: Vectors and spaces": ["Vectors: Vectors and spaces", "Linear combinations and spans: Vectors and spaces", "Linear dependence and independence: Vectors and spaces", "Subspaces and the basis for a subspace: Vectors and spaces", "Vector dot and cross products: Vectors and spaces", "Matrices for solving systems by elimination: Vectors and spaces", "Null space and column space: Vectors and spaces"], "Unit 2: Matrix transformations": ["Functions and linear transformations: Matrix transformations", "Linear transformation examples: Matrix transformations", "Transformations and matrix multiplication: Matrix transformations", "Inverse functions and transformations: Matrix transformations", "Finding inverses and determinants: Matrix transformations", "More determinant depth: Matrix transformations", "Transpose of a matrix: Matrix transformations"], "Unit 3: Alternate coordinate systems (bases)": ["Orthogonal complements: Alternate coordinate systems (bases)", "Orthogonal projections: Alternate coordinate systems (bases)", "Change of basis: Alternate coordinate systems (bases)", "Orthonormal bases and the Gram-Schmidt process: Alternate coordinate systems (bases)", "Eigen-everything: Alternate coordinate systems (bases)"]}}}}
{"course_title": "SAT (Fall 2023)", "course_url": "/sat/start", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Digital SATNEW", "course_url": "/digital-sat/start", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Counting": ["Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting"], "Unit 2: Addition and subtraction intro": ["What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro"], "Unit 3: Place value (tens and hundreds)": ["Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)"], "Unit 4: Addition and subtraction within 20": ["Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20"], "Unit 5: Addition and subtraction within 100": ["Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100"], "Unit 6: Addition and subtraction within 1000": ["Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000"], "Unit 7: Measurement and data": ["Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data"], "Unit 8: Geometry": ["Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Add and subtract within 20": ["Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20"], "Unit 2: Place value": ["Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value"], "Unit 3: Add and subtract within 100": ["Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100"], "Unit 4: Add and subtract within 1,000": ["Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000"], "Unit 6: Measurement": ["Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement"], "Unit 7: Data": ["Bar graphs: Data", "Line plots: Data"], "Unit 8: Geometry": ["Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Intro to multiplication": ["Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication"], "Unit 3: Addition, subtraction, and estimation": ["Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation"], "Unit 4: Intro to division": ["Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division"], "Unit 5: Understand fractions": ["Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions"], "Unit 6: Equivalent fractions and comparing fractions": ["Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions"], "Unit 7: More with multiplication and division": ["Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division"], "Unit 8: Arithmetic patterns and problem solving": ["2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving"], "Count unit squares to find area: Area": ["Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area"], "Unit 11: Perimeter": ["Perimeter: Perimeter", "Perimeter word problems: Perimeter"], "Unit 12: Time": ["Time on number line: Time", "Telling time: Time", "Elapsed time: Time"], "Unit 13: Measurement": ["Mass: Measurement", "Volume: Measurement"], "Unit 14: Represent and interpret data": ["Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Place value": ["Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value"], "Unit 2: Addition, subtraction, and estimation": ["Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation"], "Unit 3: Multiply by 1-digit numbers": ["Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers"], "Unit 4: Multiply by 2-digit numbers": ["Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers"], "Unit 5: Division": ["Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division"], "Unit 6: Factors, multiples and patterns": ["Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns"], "Unit 7: Equivalent fractions and comparing fractions": ["Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions"], "Unit 8: Add and subtract fractions": ["Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions"], "Unit 9: Multiply fractions": ["Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions"], "Unit 10: Understand decimals": ["Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals"], "Unit 11: Plane figures": ["Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures"], "Unit 12: Measuring angles": ["Measuring angles: Measuring angles", "Decomposing angles: Measuring angles"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Decimal place value": ["Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value"], "Unit 2: Add decimals": ["Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals"], "Unit 3: Subtract decimals": ["Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals"], "Unit 4: Add and subtract fractions": ["Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions"], "Unit 5: Multi-digit multiplication and division": ["Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division"], "Unit 6: Multiply fractions": ["Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions"], "Unit 7: Divide fractions": ["Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions"], "Unit 8: Multiply decimals": ["Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals"], "Unit 9: Divide decimals": ["Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals"], "Unit 10: Powers of ten": ["Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten"], "Volume with unit cubes: Volume": ["Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume"], "Unit 13: Algebraic thinking": ["Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking"], "Unit 15: Line plots": ["Graph data on line plots: Line plots", "Interpret data on line plots: Line plots"], "Unit 16: Properties of shapes": ["Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Ratios": ["Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios"], "Unit 2: Arithmetic with rational numbers": ["Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers"], "Unit 3: Rates and percentages": ["Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 4: Exponents and order of operations": ["Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations"], "Unit 5: Negative numbers": ["Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers"], "Unit 6: Variables & expressions": ["Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions"], "Unit 7: Equations & inequalities": ["Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities"], "Unit 8: Plane figures": ["Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures"], "Unit 9: Coordinate plane": ["Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane"], "Unit 10: 3D figures": ["Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures"], "Unit 11: Data and statistics": ["Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"Geometry: Unit test": ["Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles"], "Unit 1: Proportional relationships": ["Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships"], "Unit 2: Rates and percentages": ["Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 3: Integers: addition and subtraction": ["Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction"], "Unit 4: Rational numbers: addition and subtraction": ["Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction"], "Unit 5: Negative numbers: multiplication and division": ["Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division"], "Unit 6: Expressions, equations, & inequalities": ["The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities"], "Unit 7: Statistics and probability": ["Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability"], "Unit 8: Scale copies": ["Scale copies: Scale copies", "Scale drawings: Scale copies"], "Unit 9: Geometry": ["Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Numbers and operations": ["Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations"], "Unit 2: Solving equations with one unknown": ["Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown"], "Unit 3: Linear equations and functions": ["Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions"], "Unit 4: Systems of equations": ["Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 5: Geometry": ["Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry"], "Unit 6: Geometric transformations": ["Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations"], "Unit 7: Data and modeling": ["Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for addition and subtraction": ["Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction"], "Unit 2: Get ready for multiplication and division": ["Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division"], "Unit 3: Get ready for fractions": ["Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions"], "Unit 4: Get ready for patterns and problem solving": ["Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving"], "Units of length: Get ready for area and perimeter": ["Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter"], "Unit 7: Get ready for data": ["Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for place value": ["Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value"], "Unit 2: Get ready for addition, subtraction, and estimation": ["Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation"], "Unit 3: Get ready for multiplication": ["Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication"], "Unit 4: Get ready for division": ["Division intro: Get ready for division", "Relate multiplication and division: Get ready for division"], "Unit 5: Get ready for fractions": ["Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions"], "Unit 7: Get ready for area and perimeter": ["Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for decimal place value": ["Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value"], "Unit 2: Get ready for adding and subtracting decimals": ["Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals"], "Unit 3: Get ready for adding and subtracting fractions": ["Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions"], "Unit 4: Get ready for multiplication and division with whole numbers and decimals": ["Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals"], "Unit 5: Get ready for multiplying and dividing fractions": ["Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions"], "Unit 6: Get ready for powers of 10": ["How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10"], "Unit 8: Get ready for properties of shapes": ["Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Convert units of measure: Get ready for ratios, rates, and percentages": ["Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages"], "Divide unit fractions by whole numbers: Get ready for arithmetic operations": ["Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations"], "Unit 3: Get ready for negative numbers": ["Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers"], "Unit 4: Get ready for equations, expressions, and inequalities": ["Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities"], "Unit 5: Get ready for geometry": ["Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for negative number operations": ["Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations"], "Unit 2: Get ready for fractions, decimals, & percentages": ["Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages"], "Unit 3: Get ready for rates & proportional relationships": ["Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships"], "Unit 4: Get ready for expressions, equations, & inequalities": ["Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities"], "Unit 5: Get ready for geometry": ["Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry"], "Unit 6: Get ready for statistics & probability": ["Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for numbers and operations": ["Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations"], "Unit 2: Get ready for solving equations and systems of equations": ["Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations"], "Unit 3: Get ready for linear equations and functions": ["Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions"], "Unit 4: Get ready for geometry": ["Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for equations & inequalities": ["Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities"], "Unit 3: Get ready for linear relationships": ["Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships"], "Unit 4: Get ready for functions & sequences": ["Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences"], "Unit 5: Get ready for exponents, radicals, & irrational numbers": ["Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers"], "Unit 6: Get ready for quadratics": ["Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for congruence, similarity, and triangle trigonometry": ["Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry"], "Unit 2: Get ready for analytic geometry": ["Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry"], "Unit 3: Get ready for conic sections": ["Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections"], "Unit 4: Get ready for circles and solid geometry": ["Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for polynomial operations and complex numbers": ["Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers"], "Unit 2: Get ready for equations": ["Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations"], "Unit 3: Get ready for transformations of functions and modeling with functions": ["Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions"], "Unit 4: Get ready for exponential and logarithmic relationships": ["Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships"], "Unit 5: Get ready for trigonometry": ["Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry"], "Unit 6: Get ready for rational functions": ["Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Get ready for Precalculus", "course_url": "/math/get-ready-for-precalculus", "page_contents": {"syllabus": {"topics": {"The imaginary unit i: Get ready for complex numbers": ["Complex numbers introduction: Get ready for complex numbers", "The complex plane: Get ready for complex numbers", "Adding and subtracting complex numbers: Get ready for complex numbers", "Quadratic equations with complex solutions: Get ready for complex numbers"], "Unit 2: Get ready for polynomials": ["Adding and subtracting polynomials: Get ready for polynomials", "Multiplying binomials by polynomials: Get ready for polynomials", "Special products of polynomials: Get ready for polynomials", "Factoring higher degree polynomials: Get ready for polynomials", "Factoring using structure: Get ready for polynomials", "Zeros of polynomials: Get ready for polynomials", "Dividing polynomials by x: Get ready for polynomials", "Dividing quadratics by linear factors: Get ready for polynomials", "Dividing polynomials by linear factors: Get ready for polynomials"], "Unit 3: Get ready for composite and inverse functions": ["Shifting functions: Get ready for composite and inverse functions", "Reflecting functions: Get ready for composite and inverse functions", "Scaling functions: Get ready for composite and inverse functions", "Identifying function transformations: Get ready for composite and inverse functions", "Intro to domain and range of a function: Get ready for composite and inverse functions", "Intro to inverse functions: Get ready for composite and inverse functions"], "Unit circle introduction: Get ready for trigonometry": ["Radians: Get ready for trigonometry", "The Pythagorean identity: Get ready for trigonometry", "Trigonometric values of special angles: Get ready for trigonometry", "Graphing sinusoidal functions: Get ready for trigonometry", "Sinusoidal models: Get ready for trigonometry"], "Unit 5: Get ready for vectors and matrices": ["Equivalent systems of equations and the elimination method: Get ready for vectors and matrices", "Dilations: Get ready for vectors and matrices", "Solving triangles using the trigonometric ratios: Get ready for vectors and matrices"], "Unit 6: Get ready for series": ["Intro to sequences: Get ready for series", "Constructing arithmetic sequences: Get ready for series", "Constructing geometric sequences: Get ready for series", "Modeling with sequences: Get ready for series", "General sequences: Get ready for series", "Geometric series: Get ready for series"], "Unit 7: Get ready for conic sections": ["Graphs of circles intro: Get ready for conic sections", "Standard equation of a circle: Get ready for conic sections", "Expanded equation of a circle: Get ready for conic sections", "Focus and directrix of a parabola: Get ready for conic sections"], "Unit 8: Get ready for probability and combinatorics": ["Basic theoretical probability: Get ready for probability and combinatorics", "Probability using sample spaces: Get ready for probability and combinatorics", "Basic set operations: Get ready for probability and combinatorics", "Experimental probability: Get ready for probability and combinatorics", "Randomness, probability, and simulation: Get ready for probability and combinatorics", "Addition rule: Get ready for probability and combinatorics", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Calculus", "course_url": "/math/get-ready-for-ap-calc", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for limits and continuity": ["Evaluating functions: Get ready for limits and continuity", "Inputs and outputs of a function: Get ready for limits and continuity", "Composing functions: Get ready for limits and continuity", "Piecewise functions: Get ready for limits and continuity", "Introduction to factoring: Get ready for limits and continuity", "Factoring quadratics intro: Get ready for limits and continuity", "Factoring quadratics by grouping: Get ready for limits and continuity", "Factoring quadratics with difference of squares: Get ready for limits and continuity", "Factoring quadratics with perfect squares: Get ready for limits and continuity", "Factoring higher degree polynomials: Get ready for limits and continuity", "Introduction to the trigonometric ratios: Get ready for limits and continuity"], "Unit circle introduction: Get ready for limits and continuity": ["Radians: Get ready for limits and continuity", "The Pythagorean identity: Get ready for limits and continuity", "Special trigonometric values in the first quadrant: Get ready for limits and continuity"], "Trigonometric identities on the unit circle: Get ready for limits and continuity": ["Angle addition identities: Get ready for limits and continuity", "Reducing rational expressions to lowest terms: Get ready for limits and continuity", "End behavior of rational functions: Get ready for limits and continuity", "Discontinuities of rational functions: Get ready for limits and continuity", "Multiplying and dividing rational expressions: Get ready for limits and continuity"], "Unit 2: Get ready for differentiation: definition and basic derivative rules": ["Intro to slope-intercept form: Get ready for differentiation: definition and basic derivative rules", "Writing slope-intercept equations: Get ready for differentiation: definition and basic derivative rules", "Point-slope form: Get ready for differentiation: definition and basic derivative rules", "Average rate of change: Get ready for differentiation: definition and basic derivative rules", "Rational exponents: Get ready for differentiation: definition and basic derivative rules", "Properties of exponents: Get ready for differentiation: definition and basic derivative rules", "Introduction to logarithms: Get ready for differentiation: definition and basic derivative rules"], "Unit 3: Get ready for differentiation: composite, implicit, and inverse functions": ["Composing functions: Get ready for differentiation: composite, implicit, and inverse functions", "Linear equations with unknown coefficients: Get ready for differentiation: composite, implicit, and inverse functions", "Intro to inverse functions: Get ready for differentiation: composite, implicit, and inverse functions", "Invertible functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse trigonometric functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse functions in graphs and tables: Get ready for differentiation: composite, implicit, and inverse functions", "Verifying inverse functions by composition: Get ready for differentiation: composite, implicit, and inverse functions"], "Word problems with multiple units: Get ready for contextual applications of differentiation": ["Linear equations word problems: Get ready for contextual applications of differentiation", "Interpreting function notation: Get ready for contextual applications of differentiation", "Average rate of change word problems: Get ready for contextual applications of differentiation", "Modeling with composite functions: Get ready for contextual applications of differentiation", "Modeling with right triangles: Get ready for contextual applications of differentiation", "Volume and surface area: Get ready for contextual applications of differentiation"], "Unit 5: Get ready for applying derivatives to analyze functions": ["Maximum and minimum points: Get ready for applying derivatives to analyze functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for applying derivatives to analyze functions", "Interpreting features of graphs: Get ready for applying derivatives to analyze functions", "Distance formula: Get ready for applying derivatives to analyze functions", "Square-root equations: Get ready for applying derivatives to analyze functions", "Zeros of polynomials: Get ready for applying derivatives to analyze functions", "Positive and negative intervals of polynomials: Get ready for applying derivatives to analyze functions"], "Unit 6: Get ready for integration and accumulation of change": ["Completing the square: Get ready for integration and accumulation of change", "Dividing quadratics by linear factors: Get ready for integration and accumulation of change", "Dividing polynomials by linear factors: Get ready for integration and accumulation of change", "Partial fraction expansion: Get ready for integration and accumulation of change", "Summation notation: Get ready for integration and accumulation of change"], "Unit 7: Get ready for applications of integration": ["Rational equations: Get ready for applications of integration", "Square-root equations: Get ready for applications of integration", "Extraneous solutions: Get ready for applications of integration", "Sinusoidal equations: Get ready for applications of integration", "Manipulating formulas: Get ready for applications of integration", "Solving equations by graphing: Get ready for applications of integration"], "Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)": ["Sectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vectors introduction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Magnitude of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Scalar multiplication: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Direction of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components from magnitude & direction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)"], "Unit 9: Get ready for infinite sequences and series (BC only)": ["Arithmetic sequences: Get ready for infinite sequences and series (BC only)", "Geometric sequences: Get ready for infinite sequences and series (BC only)", "Summation notation: Get ready for infinite sequences and series (BC only)", "Arithmetic series: Get ready for infinite sequences and series (BC only)", "Geometric series: Get ready for infinite sequences and series (BC only)", "End behavior of rational functions: Get ready for infinite sequences and series (BC only)", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Statistics", "course_url": "/math/get-ready-for-ap-statistics", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for exploring categorical data": ["Frequency tables: Get ready for exploring categorical data", "Bar graphs: Get ready for exploring categorical data", "Fractions, decimals, and percentages: Get ready for exploring categorical data"], "Unit 2: Get ready for exploring one-variable quantitative data": ["Frequency tables and dot plots: Get ready for exploring one-variable quantitative data", "Box and whisker plots: Get ready for exploring one-variable quantitative data", "Comparing data displays: Get ready for exploring one-variable quantitative data", "Mean, median, and mode: Get ready for exploring one-variable quantitative data", "Mean absolute deviation: Get ready for exploring one-variable quantitative data", "Linear equations with variables on both sides: Get ready for exploring one-variable quantitative data", "Linear equations with unknown coefficients: Get ready for exploring one-variable quantitative data"], "Unit 3: Get ready for exploring two-variable quantitative data": ["Introduction to scatter plots: Get ready for exploring two-variable quantitative data", "Estimating with trend lines: Get ready for exploring two-variable quantitative data", "Logarithms: Get ready for exploring two-variable quantitative data"], "Unit 4: Get ready for probability": ["Fractions, decimals, and percentages: Get ready for probability", "Comparing decimals and fractions: Get ready for probability", "Arithmetic with fractions: Get ready for probability", "Probability introduction: Get ready for probability", "Experimental probability: Get ready for probability"], "Unit 5: Get ready for random variables and probability distributions": ["Predictions with probability: Get ready for random variables and probability distributions", "The counting principle: Get ready for random variables and probability distributions", "Probability distributions introduction: Get ready for random variables and probability distributions", "Start Course challenge"]}}}}
{"course_title": "Algebra 1", "course_url": "/math/algebra", "page_contents": {"syllabus": {"topics": {"Unit 1: Algebra foundations": ["Overview and history of algebra: Algebra foundations", "Introduction to variables: Algebra foundations", "Substitution and evaluating expressions: Algebra foundations", "Combining like terms: Algebra foundations", "Introduction to equivalent expressions: Algebra foundations", "Division by zero: Algebra foundations"], "Unit 2: Solving equations & inequalities": ["Linear equations with variables on both sides: Solving equations & inequalities", "Linear equations with parentheses: Solving equations & inequalities", "Analyzing the number of solutions to linear equations: Solving equations & inequalities", "Linear equations with unknown coefficients: Solving equations & inequalities", "Multi-step inequalities: Solving equations & inequalities", "Compound inequalities: Solving equations & inequalities"], "Unit 4: Linear equations & graphs": ["Two-variable linear equations intro: Linear equations & graphs", "Slope: Linear equations & graphs", "Horizontal & vertical lines: Linear equations & graphs", "x-intercepts and y-intercepts: Linear equations & graphs", "Applying intercepts and slope: Linear equations & graphs", "Modeling with linear equations and inequalities: Linear equations & graphs"], "Unit 5: Forms of linear equations": ["Intro to slope-intercept form: Forms of linear equations", "Graphing slope-intercept equations: Forms of linear equations", "Writing slope-intercept equations: Forms of linear equations", "Point-slope form: Forms of linear equations", "Standard form: Forms of linear equations", "Summary: Forms of two-variable linear equations: Forms of linear equations"], "Unit 6: Systems of equations": ["Introduction to systems of equations: Systems of equations", "Solving systems of equations with substitution: Systems of equations", "Solving systems of equations with elimination: Systems of equations", "Equivalent systems of equations: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 7: Inequalities (systems & graphs)": ["Checking solutions of two-variable inequalities: Inequalities (systems & graphs)", "Graphing two-variable inequalities: Inequalities (systems & graphs)", "Modeling with linear inequalities: Inequalities (systems & graphs)"], "Unit 8: Functions": ["Evaluating functions: Functions", "Inputs and outputs of a function: Functions", "Functions and equations: Functions", "Interpreting function notation: Functions", "Introduction to the domain and range of a function: Functions", "Determining the domain of a function: Functions", "Recognizing functions: Functions", "Maximum and minimum points: Functions", "Intervals where a function is positive, negative, increasing, or decreasing: Functions", "Interpreting features of graphs: Functions", "Average rate of change: Functions", "Average rate of change word problems: Functions", "Intro to inverse functions: Functions"], "Unit 9: Sequences": ["Introduction to arithmetic sequences: Sequences", "Constructing arithmetic sequences: Sequences", "Introduction to geometric sequences: Sequences", "Constructing geometric sequences: Sequences", "Modeling with sequences: Sequences", "General sequences: Sequences"], "Unit 10: Absolute value & piecewise functions": ["Graphs of absolute value functions: Absolute value & piecewise functions", "Piecewise functions: Absolute value & piecewise functions"], "Unit 11: Exponents & radicals": ["Exponent properties review: Exponents & radicals", "Radicals: Exponents & radicals", "Simplifying square roots: Exponents & radicals"], "Unit 12: Exponential growth & decay": ["Exponential vs. linear growth: Exponential growth & decay", "Exponential expressions: Exponential growth & decay", "Graphs of exponential growth: Exponential growth & decay", "Exponential vs. linear growth over time: Exponential growth & decay", "Exponential growth & decay: Exponential growth & decay", "Exponential functions from tables & graphs: Exponential growth & decay", "Exponential vs. linear models: Exponential growth & decay"], "Unit 13: Quadratics: Multiplying & factoring": ["Multiplying monomials by polynomials: Quadratics: Multiplying & factoring", "Multiplying binomials: Quadratics: Multiplying & factoring", "Special products of binomials: Quadratics: Multiplying & factoring", "Introduction to factoring: Quadratics: Multiplying & factoring", "Factoring quadratics intro: Quadratics: Multiplying & factoring", "Factoring quadratics by grouping: Quadratics: Multiplying & factoring", "Factoring quadratics with difference of squares: Quadratics: Multiplying & factoring", "Factoring quadratics with perfect squares: Quadratics: Multiplying & factoring", "Strategy in factoring quadratics: Quadratics: Multiplying & factoring"], "Unit 14: Quadratic functions & equations": ["Intro to parabolas: Quadratic functions & equations", "Solving and graphing with factored form: Quadratic functions & equations", "Solving by taking the square root: Quadratic functions & equations", "Vertex form: Quadratic functions & equations", "Solving quadratics by factoring: Quadratic functions & equations", "The quadratic formula: Quadratic functions & equations", "Completing the square intro: Quadratic functions & equations", "More on completing the square: Quadratic functions & equations", "Strategizing to solve quadratic equations: Quadratic functions & equations", "Quadratic standard form: Quadratic functions & equations", "Features & forms of quadratic functions: Quadratic functions & equations", "Comparing quadratic functions: Quadratic functions & equations", "Transforming quadratic functions: Quadratic functions & equations"], "Unit 15: Irrational numbers": ["Irrational numbers: Irrational numbers", "Sums and products of rational and irrational numbers: Irrational numbers", "Proofs concerning irrational numbers: Irrational numbers"], "Unit 16: Creativity in algebra": ["Creativity in algebra: Creativity in algebra", "Start Course challenge"]}}}}
{"course_title": "Geometry", "course_url": "/math/geometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Performing transformations": ["Introduction to rigid transformations: Performing transformations", "Translations: Performing transformations", "Rotations: Performing transformations", "Reflections: Performing transformations", "Dilations: Performing transformations"], "Unit 2: Transformation properties and proofs": ["Dilation preserved properties: Transformation properties and proofs", "Properties & definitions of transformations: Transformation properties and proofs", "Symmetry: Transformation properties and proofs", "Proofs with transformations: Transformation properties and proofs"], "Unit 3: Congruence": ["Triangle congruence from transformations: Congruence", "Congruent triangles: Congruence", "Working with triangles: Congruence", "Theorems concerning quadrilateral properties: Congruence", "Proofs of general theorems: Congruence", "Constructing lines & angles: Congruence"], "Unit 4: Similarity": ["Introduction to triangle similarity: Similarity", "Solving similar triangles: Similarity", "Angle bisector theorem: Similarity", "Solving problems with similar & congruent triangles: Similarity", "Proving relationships using similarity: Similarity", "Solving modeling problems with similar & congruent triangles: Similarity"], "Unit 5: Right triangles & trigonometry": ["Pythagorean theorem proofs: Right triangles & trigonometry", "Special right triangles: Right triangles & trigonometry", "Introduction to the trigonometric ratios: Right triangles & trigonometry", "Solving for a side in a right triangle using the trigonometric ratios: Right triangles & trigonometry", "Sine & cosine of complementary angles: Right triangles & trigonometry", "Modeling with right triangles: Right triangles & trigonometry"], "Unit 6: Analytic geometry": ["Dividing line segments: Analytic geometry", "Problem solving with distance on the coordinate plane: Analytic geometry", "Parallel & perpendicular lines on the coordinate plane: Analytic geometry", "Equations of parallel & perpendicular lines: Analytic geometry"], "Unit 7: Conic sections": ["Standard equation of a circle: Conic sections", "Expanded equation of a circle: Conic sections", "Focus and directrix of a parabola: Conic sections"], "Unit 8: Circles": ["Arc measure: Circles", "Arc length (from degrees): Circles", "Introduction to radians: Circles", "Arc length (from radians): Circles", "Sectors: Circles", "Inscribed angles: Circles", "Inscribed shapes problem solving: Circles", "Proofs with inscribed shapes: Circles", "Properties of tangents: Circles", "Constructing regular polygons inscribed in circles: Circles", "Constructing circumcircles & incircles: Circles", "Constructing a line tangent to a circle: Circles"], "Unit 9: Solid geometry": ["Volume and surface area: Solid geometry", "Density: Solid geometry", "Start Course challenge", "Modeling with right triangles", "Volume and surface area", "Special right triangles", "Introduction to triangle similarity"]}}}}
{"course_title": "Algebra 2", "course_url": "/math/algebra2", "page_contents": {"syllabus": {"topics": {"Unit 1: Polynomial arithmetic": ["Intro to polynomials: Polynomial arithmetic", "Average rate of change of polynomials: Polynomial arithmetic", "Adding and subtracting polynomials: Polynomial arithmetic", "Multiplying monomials by polynomials: Polynomial arithmetic", "Multiplying binomials by polynomials: Polynomial arithmetic", "Special products of polynomials: Polynomial arithmetic"], "The imaginary unit i: Complex numbers": ["Complex numbers introduction: Complex numbers", "The complex plane: Complex numbers", "Adding and subtracting complex numbers: Complex numbers", "Quadratic equations with complex solutions: Complex numbers"], "Unit 3: Polynomial factorization": ["Factoring monomials: Polynomial factorization", "Greatest common factor: Polynomial factorization", "Taking common factors: Polynomial factorization", "Factoring higher degree polynomials: Polynomial factorization", "Factoring using structure: Polynomial factorization", "Polynomial identities: Polynomial factorization", "Geometric series: Polynomial factorization"], "Unit 4: Polynomial division": ["Dividing polynomials by x: Polynomial division", "Dividing quadratics by linear factors: Polynomial division", "Dividing polynomials by linear factors: Polynomial division", "Polynomial Remainder Theorem: Polynomial division"], "Unit 5: Polynomial graphs": ["Zeros of polynomials: Polynomial graphs", "Positive and negative intervals of polynomials: Polynomial graphs", "End behavior of polynomials: Polynomial graphs"], "Unit 6: Rational exponents and radicals": ["Rational exponents: Rational exponents and radicals", "Properties of exponents (rational exponents): Rational exponents and radicals", "Evaluating exponents & radicals: Rational exponents and radicals", "Equivalent forms of exponential expressions: Rational exponents and radicals", "Solving exponential equations using properties of exponents: Rational exponents and radicals"], "Unit 7: Exponential models": ["Interpreting the rate of change of exponential models: Exponential models", "Constructing exponential models according to rate of change: Exponential models", "Advanced interpretation of exponential models: Exponential models"], "Unit 8: Logarithms": ["Introduction to logarithms: Logarithms", "The constant e and the natural logarithm: Logarithms", "Properties of logarithms: Logarithms", "The change of base formula for logarithms: Logarithms", "Solving exponential equations with logarithms: Logarithms", "Solving exponential models: Logarithms"], "Unit 9: Transformations of functions": ["Shifting functions: Transformations of functions", "Reflecting functions: Transformations of functions", "Symmetry of functions: Transformations of functions", "Scaling functions: Transformations of functions", "Putting it all together: Transformations of functions", "Graphs of square and cube root functions: Transformations of functions", "Graphs of exponential functions: Transformations of functions", "Graphs of logarithmic functions: Transformations of functions"], "Unit 10: Equations": ["Rational equations: Equations", "Square-root equations: Equations", "Extraneous solutions: Equations", "Cube-root equations: Equations", "Quadratic systems: Equations", "Solving equations by graphing: Equations"], "Unit circle introduction: Trigonometry": ["Radians: Trigonometry", "The Pythagorean identity: Trigonometry", "Trigonometric values of special angles: Trigonometry", "Graphs of sin(x), cos(x), and tan(x): Trigonometry", "Amplitude, midline and period: Trigonometry", "Transforming sinusoidal graphs: Trigonometry", "Graphing sinusoidal functions: Trigonometry", "Sinusoidal models: Trigonometry"], "Unit 12: Modeling": ["Modeling with function combination: Modeling", "Interpreting features of functions: Modeling", "Manipulating formulas: Modeling", "Modeling with two variables: Modeling", "Modeling with multiple variables: Modeling", "Start Course challenge"]}}}}
{"course_title": "Integrated math 1", "course_url": "/math/math1", "page_contents": {"syllabus": {"topics": {"Unit 1: Algebra foundations": ["Overview and history of algebra: Algebra foundations", "Introduction to variables: Algebra foundations", "Substitution and evaluating expressions: Algebra foundations", "Combining like terms: Algebra foundations", "Introduction to equivalent expressions: Algebra foundations", "Division by zero: Algebra foundations"], "Unit 2: Solving equations & inequalities": ["Linear equations with variables on both sides: Solving equations & inequalities", "Linear equations with parentheses: Solving equations & inequalities", "Analyzing the number of solutions to linear equations: Solving equations & inequalities", "Linear equations with unknown coefficients: Solving equations & inequalities", "Multi-step inequalities: Solving equations & inequalities", "Compound inequalities: Solving equations & inequalities"], "Unit 4: Linear equations & graphs": ["Two-variable linear equations intro: Linear equations & graphs", "Slope: Linear equations & graphs", "Horizontal & vertical lines: Linear equations & graphs", "x-intercepts and y-intercepts: Linear equations & graphs", "Applying intercepts and slope: Linear equations & graphs"], "Unit 5: Forms of linear equations": ["Intro to slope-intercept form: Forms of linear equations", "Graphing slope-intercept equations: Forms of linear equations", "Writing slope-intercept equations: Forms of linear equations", "Point-slope form: Forms of linear equations", "Standard form: Forms of linear equations", "Summary: Forms of two-variable linear equations: Forms of linear equations"], "Unit 6: Systems of equations": ["Introduction to systems of equations: Systems of equations", "Solving systems of equations with substitution: Systems of equations", "Equivalent systems of equations: Systems of equations", "Solving systems of equations with elimination: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 7: Inequalities (systems & graphs)": ["Checking solutions of two-variable inequalities: Inequalities (systems & graphs)", "Graphing two-variable inequalities: Inequalities (systems & graphs)", "Modeling with linear inequalities: Inequalities (systems & graphs)"], "Unit 8: Functions": ["Evaluating functions: Functions", "Inputs and outputs of a function: Functions", "Functions and equations: Functions", "Interpreting function notation: Functions", "Introduction to the domain and range of a function: Functions", "Determining the domain of a function: Functions", "Recognizing functions: Functions", "Maximum and minimum points: Functions", "Intervals where a function is positive, negative, increasing, or decreasing: Functions", "Interpreting features of graphs: Functions", "Average rate of change: Functions", "Average rate of change word problems: Functions", "Intro to inverse functions: Functions"], "Unit 9: Scatterplots": ["Creating and interpreting scatterplots: Scatterplots", "Estimating with trend lines: Scatterplots"], "Unit 10: Data distributions": ["Displays of distributions: Data distributions", "Summarizing center of distributions (central tendency): Data distributions", "Box and whisker plots: Data distributions", "Comparing distributions: Data distributions"], "Unit 12: Sequences": ["Introduction to arithmetic sequences: Sequences", "Constructing arithmetic sequences: Sequences", "Introduction to geometric sequences: Sequences", "Constructing geometric sequences: Sequences", "Modeling with sequences: Sequences", "General sequences: Sequences"], "Unit 13: Exponents & radicals": ["Exponent properties review: Exponents & radicals", "Radicals: Exponents & radicals", "Simplifying square roots: Exponents & radicals"], "Unit 14: Exponential growth & decay": ["Exponential vs. linear growth: Exponential growth & decay", "Exponential expressions: Exponential growth & decay", "Graphs of exponential growth: Exponential growth & decay", "Exponential vs. linear growth over time: Exponential growth & decay", "Exponential growth & decay: Exponential growth & decay", "Exponential functions from tables & graphs: Exponential growth & decay", "Exponential vs. linear models: Exponential growth & decay"], "Unit 15: Performing transformations": ["Translations: Performing transformations", "Rotations: Performing transformations", "Reflections: Performing transformations", "Dilations: Performing transformations"], "Unit 16: Transformation properties and proofs": ["Dilation preserved properties: Transformation properties and proofs", "Properties & definitions of transformations: Transformation properties and proofs", "Symmetry: Transformation properties and proofs", "Proofs with transformations: Transformation properties and proofs"], "Unit 17: Congruence": ["Triangle congruence from transformations: Congruence", "Congruent triangles: Congruence", "Working with triangles: Congruence", "Theorems concerning quadrilateral properties: Congruence", "Proofs of general theorems that use triangle congruence: Congruence", "Constructing lines & angles: Congruence"], "Unit 18: Analytic geometry": ["Dividing line segments: Analytic geometry", "Problem solving with distance on the coordinate plane: Analytic geometry", "Parallel & perpendicular lines on the coordinate plane: Analytic geometry", "Equations of parallel & perpendicular lines: Analytic geometry", "Start Course challenge"]}}}}
{"course_title": "Integrated math 2", "course_url": "/math/math2", "page_contents": {"syllabus": {"topics": {"Unit 1: Absolute value & piecewise functions": ["Graphs of absolute value functions: Absolute value & piecewise functions", "Piecewise functions: Absolute value & piecewise functions"], "Unit 2: Quadratics: Multiplying & factoring": ["Multiplying monomials by polynomials: Quadratics: Multiplying & factoring", "Multiplying binomials: Quadratics: Multiplying & factoring", "Special products of binomials: Quadratics: Multiplying & factoring", "Introduction to factoring: Quadratics: Multiplying & factoring", "Factoring quadratics intro: Quadratics: Multiplying & factoring", "Factoring quadratics by grouping: Quadratics: Multiplying & factoring", "Factoring quadratics with difference of squares: Quadratics: Multiplying & factoring", "Factoring quadratics with perfect squares: Quadratics: Multiplying & factoring", "Strategy in factoring quadratics: Quadratics: Multiplying & factoring"], "Unit 3: Quadratic functions & equations": ["Intro to parabolas: Quadratic functions & equations", "Solving and graphing with factored form: Quadratic functions & equations", "Solving by taking the square root: Quadratic functions & equations", "Vertex form: Quadratic functions & equations", "Solving quadratics by factoring: Quadratic functions & equations", "The quadratic formula: Quadratic functions & equations", "Completing the square: Quadratic functions & equations", "Strategizing to solve quadratic equations: Quadratic functions & equations", "Quadratics standard form: Quadratic functions & equations", "Features & forms of quadratic functions: Quadratic functions & equations", "Comparing quadratic functions: Quadratic functions & equations", "Transforming quadratic functions: Quadratic functions & equations"], "Unit 4: Irrational numbers": ["Irrational numbers: Irrational numbers", "Sums & products of rational/irrational numbers: Irrational numbers", "Proofs concerning irrational numbers: Irrational numbers"], "The imaginary unit i: Complex numbers": ["Complex numbers introduction: Complex numbers", "The complex plane: Complex numbers", "Adding & subtracting complex numbers: Complex numbers", "Quadratic equations with complex solutions: Complex numbers"], "Unit 6: Rational exponents and radicals": ["Rational exponents: Rational exponents and radicals", "Properties of exponents (rational exponents): Rational exponents and radicals", "Equivalent forms of exponential expressions: Rational exponents and radicals", "Evaluating exponents and radicals: Rational exponents and radicals", "Solving exponential expressions using properties of exponents: Rational exponents and radicals"], "Unit 7: Exponential models": ["Interpreting the rate of change of exponential models: Exponential models", "Constructing exponential models according to rate of change: Exponential models", "Advanced interpretation of exponential models: Exponential models"], "Unit 8: Similarity": ["Introduction to triangle similarity: Similarity", "Angle bisector theorem: Similarity", "Solving problems with similar & congruent triangles: Similarity", "Proving relationships using similarity: Similarity", "Solving modeling problems with similar & congruent triangles: Similarity"], "Unit 9: Right triangles & trigonometry": ["Pythagorean theorem proofs: Right triangles & trigonometry", "Special right triangles: Right triangles & trigonometry", "Introduction to the trigonometric ratios: Right triangles & trigonometry", "Sine & cosine of complementary angles: Right triangles & trigonometry", "Modeling with right triangles: Right triangles & trigonometry"], "Unit 10: Solid geometry": ["Volume and surface area: Solid geometry", "Density: Solid geometry"], "Unit 11: Circles": ["Arc measure: Circles", "Arc length (from degrees): Circles", "Introduction to radians: Circles", "Arc length (from radians): Circles", "Sectors: Circles", "Inscribed angles: Circles", "Inscribed shapes problem solving: Circles", "Proofs with inscribed shapes: Circles", "Properties of tangents: Circles", "Constructing regular polygons inscribed in circles: Circles", "Constructing circumcircles & incircles: Circles", "Constructing a line tangent to a circle: Circles"], "Unit 12: Conic sections": ["Features of a circle: Conic sections", "Standard equation of a circle: Conic sections", "Expanded equation of a circle: Conic sections", "Focus & directrix of a parabola: Conic sections"], "Unit 13: Probability": ["Probability basics: Probability", "Counting with combinations: Probability", "Probability with counting, permutations, combinations: Probability", "Multiplication rule for independent events: Probability", "Multiplication rule for dependent events: Probability", "Addition rule for probability: Probability", "Start Course challenge"]}}}}
{"course_title": "Integrated math 3", "course_url": "/math/math3", "page_contents": {"syllabus": {"topics": {"Unit 1: Polynomial arithmetic": ["Intro to polynomials: Polynomial arithmetic", "Average rate of change of polynomials: Polynomial arithmetic", "Adding and subtracting polynomials: Polynomial arithmetic", "Multiplying monomials by polynomials: Polynomial arithmetic", "Multiplying binomials by polynomials: Polynomial arithmetic", "Special products of polynomials: Polynomial arithmetic"], "Unit 2: Polynomial factorization": ["Factoring monomials: Polynomial factorization", "Greatest common factor: Polynomial factorization", "Taking common factors: Polynomial factorization", "Factoring higher degree polynomials: Polynomial factorization", "Factoring using structure: Polynomial factorization", "Polynomial identities: Polynomial factorization", "Geometric series: Polynomial factorization"], "Unit 3: Polynomial division": ["Dividing polynomials by x: Polynomial division", "Dividing quadratics by linear factors: Polynomial division", "Dividing polynomials by linear factors: Polynomial division", "Polynomial remainder theorem: Polynomial division"], "Unit 4: Polynomial graphs": ["Zeros of polynomials: Polynomial graphs", "Positive and negative intervals of polynomials: Polynomial graphs", "End behavior of polynomials: Polynomial graphs"], "Unit 5: Logarithms": ["Introduction to logarithms: Logarithms", "The constant e and the natural logarithm: Logarithms", "Properties of logarithms: Logarithms", "Change of base formula for logarithms: Logarithms", "Solving exponential equations with logarithms: Logarithms", "Solving exponential models: Logarithms"], "Unit 6: Transformations of functions": ["Shifting functions: Transformations of functions", "Reflecting functions: Transformations of functions", "Symmetry of functions: Transformations of functions", "Scaling functions: Transformations of functions", "Putting it all together: Transformations of functions", "Graphs of square and cube root functions: Transformations of functions", "Graphs of exponential functions: Transformations of functions", "Graphs of logarithmic functions: Transformations of functions"], "Unit 7: Equations": ["Rational equations: Equations", "Square-root equations: Equations", "Extraneous solutions: Equations", "Cube-root equations: Equations", "Quadratic systems: Equations", "Solving equations by graphing: Equations"], "Unit 8: Trigonometry": ["Law of sines: Trigonometry", "Law of cosines: Trigonometry", "Solving general triangles: Trigonometry"], "Unit circle introduction: Trigonometry": ["Radians: Trigonometry", "The Pythagorean identity: Trigonometry", "Trigonometric values of special angles: Trigonometry", "Graphs of sin(x), cos(x), and tan(x): Trigonometry", "Amplitude, midline, & period: Trigonometry", "Transforming sinusoidal graphs: Trigonometry", "Graphing sinusoidal functions: Trigonometry", "Sinusoidal models: Trigonometry"], "Unit 9: Modeling": ["Modeling with function combination: Modeling", "Interpreting features of functions: Modeling", "Manipulating formulas: Modeling", "Modeling with two variables: Modeling", "Modeling with multiple variables: Modeling"], "Unit 10: Study Design": ["Samples and surveys: Study Design", "Observational studies and experiments: Study Design"], "Unit 13: Rational functions": ["Cancelling common factors: Rational functions", "End behavior of rational functions: Rational functions", "Discontinuities of rational functions: Rational functions", "Graphs of rational functions: Rational functions", "Modeling with rational functions: Rational functions", "Multiplying & dividing rational expressions: Rational functions", "Adding subtracting rational expressions intro: Rational functions", "Adding subtracting rational expressions (factored): Rational functions", "Adding subtracting rational expressions (not factored): Rational functions", "Start Course challenge"]}}}}
{"course_title": "Algebra basics", "course_url": "/math/algebra-basics", "page_contents": {"syllabus": {"topics": {"Unit 1: Foundations": ["Absolute value: Foundations", "Exponents: Foundations", "Square roots: Foundations", "Order of operations: Foundations", "Fractions: Foundations", "Decimals, fractions and percentages: Foundations", "Operations with decimals: Foundations", "Area of triangles: Foundations", "Circumference and area of circles: Foundations"], "Unit 2: Algebraic expressions": ["Introduction to variables: Algebraic expressions", "Substitution & evaluating expressions: Algebraic expressions", "Writing algebraic expressions: Algebraic expressions", "Combining like terms: Algebraic expressions", "Distributive property: Algebraic expressions", "Equivalent algebraic expressions: Algebraic expressions", "Nested fractions: Algebraic expressions"], "Unit 3: Linear equations and inequalities": ["One-step equations: Linear equations and inequalities", "Two-steps equations: Linear equations and inequalities", "Multi-step equations: Linear equations and inequalities", "One-step inequalities: Linear equations and inequalities", "Two-step inequalities: Linear equations and inequalities", "Multi-step inequalities: Linear equations and inequalities", "Writing & solving proportions: Linear equations and inequalities"], "Unit 4: Graphing lines and slope": ["Coordinate plane: Graphing lines and slope", "Solutions to two-variable linear equations: Graphing lines and slope", "x-intercepts and y-intercepts: Graphing lines and slope", "Slope: Graphing lines and slope", "Horizontal & vertical lines: Graphing lines and slope", "Slope-intercept form intro: Graphing lines and slope", "Writing slope-intercept equations: Graphing lines and slope", "Graphing two-variable inequalities: Graphing lines and slope"], "Unit 5: Systems of equations": ["Systems of equations intro: Systems of equations", "Elimination method for systems of equations: Systems of equations", "Substitution method for systems of equations: Systems of equations", "Number of solutions to systems of equations: Systems of equations"], "Unit 6: Expressions with exponents": ["Exponent properties intro : Expressions with exponents", "Negative exponents: Expressions with exponents", "Exponent properties (integer exponents) : Expressions with exponents", "Scientific notation intro: Expressions with exponents", "Scientific notation word problems: Expressions with exponents"], "Unit 7: Quadratics and polynomials": ["Adding & subtracting polynomials: Quadratics and polynomials", "Multiplying binomials: Quadratics and polynomials", "Special products of binomials: Quadratics and polynomials", "Factoring polynomials by taking common factors: Quadratics and polynomials", "Factoring quadratics 1: Quadratics and polynomials", "Factoring quadratics 2: Quadratics and polynomials", "Factoring quadratics: Difference of squares: Quadratics and polynomials", "Factoring quadratics: Perfect squares: Quadratics and polynomials", "Solving quadratic equations by factoring: Quadratics and polynomials"], "Unit 8: Equations and geometry": ["Equations & geometry: Equations and geometry", "Triangle angles: Equations and geometry", "Pythagorean theorem: Equations and geometry", "Triangle similarity intro: Equations and geometry", "Start Course challenge"]}}}}
{"course_title": "Trigonometry", "course_url": "/math/trigonometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Right triangles & trigonometry": ["Introduction to the trigonometric ratios: Right triangles & trigonometry", "Solving for a side in a right triangle using the trigonometric ratios: Right triangles & trigonometry", "Sine and cosine of complementary angles: Right triangles & trigonometry", "Modeling with right triangles: Right triangles & trigonometry"], "Unit circle introduction: Trigonometric functions": ["Radians: Trigonometric functions", "The Pythagorean identity: Trigonometric functions", "Special trigonometric values in the first quadrant: Trigonometric functions"], "Trigonometric values on the unit circle: Trigonometric functions": ["Graphs of sin(x), cos(x), and tan(x): Trigonometric functions", "Amplitude, midline, and period: Trigonometric functions", "Transforming sinusoidal graphs: Trigonometric functions", "Graphing sinusoidal functions: Trigonometric functions", "Sinusoidal models: Trigonometric functions", "Long live Tau: Trigonometric functions"], "Unit 3: Non-right triangles & trigonometry": ["Law of sines: Non-right triangles & trigonometry", "Law of cosines: Non-right triangles & trigonometry", "Solving general triangles: Non-right triangles & trigonometry"], "Unit 4: Trigonometric equations and identities": ["Inverse trigonometric functions: Trigonometric equations and identities", "Sinusoidal equations: Trigonometric equations and identities", "Sinusoidal models: Trigonometric equations and identities", "Angle addition identities: Trigonometric equations and identities", "Using trigonometric identities: Trigonometric equations and identities", "Challenging trigonometry problems: Trigonometric equations and identities", "Start Course challenge", "The reciprocal trigonometric ratios"]}}}}
{"course_title": "Precalculus", "course_url": "/math/precalculus", "page_contents": {"syllabus": {"topics": {"Unit 1: Composite and inverse functions": ["Composing functions: Composite and inverse functions", "Modeling with composite functions: Composite and inverse functions", "Invertible functions: Composite and inverse functions", "Inverse functions in graphs and tables: Composite and inverse functions", "Verifying inverse functions by composition: Composite and inverse functions"], "Trigonometric identities on the unit circle: Trigonometry": ["Inverse trigonometric functions: Trigonometry", "Law of sines: Trigonometry", "Law of cosines: Trigonometry", "Solving general triangles: Trigonometry", "Sinusoidal equations: Trigonometry", "Sinusoidal models: Trigonometry", "Angle addition identities: Trigonometry", "Using trigonometric identities: Trigonometry"], "Unit 3: Complex numbers": ["The complex plane: Complex numbers", "Distance and midpoint of complex numbers: Complex numbers", "Complex conjugates and dividing complex numbers: Complex numbers", "Identities with complex numbers: Complex numbers", "Modulus (absolute value) and argument (angle) of complex numbers: Complex numbers", "Polar form of complex numbers: Complex numbers", "Graphically multiplying complex numbers: Complex numbers", "Multiplying and dividing complex numbers in polar form: Complex numbers", "The fundamental theorem of algebra: Complex numbers"], "Unit 4: Rational functions": ["End behavior of rational functions: Rational functions", "Discontinuities of rational functions: Rational functions", "Graphs of rational functions: Rational functions", "Modeling with rational functions: Rational functions", "Multiplying and dividing rational expressions: Rational functions"], "Unit 5: Conic sections": ["Introduction to conic sections: Conic sections", "Center and radii of an ellipse: Conic sections", "Foci of an ellipse: Conic sections", "Introduction to hyperbolas: Conic sections", "Foci of a hyperbola: Conic sections", "Hyperbolas not centered at the origin: Conic sections"], "Unit 6: Vectors": ["Vectors introduction: Vectors", "Vector components: Vectors", "Magnitude of vectors: Vectors", "Scalar multiplication: Vectors", "Vector addition and subtraction: Vectors", "Direction of vectors: Vectors", "Vector components from magnitude and direction: Vectors", "Adding vectors in magnitude and direction form: Vectors", "Vectors word problems: Vectors"], "Unit 7: Matrices": ["Introduction to matrices: Matrices", "Using matrices to represent data: Matrices", "Multiplying matrices by scalars: Matrices", "Adding and subtracting matrices: Matrices", "Using matrices to manipulate data: Matrices", "Matrices as transformations of the plane: Matrices", "Using matrices to transform the plane: Matrices", "Transforming 3D and 4D vectors with matrices: Matrices", "Multiplying matrices by matrices: Matrices", "Properties of matrix multiplication: Matrices", "Representing systems of equations with matrices: Matrices", "Introduction to matrix inverses: Matrices", "Finding inverses of 2x2 matrices: Matrices", "Solving linear systems with matrices: Matrices"], "Unit 8: Probability and combinatorics": ["Venn diagrams and the addition rule: Probability and combinatorics", "Multiplication rule for probabilities: Probability and combinatorics", "Permutations: Probability and combinatorics", "Combinations: Probability and combinatorics", "Probability using combinatorics: Probability and combinatorics", "Probability distributions introduction: Probability and combinatorics", "Theoretical & empirical probability distributions: Probability and combinatorics", "Decisions with probability: Probability and combinatorics", "Expected value: Probability and combinatorics"], "Unit 9: Series": ["Geometric series: Series", "Geometric series (with summation notation): Series", "The binomial theorem: Series", "Arithmetic series: Series"], "Unit 10: Limits and continuity": ["Defining limits and using limit notation: Limits and continuity", "Estimating limit values from graphs: Limits and continuity", "Estimating limit values from tables: Limits and continuity", "Determining limits using algebraic properties of limits: limit properties: Limits and continuity", "Determining limits using algebraic properties of limits: direct substitution: Limits and continuity", "Determining limits using algebraic manipulation: Limits and continuity", "Selecting procedures for determining limits: Limits and continuity", "Determining limits using the squeeze theorem: Limits and continuity", "Exploring types of discontinuities: Limits and continuity", "Defining continuity at a point: Limits and continuity", "Confirming continuity over an interval: Limits and continuity", "Removing discontinuities: Limits and continuity", "Connecting infinite limits and vertical asymptotes: Limits and continuity", "Connecting limits at infinity and horizontal asymptotes: Limits and continuity", "Working with the intermediate value theorem: Limits and continuity", "Start Course challenge"]}}}}
{"course_title": "High school statistics", "course_url": "/math/probability", "page_contents": {"syllabus": {"topics": {"Unit 1: Displaying a single quantitative variable": ["Frequency tables and dot plots: Displaying a single quantitative variable", "Histograms: Displaying a single quantitative variable", "Mean and median in data displays: Displaying a single quantitative variable", "Interquartile range: Displaying a single quantitative variable", "Box and whisker plots: Displaying a single quantitative variable"], "Unit 2: Analyzing a single quantitative variable": ["Standard deviation: Analyzing a single quantitative variable", "Comparing distributions: Analyzing a single quantitative variable", "Percentiles and z-scores: Analyzing a single quantitative variable", "Normal distributions and the empirical rule: Analyzing a single quantitative variable", "Normal distribution calculations: Analyzing a single quantitative variable"], "Unit 3: Two-way tables": ["Two-way tables introduction: Two-way tables", "Distributions in two-way tables: Two-way tables"], "Unit 4: Scatterplots": ["Fitting trend lines to scatterplots: Scatterplots", "Analyzing trend lines in scatterplots: Scatterplots", "Residuals: Scatterplots"], "Unit 5: Study design": ["Introduction to planning a study: Study design", "Potential problems with sampling: Study design", "Sampling methods: Study design", "Introduction to experimental design: Study design", "Inference and experiments: Study design"], "Unit 6: Probability": ["Venn diagrams and the addition rule: Probability", "Multiplication rule for probabilities: Probability", "Conditional probability: Probability", "Probability from simulations: Probability", "Permutations: Probability", "Combinations: Probability", "Probability using combinatorics: Probability"], "Unit 7: Probability distributions & expected value": ["Probability distributions introduction: Probability distributions & expected value", "Theoretical & empirical probability distributions: Probability distributions & expected value", "Decisions with probability: Probability distributions & expected value", "Expected value: Probability distributions & expected value", "Start Course challenge"]}}}}
{"course_title": "Statistics & probability", "course_url": "/math/statistics-probability", "page_contents": {"syllabus": {"topics": {"Unit 1: Analyzing categorical data": ["Analyzing one categorical variable: Analyzing categorical data", "Two-way tables: Analyzing categorical data", "Distributions in two-way tables: Analyzing categorical data"], "Unit 2: Displaying and comparing quantitative data": ["Displaying quantitative data with graphs: Displaying and comparing quantitative data", "Describing and comparing distributions: Displaying and comparing quantitative data", "More on data displays: Displaying and comparing quantitative data"], "Unit 3: Summarizing quantitative data": ["Measuring center in quantitative data: Summarizing quantitative data", "Interquartile range (IQR): Summarizing quantitative data", "Variance and standard deviation of a population: Summarizing quantitative data", "Variance and standard deviation of a sample: Summarizing quantitative data", "More on standard deviation: Summarizing quantitative data", "Box and whisker plots: Summarizing quantitative data", "Other measures of spread: Summarizing quantitative data"], "Unit 4: Modeling data distributions": ["Percentiles: Modeling data distributions", "Z-scores: Modeling data distributions", "Effects of linear transformations: Modeling data distributions", "Density curves: Modeling data distributions", "Normal distributions and the empirical rule: Modeling data distributions", "Normal distribution calculations: Modeling data distributions", "More on normal distributions: Modeling data distributions"], "Unit 5: Exploring bivariate numerical data": ["Introduction to scatterplots: Exploring bivariate numerical data", "Correlation coefficients: Exploring bivariate numerical data", "Introduction to trend lines: Exploring bivariate numerical data", "Least-squares regression equations: Exploring bivariate numerical data", "Assessing the fit in least-squares regression: Exploring bivariate numerical data", "More on regression: Exploring bivariate numerical data"], "Unit 6: Study design": ["Statistical questions: Study design", "Sampling and observational studies: Study design", "Sampling methods: Study design", "Types of studies (experimental vs. observational): Study design", "Experiments: Study design"], "Unit 7: Probability": ["Basic theoretical probability: Probability", "Probability using sample spaces: Probability", "Basic set operations: Probability", "Experimental probability: Probability", "Randomness, probability, and simulation: Probability", "Addition rule: Probability", "Multiplication rule for independent events: Probability", "Multiplication rule for dependent events: Probability", "Conditional probability and independence: Probability"], "Unit 8: Counting, permutations, and combinations": ["Counting principle and factorial: Counting, permutations, and combinations", "Permutations: Counting, permutations, and combinations", "Combinations: Counting, permutations, and combinations", "Combinatorics and probability: Counting, permutations, and combinations"], "Unit 9: Random variables": ["Discrete random variables: Random variables", "Continuous random variables: Random variables", "Transforming random variables: Random variables", "Combining random variables: Random variables", "Binomial random variables: Random variables", "Binomial mean and standard deviation formulas: Random variables", "Geometric random variables: Random variables", "More on expected value: Random variables", "Poisson distribution: Random variables"], "Unit 10: Sampling distributions": ["What is a sampling distribution?: Sampling distributions", "Sampling distribution of a sample proportion: Sampling distributions", "Sampling distribution of a sample mean: Sampling distributions"], "Unit 11: Confidence intervals": ["Introduction to confidence intervals: Confidence intervals", "Estimating a population proportion: Confidence intervals", "Estimating a population mean: Confidence intervals", "More confidence interval videos: Confidence intervals"], "Unit 12: Significance tests (hypothesis testing)": ["The idea of significance tests: Significance tests (hypothesis testing)", "Error probabilities and power: Significance tests (hypothesis testing)", "Tests about a population proportion: Significance tests (hypothesis testing)", "Tests about a population mean: Significance tests (hypothesis testing)", "More significance testing videos: Significance tests (hypothesis testing)"], "Unit 13: Two-sample inference for the difference between groups": ["Comparing two proportions: Two-sample inference for the difference between groups", "Comparing two means: Two-sample inference for the difference between groups"], "Unit 14: Inference for categorical data (chi-square tests)": ["Chi-square goodness-of-fit tests: Inference for categorical data (chi-square tests)", "Chi-square tests for relationships: Inference for categorical data (chi-square tests)"], "Unit 15: Advanced regression (inference and transforming)": ["Inference about slope: Advanced regression (inference and transforming)", "Nonlinear regression: Advanced regression (inference and transforming)"], "Unit 16: Analysis of variance (ANOVA)": ["Analysis of variance (ANOVA): Analysis of variance (ANOVA)", "Start Course challenge"]}}}}
{"course_title": "College algebraNEW", "course_url": "/math/college-algebra", "page_contents": {"syllabus": {"topics": {"Unit 1: Linear equations and inequalities": ["Solving equations with one unknown: Linear equations and inequalities", "Solutions to linear equations: Linear equations and inequalities", "Multi-step linear inequalities: Linear equations and inequalities", "Compound inequalities: Linear equations and inequalities", "Modeling with linear equations and inequalities: Linear equations and inequalities", "Absolute value equations: Linear equations and inequalities"], "Unit 2: Graphs and forms of linear equations": ["Intercepts: Graphs and forms of linear equations", "Graphing from slope: Graphs and forms of linear equations", "Horizontal and vertical lines: Graphs and forms of linear equations", "Slope-intercept form: Graphs and forms of linear equations", "Point-slope form: Graphs and forms of linear equations", "Writing linear equations in any form: Graphs and forms of linear equations", "Equations of parallel and perpendicular lines: Graphs and forms of linear equations"], "Unit 3: Functions": ["Evaluating functions: Functions", "Inputs and outputs of a function: Functions", "Domain and range of a function: Functions", "Recognizing functions: Functions", "Intervals where a function is positive, negative, increasing, or decreasing: Functions", "Intro to inverse functions: Functions"], "Unit 4: Quadratics: Multiplying and factoring": ["Multiplying binomials: Quadratics: Multiplying and factoring", "Special products of binomials: Quadratics: Multiplying and factoring", "Factoring quadratics intro: Quadratics: Multiplying and factoring", "Factoring quadratics by grouping: Quadratics: Multiplying and factoring", "Factoring quadratics with difference of squares: Quadratics: Multiplying and factoring", "Factoring quadratics with perfect squares: Quadratics: Multiplying and factoring"], "Unit 5: Quadratic functions and equations": ["Solving quadratics by taking the square root: Quadratic functions and equations", "Vertex form: Quadratic functions and equations", "Solving quadratics by factoring: Quadratic functions and equations", "The quadratic formula: Quadratic functions and equations", "Completing the square: Quadratic functions and equations", "Forms and features of quadratic functions: Quadratic functions and equations"], "The imaginary unit i: Complex numbers": ["Adding and subtracting complex numbers: Complex numbers", "Complex conjugates and dividing complex numbers: Complex numbers"], "Unit 7: Exponents and radicals": ["Exponent properties (integer exponents): Exponents and radicals", "Simplifying square roots: Exponents and radicals", "Exponential expressions: Exponents and radicals", "Graphing exponential growth and decay: Exponents and radicals"], "Unit 8: Rational expressions and equations": ["Rational equations: Rational expressions and equations", "Modeling with rational expressions: Rational expressions and equations", "Multiplying and dividing rational expressions: Rational expressions and equations"], "Unit 9: Relating algebra and geometry": ["Distance and midpoints: Relating algebra and geometry", "Standard equation of a circle: Relating algebra and geometry", "Expanded equation of a circle: Relating algebra and geometry"], "Unit 10: Polynomial arithmetic": ["Average rate of change of polynomials: Polynomial arithmetic", "Adding and subtracting polynomials: Polynomial arithmetic", "Taking common factors: Polynomial arithmetic", "Factoring higher degree polynomials: Polynomial arithmetic", "Factoring using structure: Polynomial arithmetic"], "Unit 11: Advanced function types": ["Graphs of absolute value functions: Advanced function types", "Piecewise functions: Advanced function types", "Composing functions: Advanced function types", "Verifying inverse functions by composition: Advanced function types"], "Unit 12: Transformations of functions": ["Shifting functions: Transformations of functions", "Reflecting functions: Transformations of functions", "Symmetry of functions: Transformations of functions", "Scaling functions: Transformations of functions"], "Unit 13: Rational exponents and radicals": ["Rational exponents: Rational exponents and radicals", "Properties of exponents (rational exponents): Rational exponents and radicals", "Evaluating exponents and radicals: Rational exponents and radicals", "Solving exponential equations using properties of exponents: Rational exponents and radicals", "Interpreting the rate of change of exponential models: Rational exponents and radicals", "Square-root equations: Rational exponents and radicals"], "Unit 14: Logarithms": ["Introduction to logarithms: Logarithms", "Properties of logarithms: Logarithms", "The change of base formula for logarithms: Logarithms", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Calculus AB", "course_url": "/math/ap-calculus-ab", "page_contents": {"syllabus": {"topics": {"Unit 10Unit 10: AP\u00ae\ufe0e Calculus AB Standards mappings": ["Start Course challenge", "Watch an introduction video3:263 minutes 26 seconds", "Learn more", "Learn more", "Watch an introduction video3:263 minutes 26 seconds"], "Unit 1: Limits and continuity": ["About the course: Limits and continuity", "Defining limits and using limit notation: Limits and continuity", "Estimating limit values from graphs: Limits and continuity", "Estimating limit values from tables: Limits and continuity", "Determining limits using algebraic properties of limits: limit properties: Limits and continuity", "Determining limits using algebraic properties of limits: direct substitution: Limits and continuity", "Determining limits using algebraic manipulation: Limits and continuity", "Selecting procedures for determining limits: Limits and continuity", "Determining limits using the squeeze theorem: Limits and continuity", "Exploring types of discontinuities: Limits and continuity", "Defining continuity at a point: Limits and continuity", "Confirming continuity over an interval: Limits and continuity", "Removing discontinuities: Limits and continuity", "Connecting infinite limits and vertical asymptotes: Limits and continuity", "Connecting limits at infinity and horizontal asymptotes: Limits and continuity", "Working with the intermediate value theorem: Limits and continuity", "Optional videos: Limits and continuity"], "Unit 2: Differentiation: definition and basic derivative rules": ["Defining average and instantaneous rates of change at a point: Differentiation: definition and basic derivative rules", "Defining the derivative of a function and using derivative notation: Differentiation: definition and basic derivative rules", "Estimating derivatives of a function at a point: Differentiation: definition and basic derivative rules", "Connecting differentiability and continuity: determining when derivatives do and do not exist: Differentiation: definition and basic derivative rules", "Applying the power rule: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: introduction: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule: Differentiation: definition and basic derivative rules", "Derivatives of cos(x), sin(x), \ud835\udc52\u02e3, and ln(x): Differentiation: definition and basic derivative rules", "The product rule: Differentiation: definition and basic derivative rules", "The quotient rule: Differentiation: definition and basic derivative rules", "Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions: Differentiation: definition and basic derivative rules", "Optional videos: Differentiation: definition and basic derivative rules"], "Unit 3: Differentiation: composite, implicit, and inverse functions": ["The chain rule: introduction: Differentiation: composite, implicit, and inverse functions", "The chain rule: further practice: Differentiation: composite, implicit, and inverse functions", "Implicit differentiation: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse functions: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse trigonometric functions: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: strategy: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: multiple rules: Differentiation: composite, implicit, and inverse functions", "Calculating higher-order derivatives: Differentiation: composite, implicit, and inverse functions", "Further practice connecting derivatives and limits: Differentiation: composite, implicit, and inverse functions", "Optional videos: Differentiation: composite, implicit, and inverse functions"], "Unit 4: Contextual applications of differentiation": ["Interpreting the meaning of the derivative in context: Contextual applications of differentiation", "Straight-line motion: connecting position, velocity, and acceleration: Contextual applications of differentiation", "Rates of change in other applied contexts (non-motion problems): Contextual applications of differentiation", "Introduction to related rates: Contextual applications of differentiation", "Approximating values of a function using local linearity and linearization: Contextual applications of differentiation", "Using L\u2019H\u00f4pital\u2019s rule for finding limits of indeterminate forms: Contextual applications of differentiation", "Optional videos: Contextual applications of differentiation"], "Unit 5: Applying derivatives to analyze functions": ["Using the mean value theorem: Applying derivatives to analyze functions", "Extreme value theorem, global versus local extrema, and critical points: Applying derivatives to analyze functions", "Determining intervals on which a function is increasing or decreasing: Applying derivatives to analyze functions", "Using the first derivative test to find relative (local) extrema: Applying derivatives to analyze functions", "Using the candidates test to find absolute (global) extrema: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: graphical: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: algebraic: Applying derivatives to analyze functions", "Using the second derivative test to find extrema: Applying derivatives to analyze functions", "Sketching curves of functions and their derivatives: Applying derivatives to analyze functions", "Connecting a function, its first derivative, and its second derivative: Applying derivatives to analyze functions", "Solving optimization problems: Applying derivatives to analyze functions", "Exploring behaviors of implicit relations: Applying derivatives to analyze functions"], "Unit 6: Integration and accumulation of change": ["Exploring accumulations of change: Integration and accumulation of change", "Approximating areas with Riemann sums: Integration and accumulation of change", "Riemann sums, summation notation, and definite integral notation: Integration and accumulation of change", "The fundamental theorem of calculus and accumulation functions: Integration and accumulation of change", "Interpreting the behavior of accumulation functions involving area: Integration and accumulation of change", "Applying properties of definite integrals: Integration and accumulation of change", "The fundamental theorem of calculus and definite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals: Integration and accumulation of change", "Integrating using substitution: Integration and accumulation of change", "Integrating functions using long division and completing the square: Integration and accumulation of change", "Optional videos: Integration and accumulation of change"], "Unit 7: Differential equations": ["Modeling situations with differential equations: Differential equations", "Verifying solutions for differential equations: Differential equations", "Sketching slope fields: Differential equations", "Reasoning using slope fields: Differential equations", "Finding general solutions using separation of variables: Differential equations", "Finding particular solutions using initial conditions and separation of variables: Differential equations", "Exponential models with differential equations: Differential equations"], "Unit 8: Applications of integration": ["Finding the average value of a function on an interval: Applications of integration", "Connecting position, velocity, and acceleration functions using integrals: Applications of integration", "Using accumulation functions and definite integrals in applied contexts: Applications of integration", "Finding the area between curves expressed as functions of x: Applications of integration", "Finding the area between curves expressed as functions of y: Applications of integration", "Volumes with cross sections: squares and rectangles: Applications of integration", "Volumes with cross sections: triangles and semicircles: Applications of integration", "Volume with disc method: revolving around x- or y-axis: Applications of integration", "Volume with disc method: revolving around other axes: Applications of integration", "Volume with washer method: revolving around x- or y-axis: Applications of integration", "Volume with washer method: revolving around other axes: Applications of integration"], "Unit 9: AP Calculus AB solved free response questions from past exams": ["AP Calculus AB 2017 free response: AP Calculus AB solved free response questions from past exams", "AP Calculus AB 2015 free response: AP Calculus AB solved free response questions from past exams", "AP Calculus AB 2011 free response: AP Calculus AB solved free response questions from past exams"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Calculus BC", "course_url": "/math/ap-calculus-bc", "page_contents": {"syllabus": {"topics": {"Unit 1: Limits and continuity": ["About the course: Limits and continuity", "Defining limits and using limit notation: Limits and continuity", "Estimating limit values from graphs: Limits and continuity", "Estimating limit values from tables: Limits and continuity", "Determining limits using algebraic properties of limits: limit properties: Limits and continuity", "Determining limits using algebraic properties of limits: direct substitution: Limits and continuity", "Determining limits using algebraic manipulation: Limits and continuity", "Selecting procedures for determining limits: Limits and continuity", "Determining limits using the squeeze theorem: Limits and continuity", "Exploring types of discontinuities: Limits and continuity", "Defining continuity at a point: Limits and continuity", "Confirming continuity over an interval: Limits and continuity", "Removing discontinuities: Limits and continuity", "Connecting infinite limits and vertical asymptotes: Limits and continuity", "Connecting limits at infinity and horizontal asymptotes: Limits and continuity", "Working with the intermediate value theorem: Limits and continuity", "Optional videos: Limits and continuity"], "Unit 2: Differentiation: definition and basic derivative rules": ["Defining average and instantaneous rates of change at a point: Differentiation: definition and basic derivative rules", "Defining the derivative of a function and using derivative notation: Differentiation: definition and basic derivative rules", "Estimating derivatives of a function at a point: Differentiation: definition and basic derivative rules", "Connecting differentiability and continuity: determining when derivatives do and do not exist: Differentiation: definition and basic derivative rules", "Applying the power rule: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: introduction: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule: Differentiation: definition and basic derivative rules", "Derivatives of cos(x), sin(x), \ud835\udc52\u02e3, and ln(x): Differentiation: definition and basic derivative rules", "The product rule: Differentiation: definition and basic derivative rules", "The quotient rule: Differentiation: definition and basic derivative rules", "Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions: Differentiation: definition and basic derivative rules", "Optional videos: Differentiation: definition and basic derivative rules"], "Unit 3: Differentiation: composite, implicit, and inverse functions": ["The chain rule: introduction: Differentiation: composite, implicit, and inverse functions", "The chain rule: further practice: Differentiation: composite, implicit, and inverse functions", "Implicit differentiation: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse functions: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse trigonometric functions: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: strategy: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: multiple rules: Differentiation: composite, implicit, and inverse functions", "Calculating higher-order derivatives: Differentiation: composite, implicit, and inverse functions", "Further practice connecting derivatives and limits: Differentiation: composite, implicit, and inverse functions", "Optional videos: Differentiation: composite, implicit, and inverse functions"], "Unit 4: Contextual applications of differentiation": ["Interpreting the meaning of the derivative in context: Contextual applications of differentiation", "Straight-line motion: connecting position, velocity, and acceleration: Contextual applications of differentiation", "Rates of change in other applied contexts (non-motion problems): Contextual applications of differentiation", "Introduction to related rates: Contextual applications of differentiation", "Approximating values of a function using local linearity and linearization: Contextual applications of differentiation", "Using L\u2019H\u00f4pital\u2019s rule for finding limits of indeterminate forms: Contextual applications of differentiation", "Optional videos: Contextual applications of differentiation"], "Unit 5: Applying derivatives to analyze functions": ["Using the mean value theorem: Applying derivatives to analyze functions", "Extreme value theorem, global versus local extrema, and critical points: Applying derivatives to analyze functions", "Determining intervals on which a function is increasing or decreasing: Applying derivatives to analyze functions", "Using the first derivative test to find relative (local) extrema: Applying derivatives to analyze functions", "Using the candidates test to find absolute (global) extrema: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: graphical: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: algebraic: Applying derivatives to analyze functions", "Using the second derivative test to find extrema: Applying derivatives to analyze functions", "Sketching curves of functions and their derivatives: Applying derivatives to analyze functions", "Connecting a function, its first derivative, and its second derivative: Applying derivatives to analyze functions", "Solving optimization problems: Applying derivatives to analyze functions", "Exploring behaviors of implicit relations: Applying derivatives to analyze functions"], "Unit 6: Integration and accumulation of change": ["Exploring accumulations of change: Integration and accumulation of change", "Approximating areas with Riemann sums: Integration and accumulation of change", "Riemann sums, summation notation, and definite integral notation: Integration and accumulation of change", "The fundamental theorem of calculus and accumulation functions: Integration and accumulation of change", "Interpreting the behavior of accumulation functions involving area: Integration and accumulation of change", "Applying properties of definite integrals: Integration and accumulation of change", "The fundamental theorem of calculus and definite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals: Integration and accumulation of change", "Integrating using substitution: Integration and accumulation of change", "Integrating functions using long division and completing the square: Integration and accumulation of change", "Using integration by parts: Integration and accumulation of change", "Integrating using linear partial fractions: Integration and accumulation of change", "Evaluating improper integrals: Integration and accumulation of change", "Optional videos: Integration and accumulation of change"], "Unit 7: Differential equations": ["Modeling situations with differential equations: Differential equations", "Verifying solutions for differential equations: Differential equations", "Sketching slope fields: Differential equations", "Reasoning using slope fields: Differential equations", "Approximating solutions using Euler\u2019s method: Differential equations", "Finding general solutions using separation of variables: Differential equations", "Finding particular solutions using initial conditions and separation of variables: Differential equations", "Exponential models with differential equations: Differential equations", "Logistic models with differential equations: Differential equations"], "Unit 8: Applications of integration": ["Finding the average value of a function on an interval: Applications of integration", "Connecting position, velocity, and acceleration functions using integrals: Applications of integration", "Using accumulation functions and definite integrals in applied contexts: Applications of integration", "Finding the area between curves expressed as functions of x: Applications of integration", "Finding the area between curves expressed as functions of y: Applications of integration", "Volumes with cross sections: squares and rectangles: Applications of integration", "Volumes with cross sections: triangles and semicircles: Applications of integration", "Volume with disc method: revolving around x- or y-axis: Applications of integration", "Volume with disc method: revolving around other axes: Applications of integration", "Volume with washer method: revolving around x- or y-axis: Applications of integration", "Volume with washer method: revolving around other axes: Applications of integration", "The arc length of a smooth, planar curve and distance traveled: Applications of integration"], "Unit 9: Parametric equations, polar coordinates, and vector-valued functions": ["Defining and differentiating parametric equations: Parametric equations, polar coordinates, and vector-valued functions", "Second derivatives of parametric equations: Parametric equations, polar coordinates, and vector-valued functions", "Finding arc lengths of curves given by parametric equations: Parametric equations, polar coordinates, and vector-valued functions", "Defining and differentiating vector-valued functions: Parametric equations, polar coordinates, and vector-valued functions", "Solving motion problems using parametric and vector-valued functions: Parametric equations, polar coordinates, and vector-valued functions", "Defining polar coordinates and differentiating in polar form: Parametric equations, polar coordinates, and vector-valued functions", "Finding the area of a polar region or the area bounded by a single polar curve: Parametric equations, polar coordinates, and vector-valued functions", "Finding the area of the region bounded by two polar curves: Parametric equations, polar coordinates, and vector-valued functions", "Calculator-active practice: Parametric equations, polar coordinates, and vector-valued functions"], "Unit 10: Infinite sequences and series": ["Defining convergent and divergent infinite series: Infinite sequences and series", "Working with geometric series: Infinite sequences and series", "The nth-term test for divergence: Infinite sequences and series", "Integral test for convergence: Infinite sequences and series", "Harmonic series and p-series: Infinite sequences and series", "Comparison tests for convergence: Infinite sequences and series", "Alternating series test for convergence: Infinite sequences and series", "Ratio test for convergence: Infinite sequences and series", "Determining absolute or conditional convergence: Infinite sequences and series", "Alternating series error bound: Infinite sequences and series", "Finding Taylor polynomial approximations of functions: Infinite sequences and series", "Lagrange error bound: Infinite sequences and series", "Radius and interval of convergence of power series: Infinite sequences and series", "Finding Taylor or Maclaurin series for a function: Infinite sequences and series", "Representing functions as power series: Infinite sequences and series", "Optional videos: Infinite sequences and series"], "Unit 11: AP Calculus BC solved exams": ["AP Calculus BC 2017: AP Calculus BC solved exams", "AP Calculus BC 2015: AP Calculus BC solved exams", "AP Calculus BC 2011: AP Calculus BC solved exams", "AP Calculus BC 2008: AP Calculus BC solved exams"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Statistics", "course_url": "/math/ap-statistics", "page_contents": {"syllabus": {"topics": {"Unit 1: Exploring categorical data": ["The language of variation: Variables: Exploring categorical data", "Representing a categorical variable with graphs: Exploring categorical data", "Representing two categorical variables: Exploring categorical data", "Statistics for two categorical variables: Exploring categorical data"], "Unit 2: Exploring one-variable quantitative data: Displaying and describing": ["Representing a quantitative variable with dot plots: Exploring one-variable quantitative data: Displaying and describing", "Representing a quantitative variable with histograms and stem plots: Exploring one-variable quantitative data: Displaying and describing", "Describing the distribution of a quantitative variable: Exploring one-variable quantitative data: Displaying and describing", "Comparing distributions of a quantitative variable: Exploring one-variable quantitative data: Displaying and describing"], "Unit 3: Exploring one-variable quantitative data: Summary statistics": ["Measuring center in quantitative data: Exploring one-variable quantitative data: Summary statistics", "Measuring variability in quantitative data: Exploring one-variable quantitative data: Summary statistics", "Effects of linear transformations: Exploring one-variable quantitative data: Summary statistics", "More on standard deviation (optional): Exploring one-variable quantitative data: Summary statistics", "Graphical representations of summary statistics: Exploring one-variable quantitative data: Summary statistics"], "Unit 4: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution": ["Percentiles: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Z-scores: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Density curves: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Normal distributions and the empirical rule: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Normal distribution calculations: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution"], "Unit 5: Exploring two-variable quantitative data": ["Representing the relationship between two quantitative variables: Exploring two-variable quantitative data", "Correlation: Exploring two-variable quantitative data", "Residuals: Exploring two-variable quantitative data", "Least-squares regression: Exploring two-variable quantitative data"], "Unit 6: Collecting data": ["Introduction to planning a study: Collecting data", "Potential problems with sampling: Collecting data", "Random sampling and data collection: Collecting data", "Introduction to experimental design: Collecting data", "Inference and experiments: Collecting data"], "Unit 7: Probability": ["Estimating probabilities using simulation: Probability", "Mutually exclusive events and unions of events: Probability", "Conditional probability: Probability", "Independent versus dependent events and the multiplication rule: Probability"], "Unit 8: Random variables and probability distributions": ["Introduction to random variables and probability distributions: Random variables and probability distributions", "Mean and standard deviation of random variables: Random variables and probability distributions", "Transforming random variables: Random variables and probability distributions", "Combining random variables: Random variables and probability distributions", "Introduction to the binomial distribution: Random variables and probability distributions", "Parameters for a binomial distribution: Random variables and probability distributions", "The geometric distribution: Random variables and probability distributions"], "Unit 9: Sampling distributions": ["The normal distribution, revisited: Sampling distributions", "The central limit theorem: Sampling distributions", "Biased and unbiased point estimates: Sampling distributions", "Sampling distributions for sample proportions: Sampling distributions", "Sampling distributions for differences in sample proportions: Sampling distributions", "Sampling distributions for sample means: Sampling distributions", "Sampling distributions for differences in sample means: Sampling distributions"], "Unit 10: Inference for categorical data: Proportions": ["Introduction to confidence intervals: Inference for categorical data: Proportions", "Confidence intervals for proportions: Inference for categorical data: Proportions", "The idea of significance tests: Inference for categorical data: Proportions", "Setting up a test for a population proportion: Inference for categorical data: Proportions", "Carrying out a test for a population proportion: Inference for categorical data: Proportions", "Concluding a test for a population proportion: Inference for categorical data: Proportions", "Potential errors when performing tests: Inference for categorical data: Proportions", "Confidence intervals for the difference of two proportions: Inference for categorical data: Proportions", "Testing for the difference of two population proportions: Inference for categorical data: Proportions"], "Unit 11: Inference for quantitative data: Means": ["Constructing a confidence interval for a population mean: Inference for quantitative data: Means", "Setting up a test for a population mean: Inference for quantitative data: Means", "Carrying out a test for a population mean: Inference for quantitative data: Means", "Confidence intervals for the difference of two means: Inference for quantitative data: Means", "Testing for the difference of two population means: Inference for quantitative data: Means"], "Unit 12: Inference for categorical data: Chi-square": ["Chi-square test for goodness of fit: Inference for categorical data: Chi-square", "Chi square tests for relationships (homogeneity or independence): Inference for categorical data: Chi-square"], "Unit 13: Inference for quantitative data: slopes": ["Confidence intervals for the slope of a regression model: Inference for quantitative data: slopes", "Testing for the slope of a regression model: Inference for quantitative data: slopes"], "Unit 14: Prepare for the 2022 AP\u00ae\ufe0e Statistics Exam": ["Prepare for the exam: Prepare for the 2022 AP\u00ae\ufe0e Statistics Exam", "Start Course challenge"]}}}}
{"course_title": "Multivariable calculus", "course_url": "/math/multivariable-calculus", "page_contents": {"syllabus": {"topics": {"Unit 1: Thinking about multivariable functions": ["Introduction to multivariable calculus: Thinking about multivariable functions", "Visualizing scalar-valued functions: Thinking about multivariable functions", "Visualizing vector-valued functions: Thinking about multivariable functions", "Transformations: Thinking about multivariable functions"], "Unit 2: Derivatives of multivariable functions": ["Partial derivatives: Derivatives of multivariable functions", "Gradient and directional derivatives: Derivatives of multivariable functions", "Differentiating parametric curves: Derivatives of multivariable functions", "Multivariable chain rule: Derivatives of multivariable functions", "Curvature: Derivatives of multivariable functions", "Partial derivatives of vector-valued functions: Derivatives of multivariable functions", "Divergence: Derivatives of multivariable functions", "Curl: Derivatives of multivariable functions", "Laplacian: Derivatives of multivariable functions", "Jacobian: Derivatives of multivariable functions"], "Unit 3: Applications of multivariable derivatives": ["Tangent planes and local linearization: Applications of multivariable derivatives", "Quadratic approximations: Applications of multivariable derivatives", "Optimizing multivariable functions: Applications of multivariable derivatives", "Lagrange multipliers and constrained optimization: Applications of multivariable derivatives"], "Unit 4: Integrating multivariable functions": ["Line integrals for scalar functions: Integrating multivariable functions", "Line integrals in vector fields: Integrating multivariable functions", "Double integrals: Integrating multivariable functions", "Triple integrals: Integrating multivariable functions", "Surface integral preliminaries: Integrating multivariable functions", "Surface integrals: Integrating multivariable functions", "Flux in 3D: Integrating multivariable functions"], "Unit 5: Green's, Stokes', and the divergence theorems": ["2D divergence theorem: Green's, Stokes', and the divergence theorems", "Stokes' theorem: Green's, Stokes', and the divergence theorems", "3D divergence theorem: Green's, Stokes', and the divergence theorems", "Proof of Stokes' theorem: Green's, Stokes', and the divergence theorems", "Types of regions in three dimensions: Green's, Stokes', and the divergence theorems", "Divergence theorem proof: Green's, Stokes', and the divergence theorems", "Start Course challenge"]}}}}
{"course_title": "Differential equations", "course_url": "/math/differential-equations", "page_contents": {"syllabus": {"topics": {"Unit 1: First order differential equations": ["Intro to differential equations: First order differential equations", "Slope fields: First order differential equations", "Euler's Method: First order differential equations", "Separable equations: First order differential equations", "Exponential models: First order differential equations", "Logistic models: First order differential equations", "Exact equations and integrating factors: First order differential equations", "Homogeneous equations: First order differential equations"], "Unit 2: Second order linear equations": ["Linear homogeneous equations: Second order linear equations", "Complex and repeated roots of characteristic equation: Second order linear equations", "Method of undetermined coefficients: Second order linear equations"], "Unit 3: Laplace transform": ["Laplace transform: Laplace transform", "Properties of the Laplace transform: Laplace transform", "Laplace transform to solve a differential equation: Laplace transform", "The convolution integral: Laplace transform"]}}}}
{"course_title": "Linear algebra", "course_url": "/math/linear-algebra", "page_contents": {"syllabus": {"topics": {"Unit 1: Vectors and spaces": ["Vectors: Vectors and spaces", "Linear combinations and spans: Vectors and spaces", "Linear dependence and independence: Vectors and spaces", "Subspaces and the basis for a subspace: Vectors and spaces", "Vector dot and cross products: Vectors and spaces", "Matrices for solving systems by elimination: Vectors and spaces", "Null space and column space: Vectors and spaces"], "Unit 2: Matrix transformations": ["Functions and linear transformations: Matrix transformations", "Linear transformation examples: Matrix transformations", "Transformations and matrix multiplication: Matrix transformations", "Inverse functions and transformations: Matrix transformations", "Finding inverses and determinants: Matrix transformations", "More determinant depth: Matrix transformations", "Transpose of a matrix: Matrix transformations"], "Unit 3: Alternate coordinate systems (bases)": ["Orthogonal complements: Alternate coordinate systems (bases)", "Orthogonal projections: Alternate coordinate systems (bases)", "Change of basis: Alternate coordinate systems (bases)", "Orthonormal bases and the Gram-Schmidt process: Alternate coordinate systems (bases)", "Eigen-everything: Alternate coordinate systems (bases)"]}}}}
{"course_title": "Middle school biology - NGSSNEW", "course_url": "/science/ms-biology", "page_contents": {"syllabus": {"topics": {"Natural and artificial selection: Unit test": ["Start Course challenge", "Watch an introduction video2:222 minutes 22 seconds", "Learn more", "Learn more", "Watch an introduction video2:222 minutes 22 seconds"], "Unit 1: Cells and organisms": ["Cells and organisms: Cells and organisms", "Cell parts and functions: Cells and organisms", "Organization in the human body: Cells and organisms", "Sensory processing and the brain: Cells and organisms"], "Unit 2: Organism growth and reproduction": ["Sexual and asexual reproduction: Organism growth and reproduction", "Animal behavior and offspring success: Organism growth and reproduction", "Plant reproductive success: Organism growth and reproduction", "Organism growth and the environment: Organism growth and reproduction"], "Unit 3: Matter and energy in organisms": ["Photosynthesis in organisms: Matter and energy in organisms", "Food and energy in organisms: Matter and energy in organisms"], "Populations, communities, and ecosystems: Interactions in ecosystems": ["Resources and population growth: Interactions in ecosystems", "Ecological interactions: Interactions in ecosystems"], "Unit 5: Matter and energy in ecosystems": ["Photosynthesis in ecosystems: Matter and energy in ecosystems", "Matter and energy in foodwebs: Matter and energy in ecosystems"], "Unit 6: Ecosystems and biodiversity": ["Ecosystem dynamics: Ecosystems and biodiversity", "Biodiversity and ecosystem health: Ecosystems and biodiversity", "Humans and ecosystems: Ecosystems and biodiversity"], "Unit 7: Inheritance and variation": ["Chromosomes: Inheritance and variation", "Genes, proteins, and traits: Inheritance and variation", "Mutations: Inheritance and variation", "Reproduction and genetic variation: Inheritance and variation"], "Unit 8: Evolution": ["Evolution and common ancestry: Evolution", "The fossil record: Evolution", "Evidence of evolution: anatomy: Evolution", "Evidence of evolution: embryology: Evolution"], "Unit 9: Natural and artificial selection": ["Natural selection: Natural and artificial selection", "Adaptation and environmental change: Natural and artificial selection", "Artificial selection: Natural and artificial selection", "Start Course challenge"]}}}}
{"course_title": "Middle school Earth and space science - NGSSNEW", "course_url": "/science/middle-school-earth-and-space-science", "page_contents": {"syllabus": {"topics": {"Earth and society: Unit test": ["Start Course challenge", "Watch an introduction video2:512 minutes 51 seconds", "Learn more", "Learn more", "Watch an introduction video2:512 minutes 51 seconds"], "Unit 1: Earth in space": ["Earth's place in the universe: Earth in space", "Galaxies and gravity: Earth in space", "The solar system: Earth in space"], "Unit 2: The Earth-sun-moon system": ["Seasons : The Earth-sun-moon system", "The moon and its motions: The Earth-sun-moon system", "Solar eclipses: The Earth-sun-moon system"], "Unit 3: Weather and climate": ["The water cycle : Weather and climate", "Weather: Weather and climate", "Global winds and currents: Weather and climate", "Regional climates: Weather and climate"], "Unit 4: The geosphere": ["The rock cycle: The geosphere", "Fossils and rock layers: The geosphere", "Plate tectonics: The geosphere", "Weathering and erosion: The geosphere"], "Unit 5: Earth and society": ["Natural resources: Earth and society", "Natural hazards: Earth and society", "Human impacts on the environment: Earth and society", "Earth's changing climate: Earth and society", "Start Course challenge"]}}}}
{"course_title": "Middle school physics - NGSSNEW", "course_url": "/science/ms-physics", "page_contents": {"syllabus": {"topics": {"Waves: Unit test": ["Start Course challenge", "Watch an introduction video1:581 minute 58 seconds", "Learn more", "Learn more", "Watch an introduction video1:581 minute 58 seconds"], "Unit 1: Movement and forces": ["Representing motion: Movement and forces", "Forces and acceleration: Movement and forces", "Action and reaction forces: Movement and forces"], "Unit 2: Forces at a distance": ["Gravitational forces: Forces at a distance", "Electric forces: Forces at a distance", "Magnetic forces: Forces at a distance", "Fields: Forces at a distance", "Electromagnetism: Forces at a distance"], "Unit 3: Energy": ["Kinetic energy: Energy", "Potential energy: Energy"], "Unit 4: Waves": ["Wave properties: Waves", "Mechanical waves and light: Waves", "Transmission and refraction: Waves", "Absorption and reflection: Waves", "Digital signals: Waves", "Start Course challenge"]}}}}
{"course_title": "High school biology", "course_url": "/science/high-school-biology", "page_contents": {"syllabus": {"topics": {"Unit 1: Biology foundations": ["Biology and the scientific method: Biology foundations", "Important molecules for biology: Biology foundations", "Water and life: Biology foundations", "pH, acids, and bases: Biology foundations"], "Unit 2: Cells": ["Introduction to cells: Cells", "Basic cell structures: Cells", "The cell membrane: Cells", "Eukaryotic cell structures: Cells", "Prokaryotes and eukaryotes: Cells", "Plant vs animal cells: Cells"], "Unit 3: Energy and transport": ["Introduction to metabolism: Energy and transport", "Enzymes: Energy and transport", "Passive and active transport: Energy and transport", "Osmosis and tonicity: Energy and transport", "Photosynthesis: Energy and transport", "Cellular respiration: Energy and transport"], "Unit 4: Reproduction and cell division": ["Types of reproduction: Reproduction and cell division", "The cell cycle and mitosis: Reproduction and cell division", "Meiosis: Reproduction and cell division", "Fertilization and development: Reproduction and cell division"], "Unit 5: Classical genetics": ["Introduction to heredity: Classical genetics", "Non-Mendelian inheritance: Classical genetics", "Sex linkage: Classical genetics", "Pedigrees: Classical genetics"], "Unit 6: Molecular genetics": ["RNA and protein synthesis: Molecular genetics", "Biotechnology: Molecular genetics"], "Unit 7: Evolution": ["Evolution and natural selection: Evolution", "Evidence of evolution: Evolution", "Phylogeny: Evolution"], "Unit 8: Human body systems": ["Body structure and homeostasis: Human body systems", "The circulatory and respiratory systems: Human body systems", "The musculoskeletal system: Human body systems", "The digestive and excretory systems: Human body systems", "The nervous and endocrine systems: Human body systems", "The reproductive system: Human body systems", "The immune system: Human body systems"], "Community ecology: Ecology": ["Ecological relationships: Ecology", "Trophic levels: Ecology", "Biogeochemical cycles: Ecology", "Human impact on ecosystems: Ecology", "Start Course challenge"]}}}}
{"course_title": "High school biology - NGSS", "course_url": "/science/hs-biology", "page_contents": {"syllabus": {"topics": {"Unit 1: Genes, cells, and organisms": ["Cell specialization: Genes, cells, and organisms", "Genes, proteins, and cells: Genes, cells, and organisms", "Organization of multicellular organisms: Genes, cells, and organisms"], "Unit 2: Growth and feedback in organisms": ["Cell division and organism growth: Growth and feedback in organisms", "Feedback in living systems: Growth and feedback in organisms"], "Unit 3: Matter and energy in organisms": ["Photosynthesis: Matter and energy in organisms", "Formation of biomolecules: Matter and energy in organisms", "Cellular respiration: Matter and energy in organisms"], "Unit 4: Matter and energy in ecosystems": ["Population growth and carrying capacity: Matter and energy in ecosystems", "Flow of energy and cycling of matter in ecosystems: Matter and energy in ecosystems", "The carbon cycle: Matter and energy in ecosystems"], "Unit 5: Interactions in ecosystems": ["Ecosystem resilience and change: Interactions in ecosystems", "Human impacts on ecosystems: Interactions in ecosystems"], "Unit 6: Inheritance and variation": ["Gene expression and regulation: Inheritance and variation", "Sources of genetic variation: Inheritance and variation", "Genes, traits, and the environment: Inheritance and variation"], "Unit 7: Evolution and natural selection": ["Evidence of common ancestry: Evolution and natural selection", "Natural selection: Evolution and natural selection", "Natural selection and evolution: Evolution and natural selection", "Evolution of group behavior: Evolution and natural selection"], "Unit 8: Adaptation and environmental change": ["Natural selection and adaptation: Adaptation and environmental change", "Adaptation and environmental change: Adaptation and environmental change", "Species and the environment: Adaptation and environmental change", "Extinction: Adaptation and environmental change"], "Unit 9: Biodiversity and human impacts": ["Humans and biodiversity: Biodiversity and human impacts", "Sustainability and natural resource management: Biodiversity and human impacts", "Science, technology, and the environment: Biodiversity and human impacts"], "Unit 10: Creativity in biology": ["Creativity in biology: Creativity in biology", "Start Course challenge"]}}}}
{"course_title": "High school physics", "course_url": "/science/high-school-physics", "page_contents": {"syllabus": {"topics": {"Unit 1: One-dimensional motion": ["Physics foundations: One-dimensional motion", "Distance, displacement, and coordinate systems: One-dimensional motion", "Average velocity and average speed: One-dimensional motion", "Velocity and speed from graphs: One-dimensional motion", "Average and instantaneous acceleration: One-dimensional motion", "Motion with constant acceleration: One-dimensional motion", "Objects in freefall: One-dimensional motion"], "Unit 2: Forces and Newton's laws of motion": ["Introduction to forces and free body diagrams: Forces and Newton's laws of motion", "Newton's first law: Mass and inertia: Forces and Newton's laws of motion", "Newton's second law: Forces and Newton's laws of motion", "Newton's third law: Forces and Newton's laws of motion"], "Unit 3: Two-dimensional motion": ["Analyzing vectors using trigonometry: Two-dimensional motion", "Graphs of projectile motion: Two-dimensional motion", "Horizontally launched projectiles: Two-dimensional motion", "Projectiles launched at an angle: Two-dimensional motion", "Angled forces: Two-dimensional motion", "Inclined planes: Two-dimensional motion", "Friction: Two-dimensional motion"], "Unit 4: Uniform circular motion and gravitation": ["Uniform circular motion introduction: Uniform circular motion and gravitation", "Centripetal acceleration: Uniform circular motion and gravitation", "Centripetal forces: Uniform circular motion and gravitation", "Newton's law of gravitation: Uniform circular motion and gravitation"], "Unit 5: Work and energy": ["Introduction to work: Work and energy", "Work-energy theorem: Work and energy", "Spring potential energy and Hooke's law: Work and energy", "Gravitational potential energy and conservative forces: Work and energy", "Conservation of energy: Work and energy", "Power: Work and energy"], "Unit 6: Linear momentum and collisions": ["Introduction to linear momentum and impulse: Linear momentum and collisions", "Inelastic collisions: Linear momentum and collisions", "Center of mass and two-dimensional collisions: Linear momentum and collisions"], "Unit 7: Torque and angular momentum": ["Introduction to rotational motion: Torque and angular momentum", "Angular kinematics: Torque and angular momentum", "Torque and equilibrium: Torque and angular momentum", "Rotational inertia and angular second law: Torque and angular momentum", "Rotational kinetic energy: Torque and angular momentum", "Angular momentum and angular impulse: Torque and angular momentum", "Conservation of angular momentum: Torque and angular momentum", "Gravitational potential energy at large distances: Torque and angular momentum"], "Unit 8: Simple harmonic motion": ["Introduction to simple harmonic motion: Simple harmonic motion", "Simple harmonic motion in spring-mass systems: Simple harmonic motion", "Simple pendulums: Simple harmonic motion", "Energy in simple harmonic oscillators: Simple harmonic motion"], "Unit 9: Waves": ["Introduction to waves: Waves", "Wave characteristics: Waves", "Standing waves: Waves", "Wave interference: Waves"], "Unit 10: Sound": ["Introduction to sound: Sound", "Standing sound waves: Sound", "Beats and interference of sound waves: Sound", "Doppler effect: Sound"], "Unit 11: Static electricity": ["Electric charge: Static electricity", "Conservation of charge: Static electricity", "Coulomb's law and electric force: Static electricity", "Explore electrostatics: Static electricity"], "Unit 12: DC Circuits": ["Electric current, resistivity, and Ohm's law: DC Circuits", "Electric power and DC circuits: DC Circuits", "Series and parallel resistors: DC Circuits", "DC Ammeters and voltmeters: DC Circuits", "Discovery of resistors: DC Circuits", "Explore electric motors: DC Circuits", "Start Course challenge"]}}}}
{"course_title": "High school physics - NGSS", "course_url": "/science/hs-physics", "page_contents": {"syllabus": {"topics": {"Unit 1: Forces and motion": ["Force, mass, and acceleration: Forces and motion", "Introduction to momentum: Forces and motion"], "Unit 2: Types of interactions": ["Newton's law of universal gravitation: Types of interactions", "Coulomb's law: Types of interactions", "Electric and magnetic fields: Types of interactions"], "Unit 3: Introduction to energy": ["Introduction to energy: Introduction to energy", "Forms of energy: Introduction to energy", "Energy and fields: Introduction to energy", "Energy at the microscopic scale: Introduction to energy"], "Unit 4: Modeling energy": ["Calculating energy: Modeling energy", "Energy in systems: Modeling energy", "Predictions using energy: Modeling energy", "Thermodynamics: Modeling energy"], "Unit 5: Wave properties": ["Waves: Wave properties", "Wave interference: Wave properties"], "Unit 6: Electromagnetic radiation": ["Wave\u2013particle duality: Electromagnetic radiation", "Electromagnetic radiation and matter: Electromagnetic radiation", "Emission of electromagnetic radiation: Electromagnetic radiation"], "Unit 7: Information technologies": ["Information in waves: Information technologies", "Technology and waves: Information technologies", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Biology", "course_url": "/science/ap-biology", "page_contents": {"syllabus": {"topics": {"Unit 1: Chemistry of life": ["Structure of water and hydrogen bonding: Chemistry of life", "Elements of life: Chemistry of life", "Introduction to biological macromolecules: Chemistry of life", "Properties, structure, and function of biological macromolecules: Chemistry of life", "Nucleic acids: Chemistry of life"], "Unit 2: Cell structure and function": ["Cell structures and their functions: Cell structure and function", "Cell size: Cell structure and function", "Plasma membranes: Cell structure and function", "Membrane permeability : Cell structure and function", "Membrane transport: Cell structure and function", "Facilitated diffusion: Cell structure and function", "Mechanisms of transport:  tonicity and osmoregulation: Cell structure and function", "Cell compartmentalization and its origins: Cell structure and function"], "Unit 3: Cellular energetics": ["Enzyme structure and catalysis: Cellular energetics", "Cellular energy: Cellular energetics", "Photosynthesis: Cellular energetics", "Cellular respiration: Cellular energetics", "Fitness: Cellular energetics"], "Unit 4: Cell communication and cell cycle": ["Cell communication: Cell communication and cell cycle", "Signal transduction: Cell communication and cell cycle", "Changes in signal transduction pathways: Cell communication and cell cycle", "Feedback: Cell communication and cell cycle", "Cell cycle: Cell communication and cell cycle", "Regulation of cell cycle: Cell communication and cell cycle"], "Unit 5: Heredity": ["Meiosis and genetic diversity: Heredity", "Mendelian genetics: Heredity", "Environmental effects on phenotype: Heredity", "Chromosomal inheritance: Heredity"], "Unit 6: Gene expression and regulation": ["DNA and RNA structure: Gene expression and regulation", "Replication: Gene expression and regulation", "Transcription and RNA processing: Gene expression and regulation", "Translation: Gene expression and regulation", "Regulation of gene expression and cell specialization: Gene expression and regulation", "Mutations: Gene expression and regulation", "Biotechnology: Gene expression and regulation"], "Unit 7: Natural selection": ["Natural selection: Natural selection", "Population genetics: Natural selection", "Hardy-Weinberg equilibrium: Natural selection", "Evidence for evolution: Natural selection", "Common ancestry and continuing evolution: Natural selection", "Phylogeny: Natural selection", "Speciation: Natural selection", "Extinction: Natural selection", "Variations in populations: Natural selection", "Origins of life on earth: Natural selection"], "Community ecology: Ecology": ["Biodiversity: Ecology", "Disruptions to ecosystems: Ecology"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Chemistry", "course_url": "/science/ap-chemistry-beta", "page_contents": {"syllabus": {"topics": {"Unit 1: Atomic structure and properties": ["Moles and molar mass: Atomic structure and properties", "Mass spectrometry of elements: Atomic structure and properties", "Elemental composition of pure substances: Atomic structure and properties", "Composition of mixtures: Atomic structure and properties", "Periodic trends: Atomic structure and properties", "Valence electrons and ionic compounds: Atomic structure and properties", "Photoelectron spectroscopy: Atomic structure and properties"], "Unit 2: Molecular and ionic compound structure and properties": ["Types of chemical bonds: Molecular and ionic compound structure and properties", "Intramolecular force and potential energy: Molecular and ionic compound structure and properties", "Structure of ionic solids: Molecular and ionic compound structure and properties", "Structure of metals and alloys: Molecular and ionic compound structure and properties", "Lewis diagrams: Molecular and ionic compound structure and properties", "Resonance and formal charge: Molecular and ionic compound structure and properties", "VSEPR: Molecular and ionic compound structure and properties", "Bond hybridization: Molecular and ionic compound structure and properties"], "Unit 3: Intermolecular forces and properties": ["Intermolecular forces: Intermolecular forces and properties", "Properties of solids: Intermolecular forces and properties", "Solids, liquids, and gases: Intermolecular forces and properties", "Ideal gas law: Intermolecular forces and properties", "Kinetic molecular theory: Intermolecular forces and properties", "Deviation from ideal gas law: Intermolecular forces and properties", "Solutions and mixtures: Intermolecular forces and properties", "Representations of solutions: Intermolecular forces and properties", "Separation of solutions and mixtures chromatography: Intermolecular forces and properties", "Solubility: Intermolecular forces and properties", "Spectroscopy and the electromagnetic spectrum: Intermolecular forces and properties", "Electronic transitions in spectroscopy: Intermolecular forces and properties", "Beer\u2013Lambert law: Intermolecular forces and properties"], "Unit 4: Chemical reactions": ["Net ionic equations: Chemical reactions", "Representations of reactions: Chemical reactions", "Physical and chemical changes: Chemical reactions", "Introduction to acid\u2013base reactions: Chemical reactions", "Introduction to titration: Chemical reactions"], "Unit 5: Kinetics": ["Reaction rates: Kinetics", "Introduction to rate law: Kinetics", "Concentration changes over time: Kinetics", "Reaction mechanisms: Kinetics", "Activation energy and reaction rate: Kinetics", "Catalysis: Kinetics"], "Unit 6: Thermodynamics": ["Endothermic and exothermic processes: Thermodynamics", "Heat transfer and thermal equilibrium: Thermodynamics", "Heat capacity and calorimetry: Thermodynamics", "Energy of phase changes: Thermodynamics", "Introduction to enthalpy of reaction: Thermodynamics", "Hess's law: Thermodynamics", "Enthalpy of formation: Thermodynamics", "Bond enthalpies: Thermodynamics"], "Unit 7: Equilibrium": ["Introduction to equilibrium: Equilibrium", "Equilibrium constant and reaction quotient: Equilibrium", "Calculating the equilibrium constant: Equilibrium", "Magnitude and properties of the equilibrium constant: Equilibrium", "Calculating equilibrium concentrations: Equilibrium", "Using the reaction quotient: Equilibrium", "Le Ch\u00e2telier's principle: Equilibrium", "Solubility equilibria: Equilibrium"], "Unit 8: Acids and bases": ["Introduction to acids and bases: Acids and bases", "pH and pOH of strong acids and bases: Acids and bases", "Weak acid and base equilibria: Acids and bases", "Molecular structure of acids and bases: Acids and bases", "Acid\u2013base reactions: Acids and bases", "Buffers: Acids and bases", "Acid\u2013base titrations: Acids and bases"], "Unit 9: Applications of thermodynamics": ["Entropy: Applications of thermodynamics", "Gibbs free energy and thermodynamic favorability: Applications of thermodynamics", "Free energy of dissolution: Applications of thermodynamics", "Thermodynamics vs. kinetics: Applications of thermodynamics", "Free energy and equilibrium: Applications of thermodynamics", "Coupled reactions: Applications of thermodynamics", "Galvanic (voltaic) and electrolytic cells: Applications of thermodynamics", "Cell potential and free energy: Applications of thermodynamics", "Cell potential under nonstandard conditions: Applications of thermodynamics", "Electrolysis and Faraday's law: Applications of thermodynamics", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Environmental Science", "course_url": "/science/ap-college-environmental-science", "page_contents": {"syllabus": {"topics": {"Unit 1: The living world: ecosystems and biodiversity": ["Ecosystems and biomes: The living world: ecosystems and biodiversity", "Biogeochemical cycles: The living world: ecosystems and biodiversity", "Matter and energy flow: The living world: ecosystems and biodiversity", "Intro to biodiversity and biogeography: The living world: ecosystems and biodiversity", "Changes to ecosystems: The living world: ecosystems and biodiversity"], "Unit 2: Populations": ["Species growth: Populations", "Population growth: Populations", "Human populations: Populations"], "Unit 3: Earth systems and resources": ["Plate tectonics: Earth systems and resources", "Earth's climate: Earth systems and resources"], "Unit 4: Land and water use": ["Intro to land and water use: Land and water use", "Effects of land and water use I: Land and water use", "Effect of land and water use II: Land and water use", "Intro to sustainable practices: Land and water use", "Types of sustainable practices: Land and water use"], "Unit 5: Energy resources and consumption": ["Intro to energy resources and consumption: Energy resources and consumption", "Fuel types and uses II: Energy resources and consumption", "Energy conservation: Energy resources and consumption"], "Unit 6: Atmospheric pollution": ["Air pollution: Atmospheric pollution", "Reducing air pollution: Atmospheric pollution", "Other atmospheric pollution: Atmospheric pollution"], "Unit 7: Aquatic and terrestrial pollution": ["Sources of pollution: Aquatic and terrestrial pollution", "Types of aquatic and terrestrial pollution: Aquatic and terrestrial pollution", "Waste disposal, reduction, and treatment: Aquatic and terrestrial pollution", "Pollution and health: Aquatic and terrestrial pollution", "Pathogens: Aquatic and terrestrial pollution"], "Unit 8: Global change": ["Ozone: Global change", "Greenhouse effect: Global change", "Climate change: Global change", "Human impact on species: Global change", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Physics 1", "course_url": "/science/ap-college-physics-1", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Health and Medicine", "course_url": "/science/health-and-medicine", "page_contents": {"syllabus": {"topics": {"Unit 1: Introduction to human body systems": ["Circulatory system introduction: Introduction to human body systems", "Respiratory system introduction: Introduction to human body systems", "Hematologic system introduction: Introduction to human body systems", "Endocrine system introduction: Introduction to human body systems", "Nervous system introduction: Introduction to human body systems", "Gastrointestinal system introduction: Introduction to human body systems", "Musculoskeletal system introduction: Introduction to human body systems", "Reproductive system introduction: Introduction to human body systems", "Immunologic system introduction: Introduction to human body systems", "Urinary system introduction: Introduction to human body systems", "Integumentary system introduction: Introduction to human body systems", "Lymphatic system introduction: Introduction to human body systems"], "Unit 2: Circulatory system anatomy and physiology": ["Circulatory anatomy and blood flow: Circulatory system anatomy and physiology", "Heart muscle contraction: Circulatory system anatomy and physiology", "Heart depolarization: Circulatory system anatomy and physiology", "Blood pressure: Circulatory system anatomy and physiology", "Blood vessels: Circulatory system anatomy and physiology", "Blood pressure control by the kidney: Circulatory system anatomy and physiology", "Nerve regulation of the heart: Circulatory system anatomy and physiology", "Preload and afterload: Circulatory system anatomy and physiology", "Pressure volume loops: Circulatory system anatomy and physiology", "Changing the PV loop: Circulatory system anatomy and physiology", "Fetal circulation: Circulatory system anatomy and physiology"], "Unit 3: Circulatory system diseases": ["Heart disease and heart attacks: Circulatory system diseases", "Atherosclerosis, arteriosclerosis, and arteriolosclerosis: Circulatory system diseases", "Stroke diagnosis and management: Circulatory system diseases", "Aortic dissection and aneurysm: Circulatory system diseases", "Myocarditis and pericarditis : Circulatory system diseases", "Cardiomyopathy: Circulatory system diseases", "Cardiac dysrhythmias and tachycardias: Circulatory system diseases", "Heart valve diseases: Circulatory system diseases", "Acyanotic heart diseases: Circulatory system diseases", "Cyanotic heart diseases: Circulatory system diseases", "Shock: Circulatory system diseases", "Vasculitis: Circulatory system diseases"], "Unit 4: Respiratory system anatomy and physiology": ["Lung structure and function: Respiratory system anatomy and physiology", "Gas exchange: Respiratory system anatomy and physiology", "Breathing control: Respiratory system anatomy and physiology"], "Unit 5: Respiratory system diseases": ["Introduction to pulmonary diseases: Respiratory system diseases", "Asthma: Respiratory system diseases", "Emphysema (COPD): Respiratory system diseases", "Chronic Bronchitis (COPD): Respiratory system diseases", "Cystic fibrosis: Respiratory system diseases", "Occupational lung diseases: Respiratory system diseases", "Pulmonary hypertension: Respiratory system diseases", "Pneumonia: Respiratory system diseases", "Pleural Effusion: Respiratory system diseases", "Lung cancer: Respiratory system diseases", "Nose, sinus, and upper respiratory conditions: Respiratory system diseases", "Throat conditions: Respiratory system diseases", "Laryngeal conditions: Respiratory system diseases", "Bronchiolitis: Respiratory system diseases"], "Unit 6: Hematologic system physiology and disease": ["Blood and blood cells: Hematologic system physiology and disease", "Hemoglobin: Hematologic system physiology and disease", "Bleeding and impaired hemostasis: Hematologic system physiology and disease", "Leukemia: Hematologic system physiology and disease", "Iron deficiency anemia and anemia of chronic disease: Hematologic system physiology and disease", "Plasma cell dyscrasias: Hematologic system physiology and disease", "Myeloproliferative disorders: Hematologic system physiology and disease"], "Unit 7: Endocrine system physiology and disease": ["Intro to endocrine hormones: Endocrine system physiology and disease", "Biological basis of behavior: Endocrine system: Endocrine system physiology and disease"], "Unit 8: Nervous system physiology and disease": ["Structure and function of the nervous system: Nervous system physiology and disease", "Neural cell types: Nervous system physiology and disease", "Function of neurons and neurotransmitters: Nervous system physiology and disease", "Neuron membrane potentials: Nervous system physiology and disease", "Sensory perception: Nervous system physiology and disease", "Sight (vision): Nervous system physiology and disease", "Sound (Audition): Nervous system physiology and disease", "Somatosensation: Nervous system physiology and disease", "Taste (gustation) and smell (olfaction): Nervous system physiology and disease", "Multiple sclerosis: Nervous system physiology and disease", "Miscellaneous topics: Nervous system physiology and disease"], "Unit 9: Brain function and mental health": ["Cognition: Brain function and mental health", "Attention and language: Brain function and mental health", "Sleep and consciousness: Brain function and mental health", "Memory: Brain function and mental health", "Emotion: Brain function and mental health"], "Unit 10: Gastrointestinal system physiology and disease": ["Components of the GI tract: Gastrointestinal system physiology and disease", "Inflammatory bowel disease: Gastrointestinal system physiology and disease", "Celiac disease: Gastrointestinal system physiology and disease", "Colon diseases: Gastrointestinal system physiology and disease", "BMI and diet: Gastrointestinal system physiology and disease"], "Unit 11: Musculoskeletal system physiology and disease": ["Muscle contraction: Musculoskeletal system physiology and disease", "Muscle innervation : Musculoskeletal system physiology and disease", "Skeletal system introduction: Musculoskeletal system physiology and disease"], "Unit 12: Reproductive system and pregnancy": ["Female reproductive system: Reproductive system and pregnancy", "Male reproductive system: Reproductive system and pregnancy", "Pregnancy anatomy and physiology: Reproductive system and pregnancy", "Pregnancy complications: Reproductive system and pregnancy", "Fetal circulation: Reproductive system and pregnancy"], "Unit 13: Infectious diseases": ["Bacteria and viruses: Infectious diseases", "Pertussis: Infectious diseases", "Influenza: Infectious diseases"], "Unit 14: Other topics in health and medicine": ["Health care system: Other topics in health and medicine", "Lab values and concentrations : Other topics in health and medicine", "Child growth and development: Other topics in health and medicine", "Cancer: Other topics in health and medicine", "Inflammation and exposures: Other topics in health and medicine"]}}}}
{"course_title": "Computer programming", "course_url": "/computing/computer-programming", "page_contents": {"syllabus": {"topics": {"Unit 1: Intro to JS: Drawing & Animation": ["Intro to programming: Intro to JS: Drawing & Animation", "Drawing basics: Intro to JS: Drawing & Animation", "Coloring: Intro to JS: Drawing & Animation", "Variables: Intro to JS: Drawing & Animation", "Interactive programs: Intro to JS: Drawing & Animation", "Text and strings: Intro to JS: Drawing & Animation", "Functions: Intro to JS: Drawing & Animation", "Logic and if Statements: Intro to JS: Drawing & Animation", "Debugging programs: Intro to JS: Drawing & Animation", "Looping: Intro to JS: Drawing & Animation", "Writing clean code: Intro to JS: Drawing & Animation", "Arrays: Intro to JS: Drawing & Animation", "Objects: Intro to JS: Drawing & Animation", "Object-Oriented Design: Intro to JS: Drawing & Animation"], "Unit 2: Intro to HTML/CSS: Making webpages": ["Intro to HTML: Intro to HTML/CSS: Making webpages", "Intro to CSS: Intro to HTML/CSS: Making webpages", "More HTML tags: Intro to HTML/CSS: Making webpages", "CSS text properties: Intro to HTML/CSS: Making webpages", "CSS layout: Intro to HTML/CSS: Making webpages", "More CSS selectors: Intro to HTML/CSS: Making webpages", "Other ways to embed CSS: Intro to HTML/CSS: Making webpages"], "Unit 3: Intro to SQL: Querying and managing data": ["SQL basics: Intro to SQL: Querying and managing data", "More advanced SQL queries: Intro to SQL: Querying and managing data"], "Unit 6: HTML/JS: Making webpages interactive": ["Get ready to make your webpages interactive: HTML/JS: Making webpages interactive", "JS and the DOM: HTML/JS: Making webpages interactive", "DOM access methods: HTML/JS: Making webpages interactive", "DOM modification: HTML/JS: Making webpages interactive", "DOM events: HTML/JS: Making webpages interactive", "DOM animation: HTML/JS: Making webpages interactive"], "Unit 7: HTML/JS: Making webpages interactive with jQuery": ["Welcome to jQuery: HTML/JS: Making webpages interactive with jQuery", "DOM access with jQuery: HTML/JS: Making webpages interactive with jQuery", "DOM modification with jQuery: HTML/JS: Making webpages interactive with jQuery", "jQuery techniques: HTML/JS: Making webpages interactive with jQuery", "DOM events with jQuery: HTML/JS: Making webpages interactive with jQuery", "DOM animation & effects with jQuery: HTML/JS: Making webpages interactive with jQuery"], "Unit 8: Meet the professional": ["Meet the professional: Meet the professional", "Watch an introduction video0:5252 seconds", "Meet the professionals", "Meet the professionals", "Watch an introduction video0:5252 seconds", "Help requests", "Browse projects"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Computer Science Principles", "course_url": "/computing/ap-computer-science-principles", "page_contents": {"syllabus": {"topics": {"Unit 7: Online data security": ["Introduction to online data security: Online data security", "PII (Personally identifiable information): Online data security"]}}}}
{"course_title": "Pixar in a Box", "course_url": "/computing/pixar", "page_contents": {"syllabus": {"topics": {"Unit 15Rendering": ["Video 2 minutes 5 seconds2:05", "Effects overview", "Introduction to particle systems", "Video 3 minutes 17 seconds3:17", "Introduction to virtual cameras", "How virtual cameras work", "Video 1 minute 48 seconds1:48", "Introduction to combinatorics", "Building crowds", "Video 2 minutes2:00", "Welcome to rigging", "Introduction to rigging", "Video 2 minutes 47 seconds2:47", "Math meets artistry", "Introduction to animation", "Watch an introduction video5:205 minutes 20 seconds", "Start here!", "Start here!", "Watch an introduction video5:205 minutes 20 seconds"], "Unit 2: The art of storytelling": ["We are all storytellers | 1: The art of storytelling", "Character | 2: The art of storytelling", "Story structure | 3: The art of storytelling", "Visual language | 4: The art of storytelling", "Film grammar | 5: The art of storytelling", "Pitching and feedback | 6: The art of storytelling"], "Unit 4: Simulation": ["Hair simulation 101: Simulation", "Code your own simulation: Simulation"], "Unit 5: Color science": ["Introduction to color: Color science", "Color spaces: Color science"], "Unit 6: Virtual cameras": ["How virtual cameras work: Virtual cameras", "Mathematics of depth of field: Virtual cameras"]}}}}
{"course_title": "US history", "course_url": "/humanities/us-history", "page_contents": {"syllabus": {"topics": {"Unit 1: Worlds collide (1491-1607)": ["Thinking like a historian: Worlds collide (1491-1607)", "Before contact: Worlds collide (1491-1607)", "Spanish colonization : Worlds collide (1491-1607)"], "Unit 2: Colonial America (1607-1754)": ["Early colonization projects: Colonial America (1607-1754)", "Chesapeake and Southern colonies: Colonial America (1607-1754)", "Colonial North America: Colonial America (1607-1754)"], "Unit 3: The road to revolution (1754-1800)": ["The American Revolution: The road to revolution (1754-1800)", "Creating a nation: The road to revolution (1754-1800)"], "Unit 4: The early republic (1800-1848)": ["The age of Jackson : The early republic (1800-1848)", "Culture and reform in the early nineteenth century: The early republic (1800-1848)"], "Unit 8: The postwar era (1945-1980)": ["The postwar era, 1945-1950: The postwar era (1945-1980)", "1950s America: The postwar era (1945-1980)"]}}}}
{"course_title": "AP\u00ae\ufe0e/College US History", "course_url": "/humanities/ap-us-history", "page_contents": {"syllabus": {"topics": {"Unit 11Unit 11: AP\u00ae\ufe0e US History standards mappings": ["Start Course challenge", "Watch an introduction video1:451 minute 45 seconds", "Learn more", "Learn more", "Watch an introduction video1:451 minute 45 seconds"], "Unit 1: Period 1: 1491-1607": ["Thinking like a historian: Period 1: 1491-1607", "Native American societies before contact: Period 1: 1491-1607", "Columbian Exchange, Spanish exploration, and conquest: Period 1: 1491-1607", "Labor, slavery, and caste in the Spanish colonial system : Period 1: 1491-1607", "Cultural interactions between Europeans, Native Americans, and Africans: Period 1: 1491-1607", "Causation in Period 1: Period 1: 1491-1607"], "Unit 2: Period 2: 1607-1754": ["European colonization: Period 2: 1607-1754", "Regions of British colonies: Period 2: 1607-1754", "Interactions between American Indians and Europeans: Period 2: 1607-1754", "Slavery in the British colonies: Period 2: 1607-1754", "Comparison in Period 2: Period 2: 1607-1754"], "Unit 3: Period 3: 1754-1800": ["The Seven Years' War (The French and Indian War): Period 3: 1754-1800", "The Articles of Confederation: Period 3: 1754-1800", "The Constitutional Convention and debates over ratification: Period 3: 1754-1800", "The Constitution: Period 3: 1754-1800", "Movement in the early republic: Period 3: 1754-1800", "Continuity and change in Period 3: Period 3: 1754-1800"], "Unit 4: Period 4: 1800-1848": ["America on the world stage: Period 4: 1800-1848", "Market Revolution: industrialization: Period 4: 1800-1848", "Market Revolution: society and culture: Period 4: 1800-1848", "Jackson and federal power: Period 4: 1800-1848", "The development of an American culture: Period 4: 1800-1848", "The Second Great Awakening: Period 4: 1800-1848", "An age of reform: Period 4: 1800-1848", "Causation in Period 4: Period 4: 1800-1848"], "Unit 5: Period 5: 1844-1877": ["Manifest Destiny: Period 5: 1844-1877", "The Compromise of 1850: Period 5: 1844-1877", "Election of 1860 and secession: Period 5: 1844-1877", "Military conflict in the Civil War: Period 5: 1844-1877", "Comparison in Period 5: Period 5: 1844-1877"], "Unit 6: Period 6: 1865-1898": ["Technological innovation: Period 6: 1865-1898", "The rise of industrial capitalism: Period 6: 1865-1898", "Reform in the Gilded Age: Period 6: 1865-1898", "Continuity and change in Period 6: Period 6: 1865-1898"], "Unit 7: Period 7: 1890-1945": ["Imperialism: debates: Period 7: 1890-1945", "The Progressives: Period 7: 1890-1945", "1920s: cultural and political controversies: Period 7: 1890-1945", "Interwar foreign policy: Period 7: 1890-1945", "World War II: military: Period 7: 1890-1945", "Comparison in Period 7: Period 7: 1890-1945"], "Unit 8: Period 8: 1945-1980": ["The Cold War from 1945 to 1980: Period 8: 1945-1980", "The Vietnam War : Period 8: 1945-1980", "Continuity and change in Period 8: Period 8: 1945-1980"]}}}}
{"course_title": "US government and civics", "course_url": "/humanities/us-government-and-civics", "page_contents": {"syllabus": {"topics": {"Unit 10Unit 10: Primary documents": ["Start Course challenge", "Watch an introduction video2:332 minutes 33 seconds", "Start learning", "Start learning", "Watch an introduction video2:332 minutes 33 seconds"], "Unit 1: Foundations of American democracy": ["Welcome to US government and civics!: Foundations of American democracy", "Ideals of democracy: Foundations of American democracy", "Types of democracy: Foundations of American democracy", "Challenges of the Articles of Confederation: Foundations of American democracy", "Government power and individual rights: Foundations of American democracy", "Ratification of the US Constitution: Foundations of American democracy", "Principles of American government: Foundations of American democracy", "The relationship between the states and the federal government: Foundations of American democracy", "Constitutional interpretations of federalism : Foundations of American democracy", "Federalism in action: Foundations of American democracy"], "Unit 2: Interactions among branches of government": ["Congress: The Senate and the House of Representatives: Interactions among branches of government", "Structures, powers, and functions of Congress: Interactions among branches of government", "Congressional behavior: Interactions among branches of government", "Roles and powers of the president: Interactions among branches of government", "Checks on the presidency: Interactions among branches of government", "Expansion of presidential power: Interactions among branches of government", "Presidential communication: Interactions among branches of government", "The judicial branch: Interactions among branches of government", "Legitimacy of the judicial branch: Interactions among branches of government", "Checks on the judicial branch: Interactions among branches of government", "The bureaucracy: functions and responsibilities: Interactions among branches of government", "The bureaucracy: authority and accountability: Interactions among branches of government"], "Unit 3: Civil liberties and civil rights": ["The Bill of Rights: Civil liberties and civil rights", "The First Amendment: freedom of religion: Civil liberties and civil rights", "The Second Amendment: Civil liberties and civil rights", "Balancing individual freedom with public order and safety: Civil liberties and civil rights", "Selective incorporation: Civil liberties and civil rights", "Due process and the rights of the accused: Civil liberties and civil rights", "Social movements and equal protection: Civil liberties and civil rights", "Government responses to social movements: Civil liberties and civil rights", "Balancing minority and majority rights: Civil liberties and civil rights", "Affirmative action: Civil liberties and civil rights"], "Unit 4: Citizenship": ["What does it mean to be a citizen?: Citizenship", "What are the rights and responsibilities of citizenship?: Citizenship", "How has the definition of citizenship changed over time?: Citizenship", "What is the pathway to citizenship?: Citizenship", "How can citizens change a democracy?: Citizenship"], "Unit 5: American political ideologies and beliefs": ["American attitudes about government and politics: American political ideologies and beliefs", "Political socialization: American political ideologies and beliefs", "Influences on ideology: American political ideologies and beliefs", "Ideologies of political parties: American political ideologies and beliefs", "Ideology and economic policy: American political ideologies and beliefs", "Ideology and social policy: American political ideologies and beliefs"], "Unit 6: Political participation": ["Voting rights and models of voter behavior: Political participation", "Voter turnout: Political participation", "Political parties: Political participation", "How and why political parties change and adapt: Political participation", "Third-party politics: Political participation", "Groups influencing policymaking and policy outcomes: Political participation", "Electing a president: Political participation", "Congressional elections: Political participation", "Modern campaigns: Political participation", "Campaign finance: Political participation", "The media: Political participation", "Changing media: Political participation"], "Unit 7: Government & civics with CBS's John Dickerson": ["Why it matters: Government & civics with CBS's John Dickerson", "What has changed: Government & civics with CBS's John Dickerson", "Presidential history: Government & civics with CBS's John Dickerson"], "Unit 8: The National Constitution Center": ["The Constitution: The National Constitution Center", "The Bill of Rights: The National Constitution Center", "Landmark Supreme Court cases: The National Constitution Center"]}}}}
{"course_title": "AP\u00ae\ufe0e/College US Government & Politics", "course_url": "/humanities/ap-us-government-and-politics", "page_contents": {"syllabus": {"topics": {"Unit 1: Foundations of American democracy": ["Ideals of democracy: Foundations of American democracy", "Types of democracy: Foundations of American democracy", "Challenges of the Articles of Confederation: Foundations of American democracy", "Government power and individual rights: Foundations of American democracy", "Ratification of the US Constitution: Foundations of American democracy", "Principles of American government: Foundations of American democracy", "The relationship between the states and the federal government: Foundations of American democracy", "Constitutional interpretations of federalism : Foundations of American democracy", "Federalism in action: Foundations of American democracy"], "Unit 2: Interactions among branches of government": ["Congress: The Senate and the House of Representatives: Interactions among branches of government", "Structures, powers, and functions of Congress: Interactions among branches of government", "Congressional behavior: Interactions among branches of government", "Roles and powers of the president: Interactions among branches of government", "Checks on the presidency: Interactions among branches of government", "Expansion of presidential power: Interactions among branches of government", "Presidential communication: Interactions among branches of government", "The judicial branch: Interactions among branches of government", "Legitimacy of the judicial branch: Interactions among branches of government", "The Court in action: Interactions among branches of government", "Checks on the judicial branch: Interactions among branches of government", "The bureaucracy: Interactions among branches of government", "Discretionary and rule-making authority: Interactions among branches of government", "Holding the bureaucracy accountable: Interactions among branches of government", "Policy and the branches of government: Interactions among branches of government"], "Unit 3: Civil liberties and civil rights": ["The Bill of Rights: Civil liberties and civil rights", "The First Amendment: freedom of religion: Civil liberties and civil rights", "The Second Amendment: Civil liberties and civil rights", "Balancing individual freedom with public order and safety: Civil liberties and civil rights", "Selective incorporation: Civil liberties and civil rights", "Due process and the rights of the accused: Civil liberties and civil rights", "Social movements and equal protection: Civil liberties and civil rights", "Government responses to social movements: Civil liberties and civil rights", "Balancing minority and majority rights: Civil liberties and civil rights", "Affirmative action: Civil liberties and civil rights"], "Unit 4: American political ideologies and beliefs": ["American attitudes about government and politics: American political ideologies and beliefs", "Political socialization: American political ideologies and beliefs", "Changes in ideology: American political ideologies and beliefs", "Influence of political events on ideology: American political ideologies and beliefs", "Measuring public opinion: American political ideologies and beliefs", "Evaluating public opinion data: American political ideologies and beliefs", "Ideologies of political parties: American political ideologies and beliefs", "Ideology and policymaking: American political ideologies and beliefs", "Ideology and economic policy: American political ideologies and beliefs", "Ideology and social policy: American political ideologies and beliefs"], "Unit 5: Political participation": ["Voting rights and models of voter behavior: Political participation", "Voter turnout: Political participation", "Political parties: Political participation", "How and why political parties change and adapt: Political participation", "Third-party politics: Political participation", "Interest groups influencing policymaking : Political participation", "Groups influencing policy outcomes: Political participation", "Electing a president: Political participation", "Congressional elections: Political participation", "Modern campaigns: Political participation", "Campaign finance: Political participation", "The media: Political participation", "Changing media: Political participation"]}}}}
{"course_title": "World History Project - Origins to the Present", "course_url": "/humanities/whp-origins", "page_contents": {"syllabus": {"topics": {"Unit 7: Era 7 - The Great Convergence and Divergence (1880 CE to the future)": ["Other Materials: Era 7 - The Great Convergence and Divergence (1880 CE to the future)", "Start Course challenge"]}}}}
{"course_title": "World History Project - 1750 to the Present", "course_url": "/humanities/whp-1750", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "AP\u00ae\ufe0e/College World HistoryNEW", "course_url": "/humanities/world-history-project-ap", "page_contents": {"syllabus": {"topics": {"Unit 10Review \u2014 Introduction to World History": ["Watch an introduction video1:351 minute 35 seconds", "Looking for a review on ancient World History before you dive into this course? Click here!", "Looking for a review on ancient World History before you dive into this course? Click here!", "Watch an introduction video1:351 minute 35 seconds"]}}}}
{"course_title": "Big history", "course_url": "/humanities/big-history-project", "page_contents": {"syllabus": {"topics": {"Unit 2: The Big Bang": ["The Big Bang | 2.0 : The Big Bang", "Other Materials: The Big Bang"], "Unit 9: Acceleration": ["Transitions, Thresholds, and Turning Points in History | 9.0: Acceleration", "The Anthropocene | 9.2: Acceleration"]}}}}
{"course_title": "Math: Pre-K - 8th grade", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Early math review", "course_url": "/math/early-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Counting": ["Counting: Counting", "Counting objects: Counting", "Comparing small numbers: Counting"], "Unit 2: Addition and subtraction intro": ["What is addition? What is subtraction?: Addition and subtraction intro", "Making small numbers: Addition and subtraction intro", "Making 10: Addition and subtraction intro", "Put together, take apart: Addition and subtraction intro", "Relate addition and subtraction: Addition and subtraction intro", "Addition and subtraction word problems: Addition and subtraction intro"], "Unit 3: Place value (tens and hundreds)": ["Teens: Place value (tens and hundreds)", "Tens: Place value (tens and hundreds)", "Comparing 2-digit numbers: Place value (tens and hundreds)", "Hundreds: Place value (tens and hundreds)", "Comparing three-digit numbers: Place value (tens and hundreds)"], "Unit 4: Addition and subtraction within 20": ["Addition within 20: Addition and subtraction within 20", "Subtraction within 20: Addition and subtraction within 20", "Equal sign: Addition and subtraction within 20", "Missing number within 20: Addition and subtraction within 20", "Word problems within 20: Addition and subtraction within 20", "Word problems with \"more\" and \"fewer\": Addition and subtraction within 20", "Repeated addition: Addition and subtraction within 20"], "Unit 5: Addition and subtraction within 100": ["Skip-counting: Addition and subtraction within 100", "Adding 1s and 10s: Addition and subtraction within 100", "Subtracting 1s and 10s: Addition and subtraction within 100", "Intro to addition with 2-digit numbers: Addition and subtraction within 100", "Intro to subtraction with 2-digit numbers: Addition and subtraction within 100", "Strategies for adding and subtracting within 100: Addition and subtraction within 100", "Addition within 100: Addition and subtraction within 100", "Subtraction within 100: Addition and subtraction within 100", "Word problems within 100: Addition and subtraction within 100", "Word problems with \"more\" and \"fewer\" (within 100): Addition and subtraction within 100", "Addition and subtraction missing value problems: Addition and subtraction within 100"], "Unit 6: Addition and subtraction within 1000": ["Skip counting by 100s: Addition and subtraction within 1000", "Adding 1s, 10s, and 100s: Addition and subtraction within 1000", "Subtracting 1s, 10s, and 100s: Addition and subtraction within 1000", "Strategies for adding 2- and 3-digit numbers: Addition and subtraction within 1000", "Adding up to four 2-digit numbers: Addition and subtraction within 1000"], "Unit 7: Measurement and data": ["Measuring length: Measurement and data", "Comparing and estimating length: Measurement and data", "Length word problems: Measurement and data", "Picture graphs: Measurement and data", "Bar graphs: Measurement and data", "Line plots: Measurement and data", "Time: Measurement and data", "Money: Measurement and data"], "Unit 8: Geometry": ["Basic shapes: Geometry", "Properties of shapes: Geometry", "Composing shapes: Geometry", "Fractions of shapes: Geometry", "Start Course challenge"]}}}}
{"course_title": "2nd grade", "course_url": "/math/cc-2nd-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Add and subtract within 20": ["Add using arrays: Add and subtract within 20", "Subtract within 20: Add and subtract within 20", "Add and subtract within 20: Add and subtract within 20"], "Unit 2: Place value": ["Numbers in standard, word, and expanded form: Place value", "Regroup whole numbers: Place value", "Comparing 2 and 3 digit numbers: Place value", "Even and odd numbers: Place value", "Counting patterns within 1,000: Place value"], "Unit 3: Add and subtract within 100": ["Strategies for adding within 100: Add and subtract within 100", "Visually subtract within 100: Add and subtract within 100", "Addition and subtraction: missing values: Add and subtract within 100", "Addition and subtraction within 100 word problems: Add and subtract within 100", "Addition and subtraction within 100 word problems (multi-step): Add and subtract within 100"], "Unit 4: Add and subtract within 1,000": ["Strategies for adding within 1,000: Add and subtract within 1,000", "Strategies for subtracting within 1,000: Add and subtract within 1,000", "Adding up to four 2-digit numbers: Add and subtract within 1,000"], "Unit 6: Measurement": ["Measure lengths: Measurement", "Estimate lengths: Measurement", "Length word problems: Measurement"], "Unit 7: Data": ["Bar graphs: Data", "Line plots: Data"], "Unit 8: Geometry": ["Equal parts of shapes: Geometry", "Partition rectangles: Geometry", "Start Course challenge"]}}}}
{"course_title": "3rd grade", "course_url": "/math/cc-third-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Intro to multiplication": ["Multiplication as equal groups: Intro to multiplication", "Multiplication on the number line: Intro to multiplication", "Multiplication as groups of objects: Intro to multiplication", "Multiplication with arrays: Intro to multiplication", "Multiplication in contexts: Intro to multiplication", "Commutative property of multiplication : Intro to multiplication"], "Unit 3: Addition, subtraction, and estimation": ["Rounding to nearest 10 or 100: Addition, subtraction, and estimation", "Estimate to add multi-digit numbers: Addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Addition, subtraction, and estimation", "Adding with regrouping within 1000: Addition, subtraction, and estimation", "Estimate to subtract multi-digit numbers: Addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Addition, subtraction, and estimation", "Subtracting with regrouping within 1000: Addition, subtraction, and estimation", "Addition and subtraction missing value problems: Addition, subtraction, and estimation", "Addition and subtraction word problems: Addition, subtraction, and estimation"], "Unit 4: Intro to division": ["Division intro: Intro to division", "Division in contexts: Intro to division", "Relating multiplication and division: Intro to division"], "Unit 5: Understand fractions": ["Fractions intro: Understand fractions", "Fractions in contexts: Understand fractions", "What fractions mean: Understand fractions", "Fractions on the number line: Understand fractions", "Fractions and whole numbers: Understand fractions"], "Unit 6: Equivalent fractions and comparing fractions": ["Comparing fractions: Equivalent fractions and comparing fractions", "Comparing fractions of different wholes: Equivalent fractions and comparing fractions", "Equivalent fractions: Equivalent fractions and comparing fractions"], "Unit 7: More with multiplication and division": ["Letters and symbols in multiplication and division equations: More with multiplication and division", "Multiplication and division word problems: More with multiplication and division", "Associative property of multiplication: More with multiplication and division", "Multiplying by tens: More with multiplication and division"], "Unit 8: Arithmetic patterns and problem solving": ["2-step expressions: Arithmetic patterns and problem solving", "Estimation word problems: Arithmetic patterns and problem solving", "One and two-step word problems: Arithmetic patterns and problem solving", "Patterns in arithmetic: Arithmetic patterns and problem solving"], "Count unit squares to find area: Area": ["Area formula intuition: Area", "Multiply to find area: Area", "Area and the distributive property: Area", "Decompose figures to find area: Area"], "Unit 11: Perimeter": ["Perimeter: Perimeter", "Perimeter word problems: Perimeter"], "Unit 12: Time": ["Time on number line: Time", "Telling time: Time", "Elapsed time: Time"], "Unit 13: Measurement": ["Mass: Measurement", "Volume: Measurement"], "Unit 14: Represent and interpret data": ["Picture graphs: Represent and interpret data", "Bar graphs: Represent and interpret data", "Line plots with fractions: Represent and interpret data", "Start Course challenge"]}}}}
{"course_title": "4th grade", "course_url": "/math/cc-fourth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Place value": ["Writing whole numbers in expanded form: Place value", "Writing whole numbers in written form: Place value", "Regrouping whole numbers: Place value", "How 10 relates to place value: Place value", "Comparing multi-digit numbers: Place value"], "Unit 2: Addition, subtraction, and estimation": ["Adding multi-digit numbers: Addition, subtraction, and estimation", "Subtracting multi-digit numbers: Addition, subtraction, and estimation"], "Unit 3: Multiply by 1-digit numbers": ["Multiplication by 10s, 100s, and 1000s: Multiply by 1-digit numbers", "Multi-digit multiplication: place value and area models: Multiply by 1-digit numbers", "Estimate products: Multiply by 1-digit numbers", "Multiply with partial products: Multiply by 1-digit numbers"], "Unit 4: Multiply by 2-digit numbers": ["Multiply 2-digit numbers with area models: Multiply by 2-digit numbers", "Estimate products (2-digit numbers): Multiply by 2-digit numbers", "Multiply 2-digit numbers with partial products: Multiply by 2-digit numbers"], "Unit 5: Division": ["Divide multiples of 10, 100, and 1,000 by 1-digit numbers: Division", "Division with place value: Division", "Division with area models: Division", "Estimate quotients: Division", "Multi-digit division with partial quotients: Division", "Multiplication, division word problems: Division", "Multi-step word problems: Division"], "Unit 6: Factors, multiples and patterns": ["Prime and composite numbers: Factors, multiples and patterns", "Math patterns: Factors, multiples and patterns"], "Unit 7: Equivalent fractions and comparing fractions": ["Common denominators: Equivalent fractions and comparing fractions", "Comparing fractions with unlike denominators visually: Equivalent fractions and comparing fractions"], "Unit 8: Add and subtract fractions": ["Adding and subtracting fractions with like denominators: Add and subtract fractions", "Adding and subtracting fractions: word problems: Add and subtract fractions", "Mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers: Add and subtract fractions", "Adding and subtracting mixed numbers word problems: Add and subtract fractions", "Fractions with denominators of 10 and 100: Add and subtract fractions", "Line plots with fractions: Add and subtract fractions"], "Unit 9: Multiply fractions": ["Multiplying fractions and whole numbers visually: Multiply fractions", "Multiplying whole numbers and fractions: Multiply fractions", "Multiplying whole numbers and mixed numbers: Multiply fractions", "Multiplying whole numbers and fractions word problems: Multiply fractions"], "Unit 10: Understand decimals": ["Decimal fractions greater than 1: Understand decimals", "Writing fractions as decimals: Understand decimals", "Decimals in word form: Understand decimals", "Decimals on the number line: Understand decimals", "Regrouping decimals: Understand decimals", "Writing decimals as fractions: Understand decimals", "Common fractions and decimals: Understand decimals", "Comparing decimals visually: Understand decimals", "Comparing decimals: Understand decimals"], "Unit 11: Plane figures": ["Angle introduction: Plane figures", "Parallel and perpendicular: Plane figures", "Classifying triangles: Plane figures", "Classifying geometric shapes: Plane figures", "Line of symmetry: Plane figures"], "Unit 12: Measuring angles": ["Measuring angles: Measuring angles", "Decomposing angles: Measuring angles"]}}}}
{"course_title": "5th grade", "course_url": "/math/cc-fifth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Decimal place value": ["Decimal place value intro: Decimal place value", "Decimals on the number line: Decimal place value", "Decimals in expanded form: Decimal place value", "Decimals in written form: Decimal place value", "Decimals in different forms: Decimal place value", "Comparing decimals: Decimal place value", "Rounding decimals: Decimal place value"], "Unit 2: Add decimals": ["Common fractions and decimals: Add decimals", "Adding decimals intro: Add decimals", "Adding decimals (tenths): Add decimals", "Adding decimals (hundredths): Add decimals"], "Unit 3: Subtract decimals": ["Subtracting decimals intro: Subtract decimals", "Subtracting decimals (tenths): Subtract decimals", "Subtracting decimals (hundredths): Subtract decimals"], "Unit 4: Add and subtract fractions": ["Strategies for adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Common denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators: Add and subtract fractions", "Adding and subtracting mixed numbers with unlike denominators: Add and subtract fractions", "Adding and subtracting fractions with unlike denominators word problems: Add and subtract fractions"], "Unit 5: Multi-digit multiplication and division": ["Multi-digit multiplication estimation: Multi-digit multiplication and division", "Multi-digit multiplication: Multi-digit multiplication and division", "Multi-digit division estimation: Multi-digit multiplication and division", "Multi-digit division: Multi-digit multiplication and division"], "Unit 6: Multiply fractions": ["Multiplication as scaling: Multiply fractions", "Multiplying fractions and whole numbers: Multiply fractions", "Multiplying fractions: Multiply fractions", "Multiplying mixed numbers: Multiply fractions", "Area of rectangles with fraction side lengths: Multiply fractions", "Multiplying fractions word problems: Multiply fractions"], "Unit 7: Divide fractions": ["Fractions as division: Divide fractions", "Relate fraction division to fraction multiplication: Divide fractions"], "Unit 8: Multiply decimals": ["Multiplying decimals and whole numbers: Multiply decimals", "Multiplying decimals strategies: Multiply decimals", "Multiplying decimals: Multiply decimals"], "Unit 9: Divide decimals": ["Estimate to divide decimals: Divide decimals", "Divide whole numbers to get a decimal quotient: Divide decimals", "Divide decimals by whole numbers: Divide decimals", "Divide whole numbers by decimals: Divide decimals"], "Unit 10: Powers of ten": ["Multiplying and dividing whole numbers by 10, 100, and 1000: Powers of ten", "Multiplying and dividing decimals by 10, 100, and 1000: Powers of ten", "Powers of 10: Powers of ten", "Multiplying and dividing with powers of 10: Powers of ten", "Comparing decimal place values: Powers of ten"], "Volume with unit cubes: Volume": ["Volume of rectangular prisms: Volume", "Decompose figures to find volume: Volume", "Volume word problems: Volume"], "Unit 13: Algebraic thinking": ["Writing expressions: Algebraic thinking", "Number patterns: Algebraic thinking"], "Unit 15: Line plots": ["Graph data on line plots: Line plots", "Interpret data on line plots: Line plots"], "Unit 16: Properties of shapes": ["Triangles: Properties of shapes", "Quadrilaterals: Properties of shapes", "Start Course challenge"]}}}}
{"course_title": "6th grade", "course_url": "/math/cc-sixth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Ratios": ["Intro to ratios: Ratios", "Visualize equivalent ratios: Ratios", "Ratio application: Ratios"], "Unit 2: Arithmetic with rational numbers": ["Adding decimals: Arithmetic with rational numbers", "Subtracting decimals: Arithmetic with rational numbers", "Adding and subtracting decimals word problems: Arithmetic with rational numbers", "Dividing fractions and whole numbers: Arithmetic with rational numbers", "Dividing fractions by fractions: Arithmetic with rational numbers", "Multiplying decimals: Arithmetic with rational numbers", "Dividing whole numbers: Arithmetic with rational numbers", "Dividing decimals: Arithmetic with rational numbers"], "Unit 3: Rates and percentages": ["Intro to rates: Rates and percentages", "Intro to percents: Rates and percentages", "Visualize percents: Rates and percentages", "Equivalent representations of percent problems: Rates and percentages", "Percent problems: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 4: Exponents and order of operations": ["Meaning of exponents: Exponents and order of operations", "Powers of whole numbers: Exponents and order of operations", "Powers of fractions and decimals: Exponents and order of operations", "Order of operations introduction: Exponents and order of operations", "More on order of operations: Exponents and order of operations"], "Unit 5: Negative numbers": ["Intro to negative numbers: Negative numbers", "Negative symbol as opposite: Negative numbers", "Rational numbers on the number line: Negative numbers", "Comparing negative numbers: Negative numbers", "Ordering rational numbers: Negative numbers", "Intro to absolute value: Negative numbers", "Comparing absolute values: Negative numbers"], "Unit 6: Variables & expressions": ["Parts of algebraic expressions: Variables & expressions", "Substitution & evaluating expressions: Variables & expressions", "Evaluating expressions with multiple variables: Variables & expressions", "Expression value intuition: Variables & expressions", "Evaluating expressions word problems: Variables & expressions", "Writing algebraic expressions introduction: Variables & expressions", "Writing basic algebraic expressions word problems: Variables & expressions", "Least common multiple: Variables & expressions", "Greatest common factor: Variables & expressions", "Distributive property with variables: Variables & expressions", "Combining like terms: Variables & expressions", "Equivalent expressions: Variables & expressions"], "Unit 7: Equations & inequalities": ["Algebraic equations basics: Equations & inequalities", "One-step equations intuition: Equations & inequalities", "One-step addition & subtraction equations: Equations & inequalities", "One-step multiplication and division equations: Equations & inequalities", "Finding mistakes in one-step equations: Equations & inequalities", "One-step equation word problems: Equations & inequalities", "Intro to inequalities with variables: Equations & inequalities", "Dependent and independent variables: Equations & inequalities", "Analyzing relationships between variables: Equations & inequalities"], "Unit 8: Plane figures": ["Areas of parallelograms: Plane figures", "Areas of triangles: Plane figures", "Area of composite figures: Plane figures"], "Unit 9: Coordinate plane": ["Four quadrants: Coordinate plane", "Distance on the coordinate plane: Coordinate plane", "Polygons on the coordinate plane: Coordinate plane"], "Unit 10: 3D figures": ["Geometric solids (3D shapes): 3D figures", "Volume with fractions: 3D figures", "Nets of 3D figures: 3D figures"], "Unit 11: Data and statistics": ["Statistical questions: Data and statistics", "Dot plots & frequency tables: Data and statistics", "Histograms: Data and statistics", "Mean and median: Data and statistics", "Mean and median challenge problems: Data and statistics", "Interquartile range (IQR): Data and statistics", "Box plots: Data and statistics", "Mean absolute deviation (MAD): Data and statistics", "Comparing data displays: Data and statistics", "Shape of data distributions: Data and statistics", "Start Course challenge"]}}}}
{"course_title": "7th grade", "course_url": "/math/cc-seventh-grade-math", "page_contents": {"syllabus": {"topics": {"Geometry: Unit test": ["Start Course challenge", "Subtracting negative numbers fluently", "Multiply & divide negative numbers", "Adding negative numbers fluently", "Area and circumference of circles", "Vertical, complementary, and supplementary angles"], "Unit 1: Proportional relationships": ["Compare and interpret constants of proportionality : Proportional relationships", "Identifying proportional relationships: Proportional relationships", "Graphs of proportional relationships: Proportional relationships", "Writing & solving proportions: Proportional relationships", "Equations of proportional relationships: Proportional relationships"], "Unit 2: Rates and percentages": ["Converting fractions to decimals: Rates and percentages", "Percent word problems: Rates and percentages"], "Unit 3: Integers: addition and subtraction": ["Adding negative numbers fluently: Integers: addition and subtraction", "Intro to subtracting negative numbers: Integers: addition and subtraction", "Subtracting negative numbers fluently: Integers: addition and subtraction", "Adding & subtracting negative numbers: variables: Integers: addition and subtraction"], "Unit 4: Rational numbers: addition and subtraction": ["Absolute value: Rational numbers: addition and subtraction", "Adding & subtracting negative fractions: Rational numbers: addition and subtraction", "Adding & subtracting rational numbers: Rational numbers: addition and subtraction", "Addition & subtraction word problems with negatives: Rational numbers: addition and subtraction", "Properties of addition & subtraction: Rational numbers: addition and subtraction"], "Unit 5: Negative numbers: multiplication and division": ["Multiply & divide negative numbers: Negative numbers: multiplication and division", "Multiplication & division word problems with negatives: Negative numbers: multiplication and division", "Understanding multiplying and dividing fractions: Negative numbers: multiplication and division", "Multiply & divide negative fractions: Negative numbers: multiplication and division", "Rational number word problems: Negative numbers: multiplication and division", "Powers with rational bases: Negative numbers: multiplication and division", "Order of operations: Negative numbers: multiplication and division", "Properties of multiplication & division: Negative numbers: multiplication and division"], "Unit 6: Expressions, equations, & inequalities": ["The distributive property & equivalent expressions: Expressions, equations, & inequalities", "Interpreting linear expressions: Expressions, equations, & inequalities", "Two-step equations intro: Expressions, equations, & inequalities", "Two-step equations with decimals and fractions: Expressions, equations, & inequalities", "Two-step equation word problems: Expressions, equations, & inequalities", "One-step inequalities: Expressions, equations, & inequalities", "Two-step inequalities: Expressions, equations, & inequalities"], "Unit 7: Statistics and probability": ["Probability models: Statistics and probability", "Compound events and sample spaces: Statistics and probability", "Comparing and sampling populations: Statistics and probability"], "Unit 8: Scale copies": ["Scale copies: Scale copies", "Scale drawings: Scale copies"], "Unit 9: Geometry": ["Area and circumference challenge problems: Geometry", "Vertical, complementary, and supplementary angles: Geometry", "Missing angle problems: Geometry", "Constructing triangles: Geometry", "Slicing geometric shapes: Geometry", "Volume and surface area word problems: Geometry", "Start Course challenge"]}}}}
{"course_title": "8th grade", "course_url": "/math/cc-eighth-grade-math", "page_contents": {"syllabus": {"topics": {"Unit 1: Numbers and operations": ["Repeating decimals: Numbers and operations", "Square roots & cube roots: Numbers and operations", "Irrational numbers: Numbers and operations", "Approximating irrational numbers: Numbers and operations", "Exponents with negative bases: Numbers and operations", "Exponent properties intro : Numbers and operations", "Negative exponents: Numbers and operations", "Exponent properties (integer exponents): Numbers and operations", "Working with powers of 10: Numbers and operations", "Scientific notation intro: Numbers and operations", "Arithmetic with numbers in scientific notation: Numbers and operations", "Scientific notation word problems: Numbers and operations"], "Unit 2: Solving equations with one unknown": ["Equations with variables on both sides: Solving equations with one unknown", "Equations with parentheses: Solving equations with one unknown", "Number of solutions to equations: Solving equations with one unknown", "Equations word problems: Solving equations with one unknown"], "Unit 3: Linear equations and functions": ["Graphing proportional relationships: Linear equations and functions", "Solutions to linear equations: Linear equations and functions", "Intercepts: Linear equations and functions", "Slope: Linear equations and functions", "Intro to slope-intercept form: Linear equations and functions", "Graphing slope-intercept form: Linear equations and functions", "Writing slope-intercept equations: Linear equations and functions", "Functions: Linear equations and functions", "Linear models: Linear equations and functions", "Comparing linear functions: Linear equations and functions", "Constructing linear models for real-world relationships: Linear equations and functions", "Recognizing functions: Linear equations and functions", "Linear and nonlinear functions: Linear equations and functions"], "Unit 4: Systems of equations": ["Intro to systems of equations: Systems of equations", "Solving systems with substitution: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 5: Geometry": ["Angles between intersecting lines: Geometry", "Triangle angles: Geometry", "Pythagorean theorem: Geometry", "Pythagorean theorem application: Geometry", "Pythagorean theorem and distance between points: Geometry", "Pythagorean theorem proofs: Geometry", "Volume: Geometry"], "Unit 6: Geometric transformations": ["Transformations intro: Geometric transformations", "Translations: Geometric transformations", "Rotations: Geometric transformations", "Reflections: Geometric transformations", "Properties & definitions of transformations: Geometric transformations", "Dilations: Geometric transformations", "Congruence and similarity: Geometric transformations"], "Unit 7: Data and modeling": ["Introduction to scatter plots: Data and modeling", "Interpreting scatter plots: Data and modeling", "Estimating lines of best fit: Data and modeling", "Two-way tables: Data and modeling", "Start Course challenge", "Irrational numbers", "Negative exponents", "Repeating decimals", "Square roots & cube roots"]}}}}
{"course_title": "See Pre-K - 8th grade Math", "course_url": "/math/k-8-grades", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Math: Get ready courses", "course_url": "/math/get-ready-courses", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Get ready for 3rd grade", "course_url": "/math/get-ready-for-3rd-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for addition and subtraction": ["Place value: Get ready for addition and subtraction", "Regroup whole numbers: Get ready for addition and subtraction", "Add within 100: Get ready for addition and subtraction", "Subtract within 100: Get ready for addition and subtraction", "Visually add and subtract within 1,000: Get ready for addition and subtraction"], "Unit 2: Get ready for multiplication and division": ["Adding using arrays: Get ready for multiplication and division", "Even and odd numbers: Get ready for multiplication and division"], "Unit 3: Get ready for fractions": ["Equal parts of shapes: Get ready for fractions", "Fractions of shapes: Get ready for fractions"], "Unit 4: Get ready for patterns and problem solving": ["Addition and subtraction word problems (1-step): Get ready for patterns and problem solving", "Addition and subtraction word problems (2-step): Get ready for patterns and problem solving"], "Units of length: Get ready for area and perimeter": ["Measure length: Get ready for area and perimeter", "Partition rectangles: Get ready for area and perimeter"], "Unit 7: Get ready for data": ["Picture graphs: Get ready for data", "Bar graphs: Get ready for data", "Line plots: Get ready for data", "Start Course challenge"]}}}}
{"course_title": "Get ready for 4th grade", "course_url": "/math/get-ready-for-4th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for place value": ["Intro to place value: Get ready for place value", "Numbers in different forms: Get ready for place value", "Regroup whole numbers: Get ready for place value"], "Unit 2: Get ready for addition, subtraction, and estimation": ["Rounding to the nearest 10 or 100: Get ready for addition, subtraction, and estimation", "Strategies for adding two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Strategies for subtracting two and three-digit numbers: Get ready for addition, subtraction, and estimation", "Adding and subtracting within 1,000: Get ready for addition, subtraction, and estimation"], "Unit 3: Get ready for multiplication": ["Multiplication as equal groups: Get ready for multiplication", "Multiplication on the number line: Get ready for multiplication", "Multiplication as groups of objects: Get ready for multiplication", "Multiplication with arrays: Get ready for multiplication", "Commutative property of multiplication: Get ready for multiplication", "Associative property of multiplication: Get ready for multiplication", "Distributive property: Get ready for multiplication"], "Unit 4: Get ready for division": ["Division intro: Get ready for division", "Relate multiplication and division: Get ready for division"], "Unit 5: Get ready for fractions": ["Intro to fractions: Get ready for fractions", "Fractions in contexts: Get ready for fractions", "What fractions mean: Get ready for fractions", "Fractions on the number line: Get ready for fractions", "Fractions and whole numbers: Get ready for fractions", "Comparing fractions: Get ready for fractions", "Equivalent fractions: Get ready for fractions"], "Unit 7: Get ready for area and perimeter": ["Area formula intuition: Get ready for area and perimeter", "Multiply to find area: Get ready for area and perimeter", "Perimeter: Get ready for area and perimeter", "Start Course challenge"]}}}}
{"course_title": "Get ready for 5th grade", "course_url": "/math/get-ready-for-5th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for decimal place value": ["Whole number place value: Get ready for decimal place value", "Write whole numbers in different forms: Get ready for decimal place value", "Compare whole numbers: Get ready for decimal place value", "Compare decimals: Get ready for decimal place value", "Round whole numbers: Get ready for decimal place value"], "Unit 2: Get ready for adding and subtracting decimals": ["Adding multi-digit numbers: Get ready for adding and subtracting decimals", "Subtracting multi-digit numbers: Get ready for adding and subtracting decimals"], "Unit 3: Get ready for adding and subtracting fractions": ["Equivalent fractions: Get ready for adding and subtracting fractions", "Common denominators: Get ready for adding and subtracting fractions", "Adding and subtracting fractions with like denominators: Get ready for adding and subtracting fractions", "Adding and subtracting mixed numbers: Get ready for adding and subtracting fractions", "Fractions with denominators of 10 and 100: Get ready for adding and subtracting fractions"], "Unit 4: Get ready for multiplication and division with whole numbers and decimals": ["Multi-digit multiplication: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit multiplication: Get ready for multiplication and division with whole numbers and decimals", "Remainders: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: place value and area models: Get ready for multiplication and division with whole numbers and decimals", "Multi-digit division: Get ready for multiplication and division with whole numbers and decimals"], "Unit 5: Get ready for multiplying and dividing fractions": ["Introduction to multiplication: Get ready for multiplying and dividing fractions", "Introduction to division: Get ready for multiplying and dividing fractions", "Relating multiplication and division: Get ready for multiplying and dividing fractions", "Comparing with multiplication: Get ready for multiplying and dividing fractions", "Multiplication and division word problems: Get ready for multiplying and dividing fractions", "Area of rectangles: Get ready for multiplying and dividing fractions", "Multiply fractions and whole numbers: Get ready for multiplying and dividing fractions"], "Unit 6: Get ready for powers of 10": ["How 10 relates to place value: Get ready for powers of 10", "Decimal fractions: Get ready for powers of 10", "Decimal fractions greater than 1: Get ready for powers of 10", "Decimals and fractions in word form: Get ready for powers of 10"], "Unit 8: Get ready for properties of shapes": ["Quadrilaterals: Get ready for properties of shapes", "Start Course challenge"]}}}}
{"course_title": "Get ready for 6th grade", "course_url": "/math/get-ready-for-6th-grade", "page_contents": {"syllabus": {"topics": {"Convert units of measure: Get ready for ratios, rates, and percentages": ["Coordinate plane: Get ready for ratios, rates, and percentages", "Number patterns: Get ready for ratios, rates, and percentages", "Multiplication as scaling: Get ready for ratios, rates, and percentages", "Fractions as division: Get ready for ratios, rates, and percentages"], "Divide unit fractions by whole numbers: Get ready for arithmetic operations": ["Multi-digit multiplication: Get ready for arithmetic operations", "Multi-digit division: Get ready for arithmetic operations", "Adding decimals: Get ready for arithmetic operations", "Subtracting decimals: Get ready for arithmetic operations", "Multiplying decimals: Get ready for arithmetic operations", "Dividing decimals: Get ready for arithmetic operations"], "Unit 3: Get ready for negative numbers": ["Fractions on the number line: Get ready for negative numbers", "Coordinate plane: Get ready for negative numbers"], "Unit 4: Get ready for equations, expressions, and inequalities": ["Commutative property of multiplication: Get ready for equations, expressions, and inequalities", "Distributive property: Get ready for equations, expressions, and inequalities", "Associative property of multiplication: Get ready for equations, expressions, and inequalities", "Factors and multiples: Get ready for equations, expressions, and inequalities", "Prime and composite numbers: Get ready for equations, expressions, and inequalities", "Powers of 10: Get ready for equations, expressions, and inequalities", "Writing expressions: Get ready for equations, expressions, and inequalities"], "Unit 5: Get ready for geometry": ["Area and perimeter: Get ready for geometry", "Multiply fractions and mixed numbers: Get ready for geometry", "Area of rectangles with fractional side lengths: Get ready for geometry", "Volume of rectangular prisms: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for 7th grade", "course_url": "/math/get-ready-for-7th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for negative number operations": ["Intro to negative numbers: Get ready for negative number operations", "Negative symbol as opposite: Get ready for negative number operations", "Negative decimals & fractions on the number line: Get ready for negative number operations", "Absolute value: Get ready for negative number operations", "Adding and subtracting fractions with unlike denominators: Get ready for negative number operations", "Multiplying fractions: Get ready for negative number operations", "Fraction as division: Get ready for negative number operations", "Dividing fractions: Get ready for negative number operations"], "Unit 2: Get ready for fractions, decimals, & percentages": ["Adding and subtracting decimals word problems: Get ready for fractions, decimals, & percentages", "Percent problems: Get ready for fractions, decimals, & percentages", "Percent word problems: Get ready for fractions, decimals, & percentages"], "Unit 3: Get ready for rates & proportional relationships": ["Equivalent ratios: Get ready for rates & proportional relationships", "Ratio application: Get ready for rates & proportional relationships", "Intro to rates: Get ready for rates & proportional relationships", "Dependent and independent variables: Get ready for rates & proportional relationships", "Analyze relationships between variables: Get ready for rates & proportional relationships"], "Unit 4: Get ready for expressions, equations, & inequalities": ["Distributive property with variables: Get ready for expressions, equations, & inequalities", "Combining like terms: Get ready for expressions, equations, & inequalities", "Equivalent expressions: Get ready for expressions, equations, & inequalities", "One-step addition and subtraction equations: Get ready for expressions, equations, & inequalities", "One-step multiplication and division equations: Get ready for expressions, equations, & inequalities", "Finding mistakes in one-step equations: Get ready for expressions, equations, & inequalities", "One-step equation word problems: Get ready for expressions, equations, & inequalities", "Intro to inequalities with variables: Get ready for expressions, equations, & inequalities"], "Unit 5: Get ready for geometry": ["Decomposing angles: Get ready for geometry", "Area of parallelograms and triangles: Get ready for geometry", "Area of composite figures: Get ready for geometry", "Volume with fractions: Get ready for geometry", "Nets of 3D figures: Get ready for geometry"], "Unit 6: Get ready for statistics & probability": ["Statistical questions: Get ready for statistics & probability", "Shape of data distributions: Get ready for statistics & probability", "Start Course challenge"]}}}}
{"course_title": "Get ready for 8th grade", "course_url": "/math/get-ready-for-8th-grade", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for numbers and operations": ["Converting fractions to decimals: Get ready for numbers and operations", "Exponents: Get ready for numbers and operations", "Evaluating exponent expressions: Get ready for numbers and operations", "Order of operations: Get ready for numbers and operations", "Powers of ten: Get ready for numbers and operations", "Multiplying and dividing with powers of ten: Get ready for numbers and operations", "Estimating with multiplying and dividing decimals: Get ready for numbers and operations"], "Unit 2: Get ready for solving equations and systems of equations": ["Algebraic equations basics: Get ready for solving equations and systems of equations", "One-step addition and subtraction equations: Get ready for solving equations and systems of equations", "One-step multiplication and division equations: Get ready for solving equations and systems of equations", "Combining like terms: Get ready for solving equations and systems of equations", "The distributive property & equivalent expressions: Get ready for solving equations and systems of equations", "Two-step equations intro: Get ready for solving equations and systems of equations", "Two-step equations with decimals and fractions: Get ready for solving equations and systems of equations"], "Unit 3: Get ready for linear equations and functions": ["Constant of proportionality: Get ready for linear equations and functions", "Compare and interpret constant of proportionality: Get ready for linear equations and functions", "Identifying proportional relationships: Get ready for linear equations and functions", "Graphs of proportional relationships: Get ready for linear equations and functions", "Equations of proportional relationships: Get ready for linear equations and functions"], "Unit 4: Get ready for geometry": ["Polygons on the coordinate plane: Get ready for geometry", "Missing angle problems: Get ready for geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 1", "course_url": "/math/get-ready-for-algebra-i", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for equations & inequalities": ["Algebraic equations basics: Get ready for equations & inequalities", "One-step addition & subtraction equations: Get ready for equations & inequalities", "One-step multiplication & division equations: Get ready for equations & inequalities", "Finding mistakes in one-step equations: Get ready for equations & inequalities", "Intro to inequalities with variables: Get ready for equations & inequalities", "Testing solutions to inequalities: Get ready for equations & inequalities", "Combining like terms: Get ready for equations & inequalities", "The distributive property & equivalent expressions: Get ready for equations & inequalities", "Two-step equations: Get ready for equations & inequalities", "Finding mistakes in two-step equations: Get ready for equations & inequalities", "One- and two-step inequalities: Get ready for equations & inequalities", "Equations with variables on both sides: Get ready for equations & inequalities", "Equations with parentheses: Get ready for equations & inequalities"], "Unit 3: Get ready for linear relationships": ["Constant of proportionality: Get ready for linear relationships", "Compare and interpret constants of proportionality: Get ready for linear relationships", "Identifying proportional relationships: Get ready for linear relationships", "Graphs of proportional relationships: Get ready for linear relationships", "Writing & solving proportions: Get ready for linear relationships", "Equations of proportional relationships: Get ready for linear relationships", "Graphing proportional relationships: Get ready for linear relationships"], "Unit 4: Get ready for functions & sequences": ["Math patterns: Get ready for functions & sequences", "Patterns with variables: Get ready for functions & sequences", "Functions intro: Get ready for functions & sequences", "Linear models: Get ready for functions & sequences", "Linear & nonlinear functions: Get ready for functions & sequences"], "Unit 5: Get ready for exponents, radicals, & irrational numbers": ["Square roots & cube roots: Get ready for exponents, radicals, & irrational numbers", "Irrational numbers: Get ready for exponents, radicals, & irrational numbers", "Exponents with negative bases: Get ready for exponents, radicals, & irrational numbers", "Exponent properties intro: Get ready for exponents, radicals, & irrational numbers", "Negative exponents: Get ready for exponents, radicals, & irrational numbers", "Exponent properties (integer exponents): Get ready for exponents, radicals, & irrational numbers"], "Unit 6: Get ready for quadratics": ["Equations with square roots & cube roots: Get ready for quadratics", "Combining like terms: Get ready for quadratics", "The distributive property & equivalent expressions: Get ready for quadratics", "Interpreting graphs of functions: Get ready for quadratics", "Start Course challenge"]}}}}
{"course_title": "Get ready for Geometry", "course_url": "/math/get-ready-for-geometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for congruence, similarity, and triangle trigonometry": ["Solving proportions: Get ready for congruence, similarity, and triangle trigonometry", "Scale copies: Get ready for congruence, similarity, and triangle trigonometry", "Scale drawings: Get ready for congruence, similarity, and triangle trigonometry", "Vertical, complementary, and supplementary angles: Get ready for congruence, similarity, and triangle trigonometry", "Angles between intersecting lines: Get ready for congruence, similarity, and triangle trigonometry", "Triangle angles: Get ready for congruence, similarity, and triangle trigonometry", "Approximating irrational numbers: Get ready for congruence, similarity, and triangle trigonometry", "Pythagorean theorem: Get ready for congruence, similarity, and triangle trigonometry"], "Unit 2: Get ready for analytic geometry": ["Polygons on the coordinate plane: Get ready for analytic geometry", "Two-variable linear equations intro: Get ready for analytic geometry", "Slope: Get ready for analytic geometry", "Horizontal & vertical lines: Get ready for analytic geometry", "Forms of two-variable linear equations: Get ready for analytic geometry"], "Unit 3: Get ready for conic sections": ["Factoring quadratics intro: Get ready for conic sections", "Factoring quadratics with perfect squares: Get ready for conic sections", "Vertex form: Get ready for conic sections", "Completing the square: Get ready for conic sections"], "Unit 4: Get ready for circles and solid geometry": ["Area and circumference of circles: Get ready for circles and solid geometry", "Slicing geometric shapes: Get ready for circles and solid geometry", "Volume and surface area word problems: Get ready for circles and solid geometry", "Volume of cylinders, spheres, and cones: Get ready for circles and solid geometry", "Start Course challenge"]}}}}
{"course_title": "Get ready for Algebra 2", "course_url": "/math/get-ready-for-algebra-ii", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for polynomial operations and complex numbers": ["Combining like terms: Get ready for polynomial operations and complex numbers", "The distributive property & equivalent expressions: Get ready for polynomial operations and complex numbers", "Multiplying & dividing powers: Get ready for polynomial operations and complex numbers", "Multiplying binomials: Get ready for polynomial operations and complex numbers", "Special products of binomials: Get ready for polynomial operations and complex numbers", "Factoring quadratics intro: Get ready for polynomial operations and complex numbers", "Factoring quadratics by grouping: Get ready for polynomial operations and complex numbers", "Factoring quadratics with difference of squares: Get ready for polynomial operations and complex numbers", "Factoring quadratics with perfect squares: Get ready for polynomial operations and complex numbers"], "Unit 2: Get ready for equations": ["Solving equations with variables on both sides: Get ready for equations", "Linear equations with parentheses: Get ready for equations", "Introduction to systems of equations: Get ready for equations", "Solving systems of equations with substitution: Get ready for equations", "Equivalent systems of equations and the elimination method: Get ready for equations", "Radicals: Get ready for equations", "Solving quadratic equations by taking the square root: Get ready for equations", "Solving quadratics by factoring: Get ready for equations", "The quadratic formula: Get ready for equations"], "Unit 3: Get ready for transformations of functions and modeling with functions": ["Evaluating functions: Get ready for transformations of functions and modeling with functions", "Introduction to the domain and range of a function: Get ready for transformations of functions and modeling with functions", "Determining the domain of a function: Get ready for transformations of functions and modeling with functions", "Recognizing functions: Get ready for transformations of functions and modeling with functions", "Maximum and minimum points: Get ready for transformations of functions and modeling with functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for transformations of functions and modeling with functions", "Graphs of absolute value functions: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in factored form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in vertex form: Get ready for transformations of functions and modeling with functions", "Graphing quadratics in standard form: Get ready for transformations of functions and modeling with functions", "Features and forms of quadratic functions: Get ready for transformations of functions and modeling with functions", "Transforming quadratic functions: Get ready for transformations of functions and modeling with functions"], "Unit 4: Get ready for exponential and logarithmic relationships": ["Exponent properties (integer exponents): Get ready for exponential and logarithmic relationships", "Radicals: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth: Get ready for exponential and logarithmic relationships", "Exponential expressions: Get ready for exponential and logarithmic relationships", "Graphs of exponential growth: Get ready for exponential and logarithmic relationships", "Exponential vs. linear growth over time: Get ready for exponential and logarithmic relationships", "Exponential growth & decay: Get ready for exponential and logarithmic relationships", "Exponential functions from tables & graphs: Get ready for exponential and logarithmic relationships", "Intro to inverse functions: Get ready for exponential and logarithmic relationships"], "Unit 5: Get ready for trigonometry": ["Pythagorean theorem: Get ready for trigonometry", "Pythagorean theorem and distance between points: Get ready for trigonometry", "Ratios in right triangles: Get ready for trigonometry", "Introduction to the trigonometric ratios: Get ready for trigonometry", "Solving for sides and angles in right triangles using the trigonometric ratios: Get ready for trigonometry", "Introduction to radians: Get ready for trigonometry"], "Unit 6: Get ready for rational functions": ["Adding and subtracting fractions with unlike denominators: Get ready for rational functions", "Multiplying and dividing fractions: Get ready for rational functions", "Multiplying binomials: Get ready for rational functions", "Factoring quadratics intro: Get ready for rational functions", "Start Course challenge"]}}}}
{"course_title": "Get ready for Precalculus", "course_url": "/math/get-ready-for-precalculus", "page_contents": {"syllabus": {"topics": {"The imaginary unit i: Get ready for complex numbers": ["Complex numbers introduction: Get ready for complex numbers", "The complex plane: Get ready for complex numbers", "Adding and subtracting complex numbers: Get ready for complex numbers", "Quadratic equations with complex solutions: Get ready for complex numbers"], "Unit 2: Get ready for polynomials": ["Adding and subtracting polynomials: Get ready for polynomials", "Multiplying binomials by polynomials: Get ready for polynomials", "Special products of polynomials: Get ready for polynomials", "Factoring higher degree polynomials: Get ready for polynomials", "Factoring using structure: Get ready for polynomials", "Zeros of polynomials: Get ready for polynomials", "Dividing polynomials by x: Get ready for polynomials", "Dividing quadratics by linear factors: Get ready for polynomials", "Dividing polynomials by linear factors: Get ready for polynomials"], "Unit 3: Get ready for composite and inverse functions": ["Shifting functions: Get ready for composite and inverse functions", "Reflecting functions: Get ready for composite and inverse functions", "Scaling functions: Get ready for composite and inverse functions", "Identifying function transformations: Get ready for composite and inverse functions", "Intro to domain and range of a function: Get ready for composite and inverse functions", "Intro to inverse functions: Get ready for composite and inverse functions"], "Unit circle introduction: Get ready for trigonometry": ["Radians: Get ready for trigonometry", "The Pythagorean identity: Get ready for trigonometry", "Trigonometric values of special angles: Get ready for trigonometry", "Graphing sinusoidal functions: Get ready for trigonometry", "Sinusoidal models: Get ready for trigonometry"], "Unit 5: Get ready for vectors and matrices": ["Equivalent systems of equations and the elimination method: Get ready for vectors and matrices", "Dilations: Get ready for vectors and matrices", "Solving triangles using the trigonometric ratios: Get ready for vectors and matrices"], "Unit 6: Get ready for series": ["Intro to sequences: Get ready for series", "Constructing arithmetic sequences: Get ready for series", "Constructing geometric sequences: Get ready for series", "Modeling with sequences: Get ready for series", "General sequences: Get ready for series", "Geometric series: Get ready for series"], "Unit 7: Get ready for conic sections": ["Graphs of circles intro: Get ready for conic sections", "Standard equation of a circle: Get ready for conic sections", "Expanded equation of a circle: Get ready for conic sections", "Focus and directrix of a parabola: Get ready for conic sections"], "Unit 8: Get ready for probability and combinatorics": ["Basic theoretical probability: Get ready for probability and combinatorics", "Probability using sample spaces: Get ready for probability and combinatorics", "Basic set operations: Get ready for probability and combinatorics", "Experimental probability: Get ready for probability and combinatorics", "Randomness, probability, and simulation: Get ready for probability and combinatorics", "Addition rule: Get ready for probability and combinatorics", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Calculus", "course_url": "/math/get-ready-for-ap-calc", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for limits and continuity": ["Evaluating functions: Get ready for limits and continuity", "Inputs and outputs of a function: Get ready for limits and continuity", "Composing functions: Get ready for limits and continuity", "Piecewise functions: Get ready for limits and continuity", "Introduction to factoring: Get ready for limits and continuity", "Factoring quadratics intro: Get ready for limits and continuity", "Factoring quadratics by grouping: Get ready for limits and continuity", "Factoring quadratics with difference of squares: Get ready for limits and continuity", "Factoring quadratics with perfect squares: Get ready for limits and continuity", "Factoring higher degree polynomials: Get ready for limits and continuity", "Introduction to the trigonometric ratios: Get ready for limits and continuity"], "Unit circle introduction: Get ready for limits and continuity": ["Radians: Get ready for limits and continuity", "The Pythagorean identity: Get ready for limits and continuity", "Special trigonometric values in the first quadrant: Get ready for limits and continuity"], "Trigonometric identities on the unit circle: Get ready for limits and continuity": ["Angle addition identities: Get ready for limits and continuity", "Reducing rational expressions to lowest terms: Get ready for limits and continuity", "End behavior of rational functions: Get ready for limits and continuity", "Discontinuities of rational functions: Get ready for limits and continuity", "Multiplying and dividing rational expressions: Get ready for limits and continuity"], "Unit 2: Get ready for differentiation: definition and basic derivative rules": ["Intro to slope-intercept form: Get ready for differentiation: definition and basic derivative rules", "Writing slope-intercept equations: Get ready for differentiation: definition and basic derivative rules", "Point-slope form: Get ready for differentiation: definition and basic derivative rules", "Average rate of change: Get ready for differentiation: definition and basic derivative rules", "Rational exponents: Get ready for differentiation: definition and basic derivative rules", "Properties of exponents: Get ready for differentiation: definition and basic derivative rules", "Introduction to logarithms: Get ready for differentiation: definition and basic derivative rules"], "Unit 3: Get ready for differentiation: composite, implicit, and inverse functions": ["Composing functions: Get ready for differentiation: composite, implicit, and inverse functions", "Linear equations with unknown coefficients: Get ready for differentiation: composite, implicit, and inverse functions", "Intro to inverse functions: Get ready for differentiation: composite, implicit, and inverse functions", "Invertible functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse trigonometric functions: Get ready for differentiation: composite, implicit, and inverse functions", "Inverse functions in graphs and tables: Get ready for differentiation: composite, implicit, and inverse functions", "Verifying inverse functions by composition: Get ready for differentiation: composite, implicit, and inverse functions"], "Word problems with multiple units: Get ready for contextual applications of differentiation": ["Linear equations word problems: Get ready for contextual applications of differentiation", "Interpreting function notation: Get ready for contextual applications of differentiation", "Average rate of change word problems: Get ready for contextual applications of differentiation", "Modeling with composite functions: Get ready for contextual applications of differentiation", "Modeling with right triangles: Get ready for contextual applications of differentiation", "Volume and surface area: Get ready for contextual applications of differentiation"], "Unit 5: Get ready for applying derivatives to analyze functions": ["Maximum and minimum points: Get ready for applying derivatives to analyze functions", "Intervals where a function is positive, negative, increasing, or decreasing: Get ready for applying derivatives to analyze functions", "Interpreting features of graphs: Get ready for applying derivatives to analyze functions", "Distance formula: Get ready for applying derivatives to analyze functions", "Square-root equations: Get ready for applying derivatives to analyze functions", "Zeros of polynomials: Get ready for applying derivatives to analyze functions", "Positive and negative intervals of polynomials: Get ready for applying derivatives to analyze functions"], "Unit 6: Get ready for integration and accumulation of change": ["Completing the square: Get ready for integration and accumulation of change", "Dividing quadratics by linear factors: Get ready for integration and accumulation of change", "Dividing polynomials by linear factors: Get ready for integration and accumulation of change", "Partial fraction expansion: Get ready for integration and accumulation of change", "Summation notation: Get ready for integration and accumulation of change"], "Unit 7: Get ready for applications of integration": ["Rational equations: Get ready for applications of integration", "Square-root equations: Get ready for applications of integration", "Extraneous solutions: Get ready for applications of integration", "Sinusoidal equations: Get ready for applications of integration", "Manipulating formulas: Get ready for applications of integration", "Solving equations by graphing: Get ready for applications of integration"], "Unit 8: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)": ["Sectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vectors introduction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Magnitude of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Scalar multiplication: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Direction of vectors: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)", "Vector components from magnitude & direction: Get ready for parametric equations, polar coordinates, and vector-valued functions (BC only)"], "Unit 9: Get ready for infinite sequences and series (BC only)": ["Arithmetic sequences: Get ready for infinite sequences and series (BC only)", "Geometric sequences: Get ready for infinite sequences and series (BC only)", "Summation notation: Get ready for infinite sequences and series (BC only)", "Arithmetic series: Get ready for infinite sequences and series (BC only)", "Geometric series: Get ready for infinite sequences and series (BC only)", "End behavior of rational functions: Get ready for infinite sequences and series (BC only)", "Start Course challenge"]}}}}
{"course_title": "Get ready for AP\u00ae Statistics", "course_url": "/math/get-ready-for-ap-statistics", "page_contents": {"syllabus": {"topics": {"Unit 1: Get ready for exploring categorical data": ["Frequency tables: Get ready for exploring categorical data", "Bar graphs: Get ready for exploring categorical data", "Fractions, decimals, and percentages: Get ready for exploring categorical data"], "Unit 2: Get ready for exploring one-variable quantitative data": ["Frequency tables and dot plots: Get ready for exploring one-variable quantitative data", "Box and whisker plots: Get ready for exploring one-variable quantitative data", "Comparing data displays: Get ready for exploring one-variable quantitative data", "Mean, median, and mode: Get ready for exploring one-variable quantitative data", "Mean absolute deviation: Get ready for exploring one-variable quantitative data", "Linear equations with variables on both sides: Get ready for exploring one-variable quantitative data", "Linear equations with unknown coefficients: Get ready for exploring one-variable quantitative data"], "Unit 3: Get ready for exploring two-variable quantitative data": ["Introduction to scatter plots: Get ready for exploring two-variable quantitative data", "Estimating with trend lines: Get ready for exploring two-variable quantitative data", "Logarithms: Get ready for exploring two-variable quantitative data"], "Unit 4: Get ready for probability": ["Fractions, decimals, and percentages: Get ready for probability", "Comparing decimals and fractions: Get ready for probability", "Arithmetic with fractions: Get ready for probability", "Probability introduction: Get ready for probability", "Experimental probability: Get ready for probability"], "Unit 5: Get ready for random variables and probability distributions": ["Predictions with probability: Get ready for random variables and probability distributions", "The counting principle: Get ready for random variables and probability distributions", "Probability distributions introduction: Get ready for random variables and probability distributions", "Start Course challenge"]}}}}
{"course_title": "Algebra 1", "course_url": "/math/algebra", "page_contents": {"syllabus": {"topics": {"Unit 1: Algebra foundations": ["Overview and history of algebra: Algebra foundations", "Introduction to variables: Algebra foundations", "Substitution and evaluating expressions: Algebra foundations", "Combining like terms: Algebra foundations", "Introduction to equivalent expressions: Algebra foundations", "Division by zero: Algebra foundations"], "Unit 2: Solving equations & inequalities": ["Linear equations with variables on both sides: Solving equations & inequalities", "Linear equations with parentheses: Solving equations & inequalities", "Analyzing the number of solutions to linear equations: Solving equations & inequalities", "Linear equations with unknown coefficients: Solving equations & inequalities", "Multi-step inequalities: Solving equations & inequalities", "Compound inequalities: Solving equations & inequalities"], "Unit 4: Linear equations & graphs": ["Two-variable linear equations intro: Linear equations & graphs", "Slope: Linear equations & graphs", "Horizontal & vertical lines: Linear equations & graphs", "x-intercepts and y-intercepts: Linear equations & graphs", "Applying intercepts and slope: Linear equations & graphs", "Modeling with linear equations and inequalities: Linear equations & graphs"], "Unit 5: Forms of linear equations": ["Intro to slope-intercept form: Forms of linear equations", "Graphing slope-intercept equations: Forms of linear equations", "Writing slope-intercept equations: Forms of linear equations", "Point-slope form: Forms of linear equations", "Standard form: Forms of linear equations", "Summary: Forms of two-variable linear equations: Forms of linear equations"], "Unit 6: Systems of equations": ["Introduction to systems of equations: Systems of equations", "Solving systems of equations with substitution: Systems of equations", "Solving systems of equations with elimination: Systems of equations", "Equivalent systems of equations: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 7: Inequalities (systems & graphs)": ["Checking solutions of two-variable inequalities: Inequalities (systems & graphs)", "Graphing two-variable inequalities: Inequalities (systems & graphs)", "Modeling with linear inequalities: Inequalities (systems & graphs)"], "Unit 8: Functions": ["Evaluating functions: Functions", "Inputs and outputs of a function: Functions", "Functions and equations: Functions", "Interpreting function notation: Functions", "Introduction to the domain and range of a function: Functions", "Determining the domain of a function: Functions", "Recognizing functions: Functions", "Maximum and minimum points: Functions", "Intervals where a function is positive, negative, increasing, or decreasing: Functions", "Interpreting features of graphs: Functions", "Average rate of change: Functions", "Average rate of change word problems: Functions", "Intro to inverse functions: Functions"], "Unit 9: Sequences": ["Introduction to arithmetic sequences: Sequences", "Constructing arithmetic sequences: Sequences", "Introduction to geometric sequences: Sequences", "Constructing geometric sequences: Sequences", "Modeling with sequences: Sequences", "General sequences: Sequences"], "Unit 10: Absolute value & piecewise functions": ["Graphs of absolute value functions: Absolute value & piecewise functions", "Piecewise functions: Absolute value & piecewise functions"], "Unit 11: Exponents & radicals": ["Exponent properties review: Exponents & radicals", "Radicals: Exponents & radicals", "Simplifying square roots: Exponents & radicals"], "Unit 12: Exponential growth & decay": ["Exponential vs. linear growth: Exponential growth & decay", "Exponential expressions: Exponential growth & decay", "Graphs of exponential growth: Exponential growth & decay", "Exponential vs. linear growth over time: Exponential growth & decay", "Exponential growth & decay: Exponential growth & decay", "Exponential functions from tables & graphs: Exponential growth & decay", "Exponential vs. linear models: Exponential growth & decay"], "Unit 13: Quadratics: Multiplying & factoring": ["Multiplying monomials by polynomials: Quadratics: Multiplying & factoring", "Multiplying binomials: Quadratics: Multiplying & factoring", "Special products of binomials: Quadratics: Multiplying & factoring", "Introduction to factoring: Quadratics: Multiplying & factoring", "Factoring quadratics intro: Quadratics: Multiplying & factoring", "Factoring quadratics by grouping: Quadratics: Multiplying & factoring", "Factoring quadratics with difference of squares: Quadratics: Multiplying & factoring", "Factoring quadratics with perfect squares: Quadratics: Multiplying & factoring", "Strategy in factoring quadratics: Quadratics: Multiplying & factoring"], "Unit 14: Quadratic functions & equations": ["Intro to parabolas: Quadratic functions & equations", "Solving and graphing with factored form: Quadratic functions & equations", "Solving by taking the square root: Quadratic functions & equations", "Vertex form: Quadratic functions & equations", "Solving quadratics by factoring: Quadratic functions & equations", "The quadratic formula: Quadratic functions & equations", "Completing the square intro: Quadratic functions & equations", "More on completing the square: Quadratic functions & equations", "Strategizing to solve quadratic equations: Quadratic functions & equations", "Quadratic standard form: Quadratic functions & equations", "Features & forms of quadratic functions: Quadratic functions & equations", "Comparing quadratic functions: Quadratic functions & equations", "Transforming quadratic functions: Quadratic functions & equations"], "Unit 15: Irrational numbers": ["Irrational numbers: Irrational numbers", "Sums and products of rational and irrational numbers: Irrational numbers", "Proofs concerning irrational numbers: Irrational numbers"], "Unit 16: Creativity in algebra": ["Creativity in algebra: Creativity in algebra", "Start Course challenge"]}}}}
{"course_title": "Geometry", "course_url": "/math/geometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Performing transformations": ["Introduction to rigid transformations: Performing transformations", "Translations: Performing transformations", "Rotations: Performing transformations", "Reflections: Performing transformations", "Dilations: Performing transformations"], "Unit 2: Transformation properties and proofs": ["Dilation preserved properties: Transformation properties and proofs", "Properties & definitions of transformations: Transformation properties and proofs", "Symmetry: Transformation properties and proofs", "Proofs with transformations: Transformation properties and proofs"], "Unit 3: Congruence": ["Triangle congruence from transformations: Congruence", "Congruent triangles: Congruence", "Working with triangles: Congruence", "Theorems concerning quadrilateral properties: Congruence", "Proofs of general theorems: Congruence", "Constructing lines & angles: Congruence"], "Unit 4: Similarity": ["Introduction to triangle similarity: Similarity", "Solving similar triangles: Similarity", "Angle bisector theorem: Similarity", "Solving problems with similar & congruent triangles: Similarity", "Proving relationships using similarity: Similarity", "Solving modeling problems with similar & congruent triangles: Similarity"], "Unit 5: Right triangles & trigonometry": ["Pythagorean theorem proofs: Right triangles & trigonometry", "Special right triangles: Right triangles & trigonometry", "Introduction to the trigonometric ratios: Right triangles & trigonometry", "Solving for a side in a right triangle using the trigonometric ratios: Right triangles & trigonometry", "Sine & cosine of complementary angles: Right triangles & trigonometry", "Modeling with right triangles: Right triangles & trigonometry"], "Unit 6: Analytic geometry": ["Dividing line segments: Analytic geometry", "Problem solving with distance on the coordinate plane: Analytic geometry", "Parallel & perpendicular lines on the coordinate plane: Analytic geometry", "Equations of parallel & perpendicular lines: Analytic geometry"], "Unit 7: Conic sections": ["Standard equation of a circle: Conic sections", "Expanded equation of a circle: Conic sections", "Focus and directrix of a parabola: Conic sections"], "Unit 8: Circles": ["Arc measure: Circles", "Arc length (from degrees): Circles", "Introduction to radians: Circles", "Arc length (from radians): Circles", "Sectors: Circles", "Inscribed angles: Circles", "Inscribed shapes problem solving: Circles", "Proofs with inscribed shapes: Circles", "Properties of tangents: Circles", "Constructing regular polygons inscribed in circles: Circles", "Constructing circumcircles & incircles: Circles", "Constructing a line tangent to a circle: Circles"], "Unit 9: Solid geometry": ["Volume and surface area: Solid geometry", "Density: Solid geometry", "Start Course challenge", "Modeling with right triangles", "Volume and surface area", "Special right triangles", "Introduction to triangle similarity"]}}}}
{"course_title": "Algebra 2", "course_url": "/math/algebra2", "page_contents": {"syllabus": {"topics": {"Unit 1: Polynomial arithmetic": ["Intro to polynomials: Polynomial arithmetic", "Average rate of change of polynomials: Polynomial arithmetic", "Adding and subtracting polynomials: Polynomial arithmetic", "Multiplying monomials by polynomials: Polynomial arithmetic", "Multiplying binomials by polynomials: Polynomial arithmetic", "Special products of polynomials: Polynomial arithmetic"], "The imaginary unit i: Complex numbers": ["Complex numbers introduction: Complex numbers", "The complex plane: Complex numbers", "Adding and subtracting complex numbers: Complex numbers", "Quadratic equations with complex solutions: Complex numbers"], "Unit 3: Polynomial factorization": ["Factoring monomials: Polynomial factorization", "Greatest common factor: Polynomial factorization", "Taking common factors: Polynomial factorization", "Factoring higher degree polynomials: Polynomial factorization", "Factoring using structure: Polynomial factorization", "Polynomial identities: Polynomial factorization", "Geometric series: Polynomial factorization"], "Unit 4: Polynomial division": ["Dividing polynomials by x: Polynomial division", "Dividing quadratics by linear factors: Polynomial division", "Dividing polynomials by linear factors: Polynomial division", "Polynomial Remainder Theorem: Polynomial division"], "Unit 5: Polynomial graphs": ["Zeros of polynomials: Polynomial graphs", "Positive and negative intervals of polynomials: Polynomial graphs", "End behavior of polynomials: Polynomial graphs"], "Unit 6: Rational exponents and radicals": ["Rational exponents: Rational exponents and radicals", "Properties of exponents (rational exponents): Rational exponents and radicals", "Evaluating exponents & radicals: Rational exponents and radicals", "Equivalent forms of exponential expressions: Rational exponents and radicals", "Solving exponential equations using properties of exponents: Rational exponents and radicals"], "Unit 7: Exponential models": ["Interpreting the rate of change of exponential models: Exponential models", "Constructing exponential models according to rate of change: Exponential models", "Advanced interpretation of exponential models: Exponential models"], "Unit 8: Logarithms": ["Introduction to logarithms: Logarithms", "The constant e and the natural logarithm: Logarithms", "Properties of logarithms: Logarithms", "The change of base formula for logarithms: Logarithms", "Solving exponential equations with logarithms: Logarithms", "Solving exponential models: Logarithms"], "Unit 9: Transformations of functions": ["Shifting functions: Transformations of functions", "Reflecting functions: Transformations of functions", "Symmetry of functions: Transformations of functions", "Scaling functions: Transformations of functions", "Putting it all together: Transformations of functions", "Graphs of square and cube root functions: Transformations of functions", "Graphs of exponential functions: Transformations of functions", "Graphs of logarithmic functions: Transformations of functions"], "Unit 10: Equations": ["Rational equations: Equations", "Square-root equations: Equations", "Extraneous solutions: Equations", "Cube-root equations: Equations", "Quadratic systems: Equations", "Solving equations by graphing: Equations"], "Unit circle introduction: Trigonometry": ["Radians: Trigonometry", "The Pythagorean identity: Trigonometry", "Trigonometric values of special angles: Trigonometry", "Graphs of sin(x), cos(x), and tan(x): Trigonometry", "Amplitude, midline and period: Trigonometry", "Transforming sinusoidal graphs: Trigonometry", "Graphing sinusoidal functions: Trigonometry", "Sinusoidal models: Trigonometry"], "Unit 12: Modeling": ["Modeling with function combination: Modeling", "Interpreting features of functions: Modeling", "Manipulating formulas: Modeling", "Modeling with two variables: Modeling", "Modeling with multiple variables: Modeling", "Start Course challenge"]}}}}
{"course_title": "Integrated math 1", "course_url": "/math/math1", "page_contents": {"syllabus": {"topics": {"Unit 1: Algebra foundations": ["Overview and history of algebra: Algebra foundations", "Introduction to variables: Algebra foundations", "Substitution and evaluating expressions: Algebra foundations", "Combining like terms: Algebra foundations", "Introduction to equivalent expressions: Algebra foundations", "Division by zero: Algebra foundations"], "Unit 2: Solving equations & inequalities": ["Linear equations with variables on both sides: Solving equations & inequalities", "Linear equations with parentheses: Solving equations & inequalities", "Analyzing the number of solutions to linear equations: Solving equations & inequalities", "Linear equations with unknown coefficients: Solving equations & inequalities", "Multi-step inequalities: Solving equations & inequalities", "Compound inequalities: Solving equations & inequalities"], "Unit 4: Linear equations & graphs": ["Two-variable linear equations intro: Linear equations & graphs", "Slope: Linear equations & graphs", "Horizontal & vertical lines: Linear equations & graphs", "x-intercepts and y-intercepts: Linear equations & graphs", "Applying intercepts and slope: Linear equations & graphs"], "Unit 5: Forms of linear equations": ["Intro to slope-intercept form: Forms of linear equations", "Graphing slope-intercept equations: Forms of linear equations", "Writing slope-intercept equations: Forms of linear equations", "Point-slope form: Forms of linear equations", "Standard form: Forms of linear equations", "Summary: Forms of two-variable linear equations: Forms of linear equations"], "Unit 6: Systems of equations": ["Introduction to systems of equations: Systems of equations", "Solving systems of equations with substitution: Systems of equations", "Equivalent systems of equations: Systems of equations", "Solving systems of equations with elimination: Systems of equations", "Number of solutions to systems of equations: Systems of equations", "Systems of equations word problems: Systems of equations"], "Unit 7: Inequalities (systems & graphs)": ["Checking solutions of two-variable inequalities: Inequalities (systems & graphs)", "Graphing two-variable inequalities: Inequalities (systems & graphs)", "Modeling with linear inequalities: Inequalities (systems & graphs)"], "Unit 8: Functions": ["Evaluating functions: Functions", "Inputs and outputs of a function: Functions", "Functions and equations: Functions", "Interpreting function notation: Functions", "Introduction to the domain and range of a function: Functions", "Determining the domain of a function: Functions", "Recognizing functions: Functions", "Maximum and minimum points: Functions", "Intervals where a function is positive, negative, increasing, or decreasing: Functions", "Interpreting features of graphs: Functions", "Average rate of change: Functions", "Average rate of change word problems: Functions", "Intro to inverse functions: Functions"], "Unit 9: Scatterplots": ["Creating and interpreting scatterplots: Scatterplots", "Estimating with trend lines: Scatterplots"], "Unit 10: Data distributions": ["Displays of distributions: Data distributions", "Summarizing center of distributions (central tendency): Data distributions", "Box and whisker plots: Data distributions", "Comparing distributions: Data distributions"], "Unit 12: Sequences": ["Introduction to arithmetic sequences: Sequences", "Constructing arithmetic sequences: Sequences", "Introduction to geometric sequences: Sequences", "Constructing geometric sequences: Sequences", "Modeling with sequences: Sequences", "General sequences: Sequences"], "Unit 13: Exponents & radicals": ["Exponent properties review: Exponents & radicals", "Radicals: Exponents & radicals", "Simplifying square roots: Exponents & radicals"], "Unit 14: Exponential growth & decay": ["Exponential vs. linear growth: Exponential growth & decay", "Exponential expressions: Exponential growth & decay", "Graphs of exponential growth: Exponential growth & decay", "Exponential vs. linear growth over time: Exponential growth & decay", "Exponential growth & decay: Exponential growth & decay", "Exponential functions from tables & graphs: Exponential growth & decay", "Exponential vs. linear models: Exponential growth & decay"], "Unit 15: Performing transformations": ["Translations: Performing transformations", "Rotations: Performing transformations", "Reflections: Performing transformations", "Dilations: Performing transformations"], "Unit 16: Transformation properties and proofs": ["Dilation preserved properties: Transformation properties and proofs", "Properties & definitions of transformations: Transformation properties and proofs", "Symmetry: Transformation properties and proofs", "Proofs with transformations: Transformation properties and proofs"], "Unit 17: Congruence": ["Triangle congruence from transformations: Congruence", "Congruent triangles: Congruence", "Working with triangles: Congruence", "Theorems concerning quadrilateral properties: Congruence", "Proofs of general theorems that use triangle congruence: Congruence", "Constructing lines & angles: Congruence"], "Unit 18: Analytic geometry": ["Dividing line segments: Analytic geometry", "Problem solving with distance on the coordinate plane: Analytic geometry", "Parallel & perpendicular lines on the coordinate plane: Analytic geometry", "Equations of parallel & perpendicular lines: Analytic geometry", "Start Course challenge"]}}}}
{"course_title": "Integrated math 2", "course_url": "/math/math2", "page_contents": {"syllabus": {"topics": {"Unit 1: Absolute value & piecewise functions": ["Graphs of absolute value functions: Absolute value & piecewise functions", "Piecewise functions: Absolute value & piecewise functions"], "Unit 2: Quadratics: Multiplying & factoring": ["Multiplying monomials by polynomials: Quadratics: Multiplying & factoring", "Multiplying binomials: Quadratics: Multiplying & factoring", "Special products of binomials: Quadratics: Multiplying & factoring", "Introduction to factoring: Quadratics: Multiplying & factoring", "Factoring quadratics intro: Quadratics: Multiplying & factoring", "Factoring quadratics by grouping: Quadratics: Multiplying & factoring", "Factoring quadratics with difference of squares: Quadratics: Multiplying & factoring", "Factoring quadratics with perfect squares: Quadratics: Multiplying & factoring", "Strategy in factoring quadratics: Quadratics: Multiplying & factoring"], "Unit 3: Quadratic functions & equations": ["Intro to parabolas: Quadratic functions & equations", "Solving and graphing with factored form: Quadratic functions & equations", "Solving by taking the square root: Quadratic functions & equations", "Vertex form: Quadratic functions & equations", "Solving quadratics by factoring: Quadratic functions & equations", "The quadratic formula: Quadratic functions & equations", "Completing the square: Quadratic functions & equations", "Strategizing to solve quadratic equations: Quadratic functions & equations", "Quadratics standard form: Quadratic functions & equations", "Features & forms of quadratic functions: Quadratic functions & equations", "Comparing quadratic functions: Quadratic functions & equations", "Transforming quadratic functions: Quadratic functions & equations"], "Unit 4: Irrational numbers": ["Irrational numbers: Irrational numbers", "Sums & products of rational/irrational numbers: Irrational numbers", "Proofs concerning irrational numbers: Irrational numbers"], "The imaginary unit i: Complex numbers": ["Complex numbers introduction: Complex numbers", "The complex plane: Complex numbers", "Adding & subtracting complex numbers: Complex numbers", "Quadratic equations with complex solutions: Complex numbers"], "Unit 6: Rational exponents and radicals": ["Rational exponents: Rational exponents and radicals", "Properties of exponents (rational exponents): Rational exponents and radicals", "Equivalent forms of exponential expressions: Rational exponents and radicals", "Evaluating exponents and radicals: Rational exponents and radicals", "Solving exponential expressions using properties of exponents: Rational exponents and radicals"], "Unit 7: Exponential models": ["Interpreting the rate of change of exponential models: Exponential models", "Constructing exponential models according to rate of change: Exponential models", "Advanced interpretation of exponential models: Exponential models"], "Unit 8: Similarity": ["Introduction to triangle similarity: Similarity", "Angle bisector theorem: Similarity", "Solving problems with similar & congruent triangles: Similarity", "Proving relationships using similarity: Similarity", "Solving modeling problems with similar & congruent triangles: Similarity"], "Unit 9: Right triangles & trigonometry": ["Pythagorean theorem proofs: Right triangles & trigonometry", "Special right triangles: Right triangles & trigonometry", "Introduction to the trigonometric ratios: Right triangles & trigonometry", "Sine & cosine of complementary angles: Right triangles & trigonometry", "Modeling with right triangles: Right triangles & trigonometry"], "Unit 10: Solid geometry": ["Volume and surface area: Solid geometry", "Density: Solid geometry"], "Unit 11: Circles": ["Arc measure: Circles", "Arc length (from degrees): Circles", "Introduction to radians: Circles", "Arc length (from radians): Circles", "Sectors: Circles", "Inscribed angles: Circles", "Inscribed shapes problem solving: Circles", "Proofs with inscribed shapes: Circles", "Properties of tangents: Circles", "Constructing regular polygons inscribed in circles: Circles", "Constructing circumcircles & incircles: Circles", "Constructing a line tangent to a circle: Circles"], "Unit 12: Conic sections": ["Features of a circle: Conic sections", "Standard equation of a circle: Conic sections", "Expanded equation of a circle: Conic sections", "Focus & directrix of a parabola: Conic sections"], "Unit 13: Probability": ["Probability basics: Probability", "Counting with combinations: Probability", "Probability with counting, permutations, combinations: Probability", "Multiplication rule for independent events: Probability", "Multiplication rule for dependent events: Probability", "Addition rule for probability: Probability", "Start Course challenge"]}}}}
{"course_title": "Integrated math 3", "course_url": "/math/math3", "page_contents": {"syllabus": {"topics": {"Unit 1: Polynomial arithmetic": ["Intro to polynomials: Polynomial arithmetic", "Average rate of change of polynomials: Polynomial arithmetic", "Adding and subtracting polynomials: Polynomial arithmetic", "Multiplying monomials by polynomials: Polynomial arithmetic", "Multiplying binomials by polynomials: Polynomial arithmetic", "Special products of polynomials: Polynomial arithmetic"], "Unit 2: Polynomial factorization": ["Factoring monomials: Polynomial factorization", "Greatest common factor: Polynomial factorization", "Taking common factors: Polynomial factorization", "Factoring higher degree polynomials: Polynomial factorization", "Factoring using structure: Polynomial factorization", "Polynomial identities: Polynomial factorization", "Geometric series: Polynomial factorization"], "Unit 3: Polynomial division": ["Dividing polynomials by x: Polynomial division", "Dividing quadratics by linear factors: Polynomial division", "Dividing polynomials by linear factors: Polynomial division", "Polynomial remainder theorem: Polynomial division"], "Unit 4: Polynomial graphs": ["Zeros of polynomials: Polynomial graphs", "Positive and negative intervals of polynomials: Polynomial graphs", "End behavior of polynomials: Polynomial graphs"], "Unit 5: Logarithms": ["Introduction to logarithms: Logarithms", "The constant e and the natural logarithm: Logarithms", "Properties of logarithms: Logarithms", "Change of base formula for logarithms: Logarithms", "Solving exponential equations with logarithms: Logarithms", "Solving exponential models: Logarithms"], "Unit 6: Transformations of functions": ["Shifting functions: Transformations of functions", "Reflecting functions: Transformations of functions", "Symmetry of functions: Transformations of functions", "Scaling functions: Transformations of functions", "Putting it all together: Transformations of functions", "Graphs of square and cube root functions: Transformations of functions", "Graphs of exponential functions: Transformations of functions", "Graphs of logarithmic functions: Transformations of functions"], "Unit 7: Equations": ["Rational equations: Equations", "Square-root equations: Equations", "Extraneous solutions: Equations", "Cube-root equations: Equations", "Quadratic systems: Equations", "Solving equations by graphing: Equations"], "Unit 8: Trigonometry": ["Law of sines: Trigonometry", "Law of cosines: Trigonometry", "Solving general triangles: Trigonometry"], "Unit circle introduction: Trigonometry": ["Radians: Trigonometry", "The Pythagorean identity: Trigonometry", "Trigonometric values of special angles: Trigonometry", "Graphs of sin(x), cos(x), and tan(x): Trigonometry", "Amplitude, midline, & period: Trigonometry", "Transforming sinusoidal graphs: Trigonometry", "Graphing sinusoidal functions: Trigonometry", "Sinusoidal models: Trigonometry"], "Unit 9: Modeling": ["Modeling with function combination: Modeling", "Interpreting features of functions: Modeling", "Manipulating formulas: Modeling", "Modeling with two variables: Modeling", "Modeling with multiple variables: Modeling"], "Unit 10: Study Design": ["Samples and surveys: Study Design", "Observational studies and experiments: Study Design"], "Unit 13: Rational functions": ["Cancelling common factors: Rational functions", "End behavior of rational functions: Rational functions", "Discontinuities of rational functions: Rational functions", "Graphs of rational functions: Rational functions", "Modeling with rational functions: Rational functions", "Multiplying & dividing rational expressions: Rational functions", "Adding subtracting rational expressions intro: Rational functions", "Adding subtracting rational expressions (factored): Rational functions", "Adding subtracting rational expressions (not factored): Rational functions", "Start Course challenge"]}}}}
{"course_title": "Algebra basics", "course_url": "/math/algebra-basics", "page_contents": {"syllabus": {"topics": {"Unit 1: Foundations": ["Absolute value: Foundations", "Exponents: Foundations", "Square roots: Foundations", "Order of operations: Foundations", "Fractions: Foundations", "Decimals, fractions and percentages: Foundations", "Operations with decimals: Foundations", "Area of triangles: Foundations", "Circumference and area of circles: Foundations"], "Unit 2: Algebraic expressions": ["Introduction to variables: Algebraic expressions", "Substitution & evaluating expressions: Algebraic expressions", "Writing algebraic expressions: Algebraic expressions", "Combining like terms: Algebraic expressions", "Distributive property: Algebraic expressions", "Equivalent algebraic expressions: Algebraic expressions", "Nested fractions: Algebraic expressions"], "Unit 3: Linear equations and inequalities": ["One-step equations: Linear equations and inequalities", "Two-steps equations: Linear equations and inequalities", "Multi-step equations: Linear equations and inequalities", "One-step inequalities: Linear equations and inequalities", "Two-step inequalities: Linear equations and inequalities", "Multi-step inequalities: Linear equations and inequalities", "Writing & solving proportions: Linear equations and inequalities"], "Unit 4: Graphing lines and slope": ["Coordinate plane: Graphing lines and slope", "Solutions to two-variable linear equations: Graphing lines and slope", "x-intercepts and y-intercepts: Graphing lines and slope", "Slope: Graphing lines and slope", "Horizontal & vertical lines: Graphing lines and slope", "Slope-intercept form intro: Graphing lines and slope", "Writing slope-intercept equations: Graphing lines and slope", "Graphing two-variable inequalities: Graphing lines and slope"], "Unit 5: Systems of equations": ["Systems of equations intro: Systems of equations", "Elimination method for systems of equations: Systems of equations", "Substitution method for systems of equations: Systems of equations", "Number of solutions to systems of equations: Systems of equations"], "Unit 6: Expressions with exponents": ["Exponent properties intro : Expressions with exponents", "Negative exponents: Expressions with exponents", "Exponent properties (integer exponents) : Expressions with exponents", "Scientific notation intro: Expressions with exponents", "Scientific notation word problems: Expressions with exponents"], "Unit 7: Quadratics and polynomials": ["Adding & subtracting polynomials: Quadratics and polynomials", "Multiplying binomials: Quadratics and polynomials", "Special products of binomials: Quadratics and polynomials", "Factoring polynomials by taking common factors: Quadratics and polynomials", "Factoring quadratics 1: Quadratics and polynomials", "Factoring quadratics 2: Quadratics and polynomials", "Factoring quadratics: Difference of squares: Quadratics and polynomials", "Factoring quadratics: Perfect squares: Quadratics and polynomials", "Solving quadratic equations by factoring: Quadratics and polynomials"], "Unit 8: Equations and geometry": ["Equations & geometry: Equations and geometry", "Triangle angles: Equations and geometry", "Pythagorean theorem: Equations and geometry", "Triangle similarity intro: Equations and geometry", "Start Course challenge"]}}}}
{"course_title": "Trigonometry", "course_url": "/math/trigonometry", "page_contents": {"syllabus": {"topics": {"Unit 1: Right triangles & trigonometry": ["Introduction to the trigonometric ratios: Right triangles & trigonometry", "Solving for a side in a right triangle using the trigonometric ratios: Right triangles & trigonometry", "Sine and cosine of complementary angles: Right triangles & trigonometry", "Modeling with right triangles: Right triangles & trigonometry"], "Unit circle introduction: Trigonometric functions": ["Radians: Trigonometric functions", "The Pythagorean identity: Trigonometric functions", "Special trigonometric values in the first quadrant: Trigonometric functions"], "Trigonometric values on the unit circle: Trigonometric functions": ["Graphs of sin(x), cos(x), and tan(x): Trigonometric functions", "Amplitude, midline, and period: Trigonometric functions", "Transforming sinusoidal graphs: Trigonometric functions", "Graphing sinusoidal functions: Trigonometric functions", "Sinusoidal models: Trigonometric functions", "Long live Tau: Trigonometric functions"], "Unit 3: Non-right triangles & trigonometry": ["Law of sines: Non-right triangles & trigonometry", "Law of cosines: Non-right triangles & trigonometry", "Solving general triangles: Non-right triangles & trigonometry"], "Unit 4: Trigonometric equations and identities": ["Inverse trigonometric functions: Trigonometric equations and identities", "Sinusoidal equations: Trigonometric equations and identities", "Sinusoidal models: Trigonometric equations and identities", "Angle addition identities: Trigonometric equations and identities", "Using trigonometric identities: Trigonometric equations and identities", "Challenging trigonometry problems: Trigonometric equations and identities", "Start Course challenge", "The reciprocal trigonometric ratios"]}}}}
{"course_title": "Precalculus", "course_url": "/math/precalculus", "page_contents": {"syllabus": {"topics": {"Unit 1: Composite and inverse functions": ["Composing functions: Composite and inverse functions", "Modeling with composite functions: Composite and inverse functions", "Invertible functions: Composite and inverse functions", "Inverse functions in graphs and tables: Composite and inverse functions", "Verifying inverse functions by composition: Composite and inverse functions"], "Trigonometric identities on the unit circle: Trigonometry": ["Inverse trigonometric functions: Trigonometry", "Law of sines: Trigonometry", "Law of cosines: Trigonometry", "Solving general triangles: Trigonometry", "Sinusoidal equations: Trigonometry", "Sinusoidal models: Trigonometry", "Angle addition identities: Trigonometry", "Using trigonometric identities: Trigonometry"], "Unit 3: Complex numbers": ["The complex plane: Complex numbers", "Distance and midpoint of complex numbers: Complex numbers", "Complex conjugates and dividing complex numbers: Complex numbers", "Identities with complex numbers: Complex numbers", "Modulus (absolute value) and argument (angle) of complex numbers: Complex numbers", "Polar form of complex numbers: Complex numbers", "Graphically multiplying complex numbers: Complex numbers", "Multiplying and dividing complex numbers in polar form: Complex numbers", "The fundamental theorem of algebra: Complex numbers"], "Unit 4: Rational functions": ["End behavior of rational functions: Rational functions", "Discontinuities of rational functions: Rational functions", "Graphs of rational functions: Rational functions", "Modeling with rational functions: Rational functions", "Multiplying and dividing rational expressions: Rational functions"], "Unit 5: Conic sections": ["Introduction to conic sections: Conic sections", "Center and radii of an ellipse: Conic sections", "Foci of an ellipse: Conic sections", "Introduction to hyperbolas: Conic sections", "Foci of a hyperbola: Conic sections", "Hyperbolas not centered at the origin: Conic sections"], "Unit 6: Vectors": ["Vectors introduction: Vectors", "Vector components: Vectors", "Magnitude of vectors: Vectors", "Scalar multiplication: Vectors", "Vector addition and subtraction: Vectors", "Direction of vectors: Vectors", "Vector components from magnitude and direction: Vectors", "Adding vectors in magnitude and direction form: Vectors", "Vectors word problems: Vectors"], "Unit 7: Matrices": ["Introduction to matrices: Matrices", "Using matrices to represent data: Matrices", "Multiplying matrices by scalars: Matrices", "Adding and subtracting matrices: Matrices", "Using matrices to manipulate data: Matrices", "Matrices as transformations of the plane: Matrices", "Using matrices to transform the plane: Matrices", "Transforming 3D and 4D vectors with matrices: Matrices", "Multiplying matrices by matrices: Matrices", "Properties of matrix multiplication: Matrices", "Representing systems of equations with matrices: Matrices", "Introduction to matrix inverses: Matrices", "Finding inverses of 2x2 matrices: Matrices", "Solving linear systems with matrices: Matrices"], "Unit 8: Probability and combinatorics": ["Venn diagrams and the addition rule: Probability and combinatorics", "Multiplication rule for probabilities: Probability and combinatorics", "Permutations: Probability and combinatorics", "Combinations: Probability and combinatorics", "Probability using combinatorics: Probability and combinatorics", "Probability distributions introduction: Probability and combinatorics", "Theoretical & empirical probability distributions: Probability and combinatorics", "Decisions with probability: Probability and combinatorics", "Expected value: Probability and combinatorics"], "Unit 9: Series": ["Geometric series: Series", "Geometric series (with summation notation): Series", "The binomial theorem: Series", "Arithmetic series: Series"], "Unit 10: Limits and continuity": ["Defining limits and using limit notation: Limits and continuity", "Estimating limit values from graphs: Limits and continuity", "Estimating limit values from tables: Limits and continuity", "Determining limits using algebraic properties of limits: limit properties: Limits and continuity", "Determining limits using algebraic properties of limits: direct substitution: Limits and continuity", "Determining limits using algebraic manipulation: Limits and continuity", "Selecting procedures for determining limits: Limits and continuity", "Determining limits using the squeeze theorem: Limits and continuity", "Exploring types of discontinuities: Limits and continuity", "Defining continuity at a point: Limits and continuity", "Confirming continuity over an interval: Limits and continuity", "Removing discontinuities: Limits and continuity", "Connecting infinite limits and vertical asymptotes: Limits and continuity", "Connecting limits at infinity and horizontal asymptotes: Limits and continuity", "Working with the intermediate value theorem: Limits and continuity", "Start Course challenge"]}}}}
{"course_title": "High school statistics", "course_url": "/math/probability", "page_contents": {"syllabus": {"topics": {"Unit 1: Displaying a single quantitative variable": ["Frequency tables and dot plots: Displaying a single quantitative variable", "Histograms: Displaying a single quantitative variable", "Mean and median in data displays: Displaying a single quantitative variable", "Interquartile range: Displaying a single quantitative variable", "Box and whisker plots: Displaying a single quantitative variable"], "Unit 2: Analyzing a single quantitative variable": ["Standard deviation: Analyzing a single quantitative variable", "Comparing distributions: Analyzing a single quantitative variable", "Percentiles and z-scores: Analyzing a single quantitative variable", "Normal distributions and the empirical rule: Analyzing a single quantitative variable", "Normal distribution calculations: Analyzing a single quantitative variable"], "Unit 3: Two-way tables": ["Two-way tables introduction: Two-way tables", "Distributions in two-way tables: Two-way tables"], "Unit 4: Scatterplots": ["Fitting trend lines to scatterplots: Scatterplots", "Analyzing trend lines in scatterplots: Scatterplots", "Residuals: Scatterplots"], "Unit 5: Study design": ["Introduction to planning a study: Study design", "Potential problems with sampling: Study design", "Sampling methods: Study design", "Introduction to experimental design: Study design", "Inference and experiments: Study design"], "Unit 6: Probability": ["Venn diagrams and the addition rule: Probability", "Multiplication rule for probabilities: Probability", "Conditional probability: Probability", "Probability from simulations: Probability", "Permutations: Probability", "Combinations: Probability", "Probability using combinatorics: Probability"], "Unit 7: Probability distributions & expected value": ["Probability distributions introduction: Probability distributions & expected value", "Theoretical & empirical probability distributions: Probability distributions & expected value", "Decisions with probability: Probability distributions & expected value", "Expected value: Probability distributions & expected value", "Start Course challenge"]}}}}
{"course_title": "Statistics & probability", "course_url": "/math/statistics-probability", "page_contents": {"syllabus": {"topics": {"Unit 1: Analyzing categorical data": ["Analyzing one categorical variable: Analyzing categorical data", "Two-way tables: Analyzing categorical data", "Distributions in two-way tables: Analyzing categorical data"], "Unit 2: Displaying and comparing quantitative data": ["Displaying quantitative data with graphs: Displaying and comparing quantitative data", "Describing and comparing distributions: Displaying and comparing quantitative data", "More on data displays: Displaying and comparing quantitative data"], "Unit 3: Summarizing quantitative data": ["Measuring center in quantitative data: Summarizing quantitative data", "Interquartile range (IQR): Summarizing quantitative data", "Variance and standard deviation of a population: Summarizing quantitative data", "Variance and standard deviation of a sample: Summarizing quantitative data", "More on standard deviation: Summarizing quantitative data", "Box and whisker plots: Summarizing quantitative data", "Other measures of spread: Summarizing quantitative data"], "Unit 4: Modeling data distributions": ["Percentiles: Modeling data distributions", "Z-scores: Modeling data distributions", "Effects of linear transformations: Modeling data distributions", "Density curves: Modeling data distributions", "Normal distributions and the empirical rule: Modeling data distributions", "Normal distribution calculations: Modeling data distributions", "More on normal distributions: Modeling data distributions"], "Unit 5: Exploring bivariate numerical data": ["Introduction to scatterplots: Exploring bivariate numerical data", "Correlation coefficients: Exploring bivariate numerical data", "Introduction to trend lines: Exploring bivariate numerical data", "Least-squares regression equations: Exploring bivariate numerical data", "Assessing the fit in least-squares regression: Exploring bivariate numerical data", "More on regression: Exploring bivariate numerical data"], "Unit 6: Study design": ["Statistical questions: Study design", "Sampling and observational studies: Study design", "Sampling methods: Study design", "Types of studies (experimental vs. observational): Study design", "Experiments: Study design"], "Unit 7: Probability": ["Basic theoretical probability: Probability", "Probability using sample spaces: Probability", "Basic set operations: Probability", "Experimental probability: Probability", "Randomness, probability, and simulation: Probability", "Addition rule: Probability", "Multiplication rule for independent events: Probability", "Multiplication rule for dependent events: Probability", "Conditional probability and independence: Probability"], "Unit 8: Counting, permutations, and combinations": ["Counting principle and factorial: Counting, permutations, and combinations", "Permutations: Counting, permutations, and combinations", "Combinations: Counting, permutations, and combinations", "Combinatorics and probability: Counting, permutations, and combinations"], "Unit 9: Random variables": ["Discrete random variables: Random variables", "Continuous random variables: Random variables", "Transforming random variables: Random variables", "Combining random variables: Random variables", "Binomial random variables: Random variables", "Binomial mean and standard deviation formulas: Random variables", "Geometric random variables: Random variables", "More on expected value: Random variables", "Poisson distribution: Random variables"], "Unit 10: Sampling distributions": ["What is a sampling distribution?: Sampling distributions", "Sampling distribution of a sample proportion: Sampling distributions", "Sampling distribution of a sample mean: Sampling distributions"], "Unit 11: Confidence intervals": ["Introduction to confidence intervals: Confidence intervals", "Estimating a population proportion: Confidence intervals", "Estimating a population mean: Confidence intervals", "More confidence interval videos: Confidence intervals"], "Unit 12: Significance tests (hypothesis testing)": ["The idea of significance tests: Significance tests (hypothesis testing)", "Error probabilities and power: Significance tests (hypothesis testing)", "Tests about a population proportion: Significance tests (hypothesis testing)", "Tests about a population mean: Significance tests (hypothesis testing)", "More significance testing videos: Significance tests (hypothesis testing)"], "Unit 13: Two-sample inference for the difference between groups": ["Comparing two proportions: Two-sample inference for the difference between groups", "Comparing two means: Two-sample inference for the difference between groups"], "Unit 14: Inference for categorical data (chi-square tests)": ["Chi-square goodness-of-fit tests: Inference for categorical data (chi-square tests)", "Chi-square tests for relationships: Inference for categorical data (chi-square tests)"], "Unit 15: Advanced regression (inference and transforming)": ["Inference about slope: Advanced regression (inference and transforming)", "Nonlinear regression: Advanced regression (inference and transforming)"], "Unit 16: Analysis of variance (ANOVA)": ["Analysis of variance (ANOVA): Analysis of variance (ANOVA)", "Start Course challenge"]}}}}
{"course_title": "College algebraNEW", "course_url": "/math/college-algebra", "page_contents": {"syllabus": {"topics": {"Unit 1: Linear equations and inequalities": ["Solving equations with one unknown: Linear equations and inequalities", "Solutions to linear equations: Linear equations and inequalities", "Multi-step linear inequalities: Linear equations and inequalities", "Compound inequalities: Linear equations and inequalities", "Modeling with linear equations and inequalities: Linear equations and inequalities", "Absolute value equations: Linear equations and inequalities"], "Unit 2: Graphs and forms of linear equations": ["Intercepts: Graphs and forms of linear equations", "Graphing from slope: Graphs and forms of linear equations", "Horizontal and vertical lines: Graphs and forms of linear equations", "Slope-intercept form: Graphs and forms of linear equations", "Point-slope form: Graphs and forms of linear equations", "Writing linear equations in any form: Graphs and forms of linear equations", "Equations of parallel and perpendicular lines: Graphs and forms of linear equations"], "Unit 3: Functions": ["Evaluating functions: Functions", "Inputs and outputs of a function: Functions", "Domain and range of a function: Functions", "Recognizing functions: Functions", "Intervals where a function is positive, negative, increasing, or decreasing: Functions", "Intro to inverse functions: Functions"], "Unit 4: Quadratics: Multiplying and factoring": ["Multiplying binomials: Quadratics: Multiplying and factoring", "Special products of binomials: Quadratics: Multiplying and factoring", "Factoring quadratics intro: Quadratics: Multiplying and factoring", "Factoring quadratics by grouping: Quadratics: Multiplying and factoring", "Factoring quadratics with difference of squares: Quadratics: Multiplying and factoring", "Factoring quadratics with perfect squares: Quadratics: Multiplying and factoring"], "Unit 5: Quadratic functions and equations": ["Solving quadratics by taking the square root: Quadratic functions and equations", "Vertex form: Quadratic functions and equations", "Solving quadratics by factoring: Quadratic functions and equations", "The quadratic formula: Quadratic functions and equations", "Completing the square: Quadratic functions and equations", "Forms and features of quadratic functions: Quadratic functions and equations"], "The imaginary unit i: Complex numbers": ["Adding and subtracting complex numbers: Complex numbers", "Complex conjugates and dividing complex numbers: Complex numbers"], "Unit 7: Exponents and radicals": ["Exponent properties (integer exponents): Exponents and radicals", "Simplifying square roots: Exponents and radicals", "Exponential expressions: Exponents and radicals", "Graphing exponential growth and decay: Exponents and radicals"], "Unit 8: Rational expressions and equations": ["Rational equations: Rational expressions and equations", "Modeling with rational expressions: Rational expressions and equations", "Multiplying and dividing rational expressions: Rational expressions and equations"], "Unit 9: Relating algebra and geometry": ["Distance and midpoints: Relating algebra and geometry", "Standard equation of a circle: Relating algebra and geometry", "Expanded equation of a circle: Relating algebra and geometry"], "Unit 10: Polynomial arithmetic": ["Average rate of change of polynomials: Polynomial arithmetic", "Adding and subtracting polynomials: Polynomial arithmetic", "Taking common factors: Polynomial arithmetic", "Factoring higher degree polynomials: Polynomial arithmetic", "Factoring using structure: Polynomial arithmetic"], "Unit 11: Advanced function types": ["Graphs of absolute value functions: Advanced function types", "Piecewise functions: Advanced function types", "Composing functions: Advanced function types", "Verifying inverse functions by composition: Advanced function types"], "Unit 12: Transformations of functions": ["Shifting functions: Transformations of functions", "Reflecting functions: Transformations of functions", "Symmetry of functions: Transformations of functions", "Scaling functions: Transformations of functions"], "Unit 13: Rational exponents and radicals": ["Rational exponents: Rational exponents and radicals", "Properties of exponents (rational exponents): Rational exponents and radicals", "Evaluating exponents and radicals: Rational exponents and radicals", "Solving exponential equations using properties of exponents: Rational exponents and radicals", "Interpreting the rate of change of exponential models: Rational exponents and radicals", "Square-root equations: Rational exponents and radicals"], "Unit 14: Logarithms": ["Introduction to logarithms: Logarithms", "Properties of logarithms: Logarithms", "The change of base formula for logarithms: Logarithms", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Calculus AB", "course_url": "/math/ap-calculus-ab", "page_contents": {"syllabus": {"topics": {"Unit 10Unit 10: AP\u00ae\ufe0e Calculus AB Standards mappings": ["Start Course challenge", "Watch an introduction video3:263 minutes 26 seconds", "Learn more", "Learn more", "Watch an introduction video3:263 minutes 26 seconds"], "Unit 1: Limits and continuity": ["About the course: Limits and continuity", "Defining limits and using limit notation: Limits and continuity", "Estimating limit values from graphs: Limits and continuity", "Estimating limit values from tables: Limits and continuity", "Determining limits using algebraic properties of limits: limit properties: Limits and continuity", "Determining limits using algebraic properties of limits: direct substitution: Limits and continuity", "Determining limits using algebraic manipulation: Limits and continuity", "Selecting procedures for determining limits: Limits and continuity", "Determining limits using the squeeze theorem: Limits and continuity", "Exploring types of discontinuities: Limits and continuity", "Defining continuity at a point: Limits and continuity", "Confirming continuity over an interval: Limits and continuity", "Removing discontinuities: Limits and continuity", "Connecting infinite limits and vertical asymptotes: Limits and continuity", "Connecting limits at infinity and horizontal asymptotes: Limits and continuity", "Working with the intermediate value theorem: Limits and continuity", "Optional videos: Limits and continuity"], "Unit 2: Differentiation: definition and basic derivative rules": ["Defining average and instantaneous rates of change at a point: Differentiation: definition and basic derivative rules", "Defining the derivative of a function and using derivative notation: Differentiation: definition and basic derivative rules", "Estimating derivatives of a function at a point: Differentiation: definition and basic derivative rules", "Connecting differentiability and continuity: determining when derivatives do and do not exist: Differentiation: definition and basic derivative rules", "Applying the power rule: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: introduction: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule: Differentiation: definition and basic derivative rules", "Derivatives of cos(x), sin(x), \ud835\udc52\u02e3, and ln(x): Differentiation: definition and basic derivative rules", "The product rule: Differentiation: definition and basic derivative rules", "The quotient rule: Differentiation: definition and basic derivative rules", "Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions: Differentiation: definition and basic derivative rules", "Optional videos: Differentiation: definition and basic derivative rules"], "Unit 3: Differentiation: composite, implicit, and inverse functions": ["The chain rule: introduction: Differentiation: composite, implicit, and inverse functions", "The chain rule: further practice: Differentiation: composite, implicit, and inverse functions", "Implicit differentiation: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse functions: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse trigonometric functions: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: strategy: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: multiple rules: Differentiation: composite, implicit, and inverse functions", "Calculating higher-order derivatives: Differentiation: composite, implicit, and inverse functions", "Further practice connecting derivatives and limits: Differentiation: composite, implicit, and inverse functions", "Optional videos: Differentiation: composite, implicit, and inverse functions"], "Unit 4: Contextual applications of differentiation": ["Interpreting the meaning of the derivative in context: Contextual applications of differentiation", "Straight-line motion: connecting position, velocity, and acceleration: Contextual applications of differentiation", "Rates of change in other applied contexts (non-motion problems): Contextual applications of differentiation", "Introduction to related rates: Contextual applications of differentiation", "Approximating values of a function using local linearity and linearization: Contextual applications of differentiation", "Using L\u2019H\u00f4pital\u2019s rule for finding limits of indeterminate forms: Contextual applications of differentiation", "Optional videos: Contextual applications of differentiation"], "Unit 5: Applying derivatives to analyze functions": ["Using the mean value theorem: Applying derivatives to analyze functions", "Extreme value theorem, global versus local extrema, and critical points: Applying derivatives to analyze functions", "Determining intervals on which a function is increasing or decreasing: Applying derivatives to analyze functions", "Using the first derivative test to find relative (local) extrema: Applying derivatives to analyze functions", "Using the candidates test to find absolute (global) extrema: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: graphical: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: algebraic: Applying derivatives to analyze functions", "Using the second derivative test to find extrema: Applying derivatives to analyze functions", "Sketching curves of functions and their derivatives: Applying derivatives to analyze functions", "Connecting a function, its first derivative, and its second derivative: Applying derivatives to analyze functions", "Solving optimization problems: Applying derivatives to analyze functions", "Exploring behaviors of implicit relations: Applying derivatives to analyze functions"], "Unit 6: Integration and accumulation of change": ["Exploring accumulations of change: Integration and accumulation of change", "Approximating areas with Riemann sums: Integration and accumulation of change", "Riemann sums, summation notation, and definite integral notation: Integration and accumulation of change", "The fundamental theorem of calculus and accumulation functions: Integration and accumulation of change", "Interpreting the behavior of accumulation functions involving area: Integration and accumulation of change", "Applying properties of definite integrals: Integration and accumulation of change", "The fundamental theorem of calculus and definite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals: Integration and accumulation of change", "Integrating using substitution: Integration and accumulation of change", "Integrating functions using long division and completing the square: Integration and accumulation of change", "Optional videos: Integration and accumulation of change"], "Unit 7: Differential equations": ["Modeling situations with differential equations: Differential equations", "Verifying solutions for differential equations: Differential equations", "Sketching slope fields: Differential equations", "Reasoning using slope fields: Differential equations", "Finding general solutions using separation of variables: Differential equations", "Finding particular solutions using initial conditions and separation of variables: Differential equations", "Exponential models with differential equations: Differential equations"], "Unit 8: Applications of integration": ["Finding the average value of a function on an interval: Applications of integration", "Connecting position, velocity, and acceleration functions using integrals: Applications of integration", "Using accumulation functions and definite integrals in applied contexts: Applications of integration", "Finding the area between curves expressed as functions of x: Applications of integration", "Finding the area between curves expressed as functions of y: Applications of integration", "Volumes with cross sections: squares and rectangles: Applications of integration", "Volumes with cross sections: triangles and semicircles: Applications of integration", "Volume with disc method: revolving around x- or y-axis: Applications of integration", "Volume with disc method: revolving around other axes: Applications of integration", "Volume with washer method: revolving around x- or y-axis: Applications of integration", "Volume with washer method: revolving around other axes: Applications of integration"], "Unit 9: AP Calculus AB solved free response questions from past exams": ["AP Calculus AB 2017 free response: AP Calculus AB solved free response questions from past exams", "AP Calculus AB 2015 free response: AP Calculus AB solved free response questions from past exams", "AP Calculus AB 2011 free response: AP Calculus AB solved free response questions from past exams"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Calculus BC", "course_url": "/math/ap-calculus-bc", "page_contents": {"syllabus": {"topics": {"Unit 1: Limits and continuity": ["About the course: Limits and continuity", "Defining limits and using limit notation: Limits and continuity", "Estimating limit values from graphs: Limits and continuity", "Estimating limit values from tables: Limits and continuity", "Determining limits using algebraic properties of limits: limit properties: Limits and continuity", "Determining limits using algebraic properties of limits: direct substitution: Limits and continuity", "Determining limits using algebraic manipulation: Limits and continuity", "Selecting procedures for determining limits: Limits and continuity", "Determining limits using the squeeze theorem: Limits and continuity", "Exploring types of discontinuities: Limits and continuity", "Defining continuity at a point: Limits and continuity", "Confirming continuity over an interval: Limits and continuity", "Removing discontinuities: Limits and continuity", "Connecting infinite limits and vertical asymptotes: Limits and continuity", "Connecting limits at infinity and horizontal asymptotes: Limits and continuity", "Working with the intermediate value theorem: Limits and continuity", "Optional videos: Limits and continuity"], "Unit 2: Differentiation: definition and basic derivative rules": ["Defining average and instantaneous rates of change at a point: Differentiation: definition and basic derivative rules", "Defining the derivative of a function and using derivative notation: Differentiation: definition and basic derivative rules", "Estimating derivatives of a function at a point: Differentiation: definition and basic derivative rules", "Connecting differentiability and continuity: determining when derivatives do and do not exist: Differentiation: definition and basic derivative rules", "Applying the power rule: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: introduction: Differentiation: definition and basic derivative rules", "Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule: Differentiation: definition and basic derivative rules", "Derivatives of cos(x), sin(x), \ud835\udc52\u02e3, and ln(x): Differentiation: definition and basic derivative rules", "The product rule: Differentiation: definition and basic derivative rules", "The quotient rule: Differentiation: definition and basic derivative rules", "Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions: Differentiation: definition and basic derivative rules", "Optional videos: Differentiation: definition and basic derivative rules"], "Unit 3: Differentiation: composite, implicit, and inverse functions": ["The chain rule: introduction: Differentiation: composite, implicit, and inverse functions", "The chain rule: further practice: Differentiation: composite, implicit, and inverse functions", "Implicit differentiation: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse functions: Differentiation: composite, implicit, and inverse functions", "Differentiating inverse trigonometric functions: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: strategy: Differentiation: composite, implicit, and inverse functions", "Selecting procedures for calculating derivatives: multiple rules: Differentiation: composite, implicit, and inverse functions", "Calculating higher-order derivatives: Differentiation: composite, implicit, and inverse functions", "Further practice connecting derivatives and limits: Differentiation: composite, implicit, and inverse functions", "Optional videos: Differentiation: composite, implicit, and inverse functions"], "Unit 4: Contextual applications of differentiation": ["Interpreting the meaning of the derivative in context: Contextual applications of differentiation", "Straight-line motion: connecting position, velocity, and acceleration: Contextual applications of differentiation", "Rates of change in other applied contexts (non-motion problems): Contextual applications of differentiation", "Introduction to related rates: Contextual applications of differentiation", "Approximating values of a function using local linearity and linearization: Contextual applications of differentiation", "Using L\u2019H\u00f4pital\u2019s rule for finding limits of indeterminate forms: Contextual applications of differentiation", "Optional videos: Contextual applications of differentiation"], "Unit 5: Applying derivatives to analyze functions": ["Using the mean value theorem: Applying derivatives to analyze functions", "Extreme value theorem, global versus local extrema, and critical points: Applying derivatives to analyze functions", "Determining intervals on which a function is increasing or decreasing: Applying derivatives to analyze functions", "Using the first derivative test to find relative (local) extrema: Applying derivatives to analyze functions", "Using the candidates test to find absolute (global) extrema: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: graphical: Applying derivatives to analyze functions", "Determining concavity of intervals and finding points of inflection: algebraic: Applying derivatives to analyze functions", "Using the second derivative test to find extrema: Applying derivatives to analyze functions", "Sketching curves of functions and their derivatives: Applying derivatives to analyze functions", "Connecting a function, its first derivative, and its second derivative: Applying derivatives to analyze functions", "Solving optimization problems: Applying derivatives to analyze functions", "Exploring behaviors of implicit relations: Applying derivatives to analyze functions"], "Unit 6: Integration and accumulation of change": ["Exploring accumulations of change: Integration and accumulation of change", "Approximating areas with Riemann sums: Integration and accumulation of change", "Riemann sums, summation notation, and definite integral notation: Integration and accumulation of change", "The fundamental theorem of calculus and accumulation functions: Integration and accumulation of change", "Interpreting the behavior of accumulation functions involving area: Integration and accumulation of change", "Applying properties of definite integrals: Integration and accumulation of change", "The fundamental theorem of calculus and definite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals: Integration and accumulation of change", "Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals: Integration and accumulation of change", "Integrating using substitution: Integration and accumulation of change", "Integrating functions using long division and completing the square: Integration and accumulation of change", "Using integration by parts: Integration and accumulation of change", "Integrating using linear partial fractions: Integration and accumulation of change", "Evaluating improper integrals: Integration and accumulation of change", "Optional videos: Integration and accumulation of change"], "Unit 7: Differential equations": ["Modeling situations with differential equations: Differential equations", "Verifying solutions for differential equations: Differential equations", "Sketching slope fields: Differential equations", "Reasoning using slope fields: Differential equations", "Approximating solutions using Euler\u2019s method: Differential equations", "Finding general solutions using separation of variables: Differential equations", "Finding particular solutions using initial conditions and separation of variables: Differential equations", "Exponential models with differential equations: Differential equations", "Logistic models with differential equations: Differential equations"], "Unit 8: Applications of integration": ["Finding the average value of a function on an interval: Applications of integration", "Connecting position, velocity, and acceleration functions using integrals: Applications of integration", "Using accumulation functions and definite integrals in applied contexts: Applications of integration", "Finding the area between curves expressed as functions of x: Applications of integration", "Finding the area between curves expressed as functions of y: Applications of integration", "Volumes with cross sections: squares and rectangles: Applications of integration", "Volumes with cross sections: triangles and semicircles: Applications of integration", "Volume with disc method: revolving around x- or y-axis: Applications of integration", "Volume with disc method: revolving around other axes: Applications of integration", "Volume with washer method: revolving around x- or y-axis: Applications of integration", "Volume with washer method: revolving around other axes: Applications of integration", "The arc length of a smooth, planar curve and distance traveled: Applications of integration"], "Unit 9: Parametric equations, polar coordinates, and vector-valued functions": ["Defining and differentiating parametric equations: Parametric equations, polar coordinates, and vector-valued functions", "Second derivatives of parametric equations: Parametric equations, polar coordinates, and vector-valued functions", "Finding arc lengths of curves given by parametric equations: Parametric equations, polar coordinates, and vector-valued functions", "Defining and differentiating vector-valued functions: Parametric equations, polar coordinates, and vector-valued functions", "Solving motion problems using parametric and vector-valued functions: Parametric equations, polar coordinates, and vector-valued functions", "Defining polar coordinates and differentiating in polar form: Parametric equations, polar coordinates, and vector-valued functions", "Finding the area of a polar region or the area bounded by a single polar curve: Parametric equations, polar coordinates, and vector-valued functions", "Finding the area of the region bounded by two polar curves: Parametric equations, polar coordinates, and vector-valued functions", "Calculator-active practice: Parametric equations, polar coordinates, and vector-valued functions"], "Unit 10: Infinite sequences and series": ["Defining convergent and divergent infinite series: Infinite sequences and series", "Working with geometric series: Infinite sequences and series", "The nth-term test for divergence: Infinite sequences and series", "Integral test for convergence: Infinite sequences and series", "Harmonic series and p-series: Infinite sequences and series", "Comparison tests for convergence: Infinite sequences and series", "Alternating series test for convergence: Infinite sequences and series", "Ratio test for convergence: Infinite sequences and series", "Determining absolute or conditional convergence: Infinite sequences and series", "Alternating series error bound: Infinite sequences and series", "Finding Taylor polynomial approximations of functions: Infinite sequences and series", "Lagrange error bound: Infinite sequences and series", "Radius and interval of convergence of power series: Infinite sequences and series", "Finding Taylor or Maclaurin series for a function: Infinite sequences and series", "Representing functions as power series: Infinite sequences and series", "Optional videos: Infinite sequences and series"], "Unit 11: AP Calculus BC solved exams": ["AP Calculus BC 2017: AP Calculus BC solved exams", "AP Calculus BC 2015: AP Calculus BC solved exams", "AP Calculus BC 2011: AP Calculus BC solved exams", "AP Calculus BC 2008: AP Calculus BC solved exams"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Statistics", "course_url": "/math/ap-statistics", "page_contents": {"syllabus": {"topics": {"Unit 1: Exploring categorical data": ["The language of variation: Variables: Exploring categorical data", "Representing a categorical variable with graphs: Exploring categorical data", "Representing two categorical variables: Exploring categorical data", "Statistics for two categorical variables: Exploring categorical data"], "Unit 2: Exploring one-variable quantitative data: Displaying and describing": ["Representing a quantitative variable with dot plots: Exploring one-variable quantitative data: Displaying and describing", "Representing a quantitative variable with histograms and stem plots: Exploring one-variable quantitative data: Displaying and describing", "Describing the distribution of a quantitative variable: Exploring one-variable quantitative data: Displaying and describing", "Comparing distributions of a quantitative variable: Exploring one-variable quantitative data: Displaying and describing"], "Unit 3: Exploring one-variable quantitative data: Summary statistics": ["Measuring center in quantitative data: Exploring one-variable quantitative data: Summary statistics", "Measuring variability in quantitative data: Exploring one-variable quantitative data: Summary statistics", "Effects of linear transformations: Exploring one-variable quantitative data: Summary statistics", "More on standard deviation (optional): Exploring one-variable quantitative data: Summary statistics", "Graphical representations of summary statistics: Exploring one-variable quantitative data: Summary statistics"], "Unit 4: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution": ["Percentiles: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Z-scores: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Density curves: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Normal distributions and the empirical rule: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution", "Normal distribution calculations: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution"], "Unit 5: Exploring two-variable quantitative data": ["Representing the relationship between two quantitative variables: Exploring two-variable quantitative data", "Correlation: Exploring two-variable quantitative data", "Residuals: Exploring two-variable quantitative data", "Least-squares regression: Exploring two-variable quantitative data"], "Unit 6: Collecting data": ["Introduction to planning a study: Collecting data", "Potential problems with sampling: Collecting data", "Random sampling and data collection: Collecting data", "Introduction to experimental design: Collecting data", "Inference and experiments: Collecting data"], "Unit 7: Probability": ["Estimating probabilities using simulation: Probability", "Mutually exclusive events and unions of events: Probability", "Conditional probability: Probability", "Independent versus dependent events and the multiplication rule: Probability"], "Unit 8: Random variables and probability distributions": ["Introduction to random variables and probability distributions: Random variables and probability distributions", "Mean and standard deviation of random variables: Random variables and probability distributions", "Transforming random variables: Random variables and probability distributions", "Combining random variables: Random variables and probability distributions", "Introduction to the binomial distribution: Random variables and probability distributions", "Parameters for a binomial distribution: Random variables and probability distributions", "The geometric distribution: Random variables and probability distributions"], "Unit 9: Sampling distributions": ["The normal distribution, revisited: Sampling distributions", "The central limit theorem: Sampling distributions", "Biased and unbiased point estimates: Sampling distributions", "Sampling distributions for sample proportions: Sampling distributions", "Sampling distributions for differences in sample proportions: Sampling distributions", "Sampling distributions for sample means: Sampling distributions", "Sampling distributions for differences in sample means: Sampling distributions"], "Unit 10: Inference for categorical data: Proportions": ["Introduction to confidence intervals: Inference for categorical data: Proportions", "Confidence intervals for proportions: Inference for categorical data: Proportions", "The idea of significance tests: Inference for categorical data: Proportions", "Setting up a test for a population proportion: Inference for categorical data: Proportions", "Carrying out a test for a population proportion: Inference for categorical data: Proportions", "Concluding a test for a population proportion: Inference for categorical data: Proportions", "Potential errors when performing tests: Inference for categorical data: Proportions", "Confidence intervals for the difference of two proportions: Inference for categorical data: Proportions", "Testing for the difference of two population proportions: Inference for categorical data: Proportions"], "Unit 11: Inference for quantitative data: Means": ["Constructing a confidence interval for a population mean: Inference for quantitative data: Means", "Setting up a test for a population mean: Inference for quantitative data: Means", "Carrying out a test for a population mean: Inference for quantitative data: Means", "Confidence intervals for the difference of two means: Inference for quantitative data: Means", "Testing for the difference of two population means: Inference for quantitative data: Means"], "Unit 12: Inference for categorical data: Chi-square": ["Chi-square test for goodness of fit: Inference for categorical data: Chi-square", "Chi square tests for relationships (homogeneity or independence): Inference for categorical data: Chi-square"], "Unit 13: Inference for quantitative data: slopes": ["Confidence intervals for the slope of a regression model: Inference for quantitative data: slopes", "Testing for the slope of a regression model: Inference for quantitative data: slopes"], "Unit 14: Prepare for the 2022 AP\u00ae\ufe0e Statistics Exam": ["Prepare for the exam: Prepare for the 2022 AP\u00ae\ufe0e Statistics Exam", "Start Course challenge"]}}}}
{"course_title": "Multivariable calculus", "course_url": "/math/multivariable-calculus", "page_contents": {"syllabus": {"topics": {"Unit 1: Thinking about multivariable functions": ["Introduction to multivariable calculus: Thinking about multivariable functions", "Visualizing scalar-valued functions: Thinking about multivariable functions", "Visualizing vector-valued functions: Thinking about multivariable functions", "Transformations: Thinking about multivariable functions"], "Unit 2: Derivatives of multivariable functions": ["Partial derivatives: Derivatives of multivariable functions", "Gradient and directional derivatives: Derivatives of multivariable functions", "Differentiating parametric curves: Derivatives of multivariable functions", "Multivariable chain rule: Derivatives of multivariable functions", "Curvature: Derivatives of multivariable functions", "Partial derivatives of vector-valued functions: Derivatives of multivariable functions", "Divergence: Derivatives of multivariable functions", "Curl: Derivatives of multivariable functions", "Laplacian: Derivatives of multivariable functions", "Jacobian: Derivatives of multivariable functions"], "Unit 3: Applications of multivariable derivatives": ["Tangent planes and local linearization: Applications of multivariable derivatives", "Quadratic approximations: Applications of multivariable derivatives", "Optimizing multivariable functions: Applications of multivariable derivatives", "Lagrange multipliers and constrained optimization: Applications of multivariable derivatives"], "Unit 4: Integrating multivariable functions": ["Line integrals for scalar functions: Integrating multivariable functions", "Line integrals in vector fields: Integrating multivariable functions", "Double integrals: Integrating multivariable functions", "Triple integrals: Integrating multivariable functions", "Surface integral preliminaries: Integrating multivariable functions", "Surface integrals: Integrating multivariable functions", "Flux in 3D: Integrating multivariable functions"], "Unit 5: Green's, Stokes', and the divergence theorems": ["2D divergence theorem: Green's, Stokes', and the divergence theorems", "Stokes' theorem: Green's, Stokes', and the divergence theorems", "3D divergence theorem: Green's, Stokes', and the divergence theorems", "Proof of Stokes' theorem: Green's, Stokes', and the divergence theorems", "Types of regions in three dimensions: Green's, Stokes', and the divergence theorems", "Divergence theorem proof: Green's, Stokes', and the divergence theorems", "Start Course challenge"]}}}}
{"course_title": "Differential equations", "course_url": "/math/differential-equations", "page_contents": {"syllabus": {"topics": {"Unit 1: First order differential equations": ["Intro to differential equations: First order differential equations", "Slope fields: First order differential equations", "Euler's Method: First order differential equations", "Separable equations: First order differential equations", "Exponential models: First order differential equations", "Logistic models: First order differential equations", "Exact equations and integrating factors: First order differential equations", "Homogeneous equations: First order differential equations"], "Unit 2: Second order linear equations": ["Linear homogeneous equations: Second order linear equations", "Complex and repeated roots of characteristic equation: Second order linear equations", "Method of undetermined coefficients: Second order linear equations"], "Unit 3: Laplace transform": ["Laplace transform: Laplace transform", "Properties of the Laplace transform: Laplace transform", "Laplace transform to solve a differential equation: Laplace transform", "The convolution integral: Laplace transform"]}}}}
{"course_title": "Linear algebra", "course_url": "/math/linear-algebra", "page_contents": {"syllabus": {"topics": {"Unit 1: Vectors and spaces": ["Vectors: Vectors and spaces", "Linear combinations and spans: Vectors and spaces", "Linear dependence and independence: Vectors and spaces", "Subspaces and the basis for a subspace: Vectors and spaces", "Vector dot and cross products: Vectors and spaces", "Matrices for solving systems by elimination: Vectors and spaces", "Null space and column space: Vectors and spaces"], "Unit 2: Matrix transformations": ["Functions and linear transformations: Matrix transformations", "Linear transformation examples: Matrix transformations", "Transformations and matrix multiplication: Matrix transformations", "Inverse functions and transformations: Matrix transformations", "Finding inverses and determinants: Matrix transformations", "More determinant depth: Matrix transformations", "Transpose of a matrix: Matrix transformations"], "Unit 3: Alternate coordinate systems (bases)": ["Orthogonal complements: Alternate coordinate systems (bases)", "Orthogonal projections: Alternate coordinate systems (bases)", "Change of basis: Alternate coordinate systems (bases)", "Orthonormal bases and the Gram-Schmidt process: Alternate coordinate systems (bases)", "Eigen-everything: Alternate coordinate systems (bases)"]}}}}
{"course_title": "Middle school biology - NGSSNEW", "course_url": "/science/ms-biology", "page_contents": {"syllabus": {"topics": {"Natural and artificial selection: Unit test": ["Start Course challenge", "Watch an introduction video2:222 minutes 22 seconds", "Learn more", "Learn more", "Watch an introduction video2:222 minutes 22 seconds"], "Unit 1: Cells and organisms": ["Cells and organisms: Cells and organisms", "Cell parts and functions: Cells and organisms", "Organization in the human body: Cells and organisms", "Sensory processing and the brain: Cells and organisms"], "Unit 2: Organism growth and reproduction": ["Sexual and asexual reproduction: Organism growth and reproduction", "Animal behavior and offspring success: Organism growth and reproduction", "Plant reproductive success: Organism growth and reproduction", "Organism growth and the environment: Organism growth and reproduction"], "Unit 3: Matter and energy in organisms": ["Photosynthesis in organisms: Matter and energy in organisms", "Food and energy in organisms: Matter and energy in organisms"], "Populations, communities, and ecosystems: Interactions in ecosystems": ["Resources and population growth: Interactions in ecosystems", "Ecological interactions: Interactions in ecosystems"], "Unit 5: Matter and energy in ecosystems": ["Photosynthesis in ecosystems: Matter and energy in ecosystems", "Matter and energy in foodwebs: Matter and energy in ecosystems"], "Unit 6: Ecosystems and biodiversity": ["Ecosystem dynamics: Ecosystems and biodiversity", "Biodiversity and ecosystem health: Ecosystems and biodiversity", "Humans and ecosystems: Ecosystems and biodiversity"], "Unit 7: Inheritance and variation": ["Chromosomes: Inheritance and variation", "Genes, proteins, and traits: Inheritance and variation", "Mutations: Inheritance and variation", "Reproduction and genetic variation: Inheritance and variation"], "Unit 8: Evolution": ["Evolution and common ancestry: Evolution", "The fossil record: Evolution", "Evidence of evolution: anatomy: Evolution", "Evidence of evolution: embryology: Evolution"], "Unit 9: Natural and artificial selection": ["Natural selection: Natural and artificial selection", "Adaptation and environmental change: Natural and artificial selection", "Artificial selection: Natural and artificial selection", "Start Course challenge"]}}}}
{"course_title": "Middle school Earth and space science - NGSSNEW", "course_url": "/science/middle-school-earth-and-space-science", "page_contents": {"syllabus": {"topics": {"Earth and society: Unit test": ["Start Course challenge", "Watch an introduction video2:512 minutes 51 seconds", "Learn more", "Learn more", "Watch an introduction video2:512 minutes 51 seconds"], "Unit 1: Earth in space": ["Earth's place in the universe: Earth in space", "Galaxies and gravity: Earth in space", "The solar system: Earth in space"], "Unit 2: The Earth-sun-moon system": ["Seasons : The Earth-sun-moon system", "The moon and its motions: The Earth-sun-moon system", "Solar eclipses: The Earth-sun-moon system"], "Unit 3: Weather and climate": ["The water cycle : Weather and climate", "Weather: Weather and climate", "Global winds and currents: Weather and climate", "Regional climates: Weather and climate"], "Unit 4: The geosphere": ["The rock cycle: The geosphere", "Fossils and rock layers: The geosphere", "Plate tectonics: The geosphere", "Weathering and erosion: The geosphere"], "Unit 5: Earth and society": ["Natural resources: Earth and society", "Natural hazards: Earth and society", "Human impacts on the environment: Earth and society", "Earth's changing climate: Earth and society", "Start Course challenge"]}}}}
{"course_title": "Middle school physics - NGSSNEW", "course_url": "/science/ms-physics", "page_contents": {"syllabus": {"topics": {"Waves: Unit test": ["Start Course challenge", "Watch an introduction video1:581 minute 58 seconds", "Learn more", "Learn more", "Watch an introduction video1:581 minute 58 seconds"], "Unit 1: Movement and forces": ["Representing motion: Movement and forces", "Forces and acceleration: Movement and forces", "Action and reaction forces: Movement and forces"], "Unit 2: Forces at a distance": ["Gravitational forces: Forces at a distance", "Electric forces: Forces at a distance", "Magnetic forces: Forces at a distance", "Fields: Forces at a distance", "Electromagnetism: Forces at a distance"], "Unit 3: Energy": ["Kinetic energy: Energy", "Potential energy: Energy"], "Unit 4: Waves": ["Wave properties: Waves", "Mechanical waves and light: Waves", "Transmission and refraction: Waves", "Absorption and reflection: Waves", "Digital signals: Waves", "Start Course challenge"]}}}}
{"course_title": "High school biology", "course_url": "/science/high-school-biology", "page_contents": {"syllabus": {"topics": {"Unit 1: Biology foundations": ["Biology and the scientific method: Biology foundations", "Important molecules for biology: Biology foundations", "Water and life: Biology foundations", "pH, acids, and bases: Biology foundations"], "Unit 2: Cells": ["Introduction to cells: Cells", "Basic cell structures: Cells", "The cell membrane: Cells", "Eukaryotic cell structures: Cells", "Prokaryotes and eukaryotes: Cells", "Plant vs animal cells: Cells"], "Unit 3: Energy and transport": ["Introduction to metabolism: Energy and transport", "Enzymes: Energy and transport", "Passive and active transport: Energy and transport", "Osmosis and tonicity: Energy and transport", "Photosynthesis: Energy and transport", "Cellular respiration: Energy and transport"], "Unit 4: Reproduction and cell division": ["Types of reproduction: Reproduction and cell division", "The cell cycle and mitosis: Reproduction and cell division", "Meiosis: Reproduction and cell division", "Fertilization and development: Reproduction and cell division"], "Unit 5: Classical genetics": ["Introduction to heredity: Classical genetics", "Non-Mendelian inheritance: Classical genetics", "Sex linkage: Classical genetics", "Pedigrees: Classical genetics"], "Unit 6: Molecular genetics": ["RNA and protein synthesis: Molecular genetics", "Biotechnology: Molecular genetics"], "Unit 7: Evolution": ["Evolution and natural selection: Evolution", "Evidence of evolution: Evolution", "Phylogeny: Evolution"], "Unit 8: Human body systems": ["Body structure and homeostasis: Human body systems", "The circulatory and respiratory systems: Human body systems", "The musculoskeletal system: Human body systems", "The digestive and excretory systems: Human body systems", "The nervous and endocrine systems: Human body systems", "The reproductive system: Human body systems", "The immune system: Human body systems"], "Community ecology: Ecology": ["Ecological relationships: Ecology", "Trophic levels: Ecology", "Biogeochemical cycles: Ecology", "Human impact on ecosystems: Ecology", "Start Course challenge"]}}}}
{"course_title": "High school biology - NGSS", "course_url": "/science/hs-biology", "page_contents": {"syllabus": {"topics": {"Unit 1: Genes, cells, and organisms": ["Cell specialization: Genes, cells, and organisms", "Genes, proteins, and cells: Genes, cells, and organisms", "Organization of multicellular organisms: Genes, cells, and organisms"], "Unit 2: Growth and feedback in organisms": ["Cell division and organism growth: Growth and feedback in organisms", "Feedback in living systems: Growth and feedback in organisms"], "Unit 3: Matter and energy in organisms": ["Photosynthesis: Matter and energy in organisms", "Formation of biomolecules: Matter and energy in organisms", "Cellular respiration: Matter and energy in organisms"], "Unit 4: Matter and energy in ecosystems": ["Population growth and carrying capacity: Matter and energy in ecosystems", "Flow of energy and cycling of matter in ecosystems: Matter and energy in ecosystems", "The carbon cycle: Matter and energy in ecosystems"], "Unit 5: Interactions in ecosystems": ["Ecosystem resilience and change: Interactions in ecosystems", "Human impacts on ecosystems: Interactions in ecosystems"], "Unit 6: Inheritance and variation": ["Gene expression and regulation: Inheritance and variation", "Sources of genetic variation: Inheritance and variation", "Genes, traits, and the environment: Inheritance and variation"], "Unit 7: Evolution and natural selection": ["Evidence of common ancestry: Evolution and natural selection", "Natural selection: Evolution and natural selection", "Natural selection and evolution: Evolution and natural selection", "Evolution of group behavior: Evolution and natural selection"], "Unit 8: Adaptation and environmental change": ["Natural selection and adaptation: Adaptation and environmental change", "Adaptation and environmental change: Adaptation and environmental change", "Species and the environment: Adaptation and environmental change", "Extinction: Adaptation and environmental change"], "Unit 9: Biodiversity and human impacts": ["Humans and biodiversity: Biodiversity and human impacts", "Sustainability and natural resource management: Biodiversity and human impacts", "Science, technology, and the environment: Biodiversity and human impacts"], "Unit 10: Creativity in biology": ["Creativity in biology: Creativity in biology", "Start Course challenge"]}}}}
{"course_title": "High school physics", "course_url": "/science/high-school-physics", "page_contents": {"syllabus": {"topics": {"Unit 1: One-dimensional motion": ["Physics foundations: One-dimensional motion", "Distance, displacement, and coordinate systems: One-dimensional motion", "Average velocity and average speed: One-dimensional motion", "Velocity and speed from graphs: One-dimensional motion", "Average and instantaneous acceleration: One-dimensional motion", "Motion with constant acceleration: One-dimensional motion", "Objects in freefall: One-dimensional motion"], "Unit 2: Forces and Newton's laws of motion": ["Introduction to forces and free body diagrams: Forces and Newton's laws of motion", "Newton's first law: Mass and inertia: Forces and Newton's laws of motion", "Newton's second law: Forces and Newton's laws of motion", "Newton's third law: Forces and Newton's laws of motion"], "Unit 3: Two-dimensional motion": ["Analyzing vectors using trigonometry: Two-dimensional motion", "Graphs of projectile motion: Two-dimensional motion", "Horizontally launched projectiles: Two-dimensional motion", "Projectiles launched at an angle: Two-dimensional motion", "Angled forces: Two-dimensional motion", "Inclined planes: Two-dimensional motion", "Friction: Two-dimensional motion"], "Unit 4: Uniform circular motion and gravitation": ["Uniform circular motion introduction: Uniform circular motion and gravitation", "Centripetal acceleration: Uniform circular motion and gravitation", "Centripetal forces: Uniform circular motion and gravitation", "Newton's law of gravitation: Uniform circular motion and gravitation"], "Unit 5: Work and energy": ["Introduction to work: Work and energy", "Work-energy theorem: Work and energy", "Spring potential energy and Hooke's law: Work and energy", "Gravitational potential energy and conservative forces: Work and energy", "Conservation of energy: Work and energy", "Power: Work and energy"], "Unit 6: Linear momentum and collisions": ["Introduction to linear momentum and impulse: Linear momentum and collisions", "Inelastic collisions: Linear momentum and collisions", "Center of mass and two-dimensional collisions: Linear momentum and collisions"], "Unit 7: Torque and angular momentum": ["Introduction to rotational motion: Torque and angular momentum", "Angular kinematics: Torque and angular momentum", "Torque and equilibrium: Torque and angular momentum", "Rotational inertia and angular second law: Torque and angular momentum", "Rotational kinetic energy: Torque and angular momentum", "Angular momentum and angular impulse: Torque and angular momentum", "Conservation of angular momentum: Torque and angular momentum", "Gravitational potential energy at large distances: Torque and angular momentum"], "Unit 8: Simple harmonic motion": ["Introduction to simple harmonic motion: Simple harmonic motion", "Simple harmonic motion in spring-mass systems: Simple harmonic motion", "Simple pendulums: Simple harmonic motion", "Energy in simple harmonic oscillators: Simple harmonic motion"], "Unit 9: Waves": ["Introduction to waves: Waves", "Wave characteristics: Waves", "Standing waves: Waves", "Wave interference: Waves"], "Unit 10: Sound": ["Introduction to sound: Sound", "Standing sound waves: Sound", "Beats and interference of sound waves: Sound", "Doppler effect: Sound"], "Unit 11: Static electricity": ["Electric charge: Static electricity", "Conservation of charge: Static electricity", "Coulomb's law and electric force: Static electricity", "Explore electrostatics: Static electricity"], "Unit 12: DC Circuits": ["Electric current, resistivity, and Ohm's law: DC Circuits", "Electric power and DC circuits: DC Circuits", "Series and parallel resistors: DC Circuits", "DC Ammeters and voltmeters: DC Circuits", "Discovery of resistors: DC Circuits", "Explore electric motors: DC Circuits", "Start Course challenge"]}}}}
{"course_title": "High school physics - NGSS", "course_url": "/science/hs-physics", "page_contents": {"syllabus": {"topics": {"Unit 1: Forces and motion": ["Force, mass, and acceleration: Forces and motion", "Introduction to momentum: Forces and motion"], "Unit 2: Types of interactions": ["Newton's law of universal gravitation: Types of interactions", "Coulomb's law: Types of interactions", "Electric and magnetic fields: Types of interactions"], "Unit 3: Introduction to energy": ["Introduction to energy: Introduction to energy", "Forms of energy: Introduction to energy", "Energy and fields: Introduction to energy", "Energy at the microscopic scale: Introduction to energy"], "Unit 4: Modeling energy": ["Calculating energy: Modeling energy", "Energy in systems: Modeling energy", "Predictions using energy: Modeling energy", "Thermodynamics: Modeling energy"], "Unit 5: Wave properties": ["Waves: Wave properties", "Wave interference: Wave properties"], "Unit 6: Electromagnetic radiation": ["Wave\u2013particle duality: Electromagnetic radiation", "Electromagnetic radiation and matter: Electromagnetic radiation", "Emission of electromagnetic radiation: Electromagnetic radiation"], "Unit 7: Information technologies": ["Information in waves: Information technologies", "Technology and waves: Information technologies", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Biology", "course_url": "/science/ap-biology", "page_contents": {"syllabus": {"topics": {"Unit 1: Chemistry of life": ["Structure of water and hydrogen bonding: Chemistry of life", "Elements of life: Chemistry of life", "Introduction to biological macromolecules: Chemistry of life", "Properties, structure, and function of biological macromolecules: Chemistry of life", "Nucleic acids: Chemistry of life"], "Unit 2: Cell structure and function": ["Cell structures and their functions: Cell structure and function", "Cell size: Cell structure and function", "Plasma membranes: Cell structure and function", "Membrane permeability : Cell structure and function", "Membrane transport: Cell structure and function", "Facilitated diffusion: Cell structure and function", "Mechanisms of transport:  tonicity and osmoregulation: Cell structure and function", "Cell compartmentalization and its origins: Cell structure and function"], "Unit 3: Cellular energetics": ["Enzyme structure and catalysis: Cellular energetics", "Cellular energy: Cellular energetics", "Photosynthesis: Cellular energetics", "Cellular respiration: Cellular energetics", "Fitness: Cellular energetics"], "Unit 4: Cell communication and cell cycle": ["Cell communication: Cell communication and cell cycle", "Signal transduction: Cell communication and cell cycle", "Changes in signal transduction pathways: Cell communication and cell cycle", "Feedback: Cell communication and cell cycle", "Cell cycle: Cell communication and cell cycle", "Regulation of cell cycle: Cell communication and cell cycle"], "Unit 5: Heredity": ["Meiosis and genetic diversity: Heredity", "Mendelian genetics: Heredity", "Environmental effects on phenotype: Heredity", "Chromosomal inheritance: Heredity"], "Unit 6: Gene expression and regulation": ["DNA and RNA structure: Gene expression and regulation", "Replication: Gene expression and regulation", "Transcription and RNA processing: Gene expression and regulation", "Translation: Gene expression and regulation", "Regulation of gene expression and cell specialization: Gene expression and regulation", "Mutations: Gene expression and regulation", "Biotechnology: Gene expression and regulation"], "Unit 7: Natural selection": ["Natural selection: Natural selection", "Population genetics: Natural selection", "Hardy-Weinberg equilibrium: Natural selection", "Evidence for evolution: Natural selection", "Common ancestry and continuing evolution: Natural selection", "Phylogeny: Natural selection", "Speciation: Natural selection", "Extinction: Natural selection", "Variations in populations: Natural selection", "Origins of life on earth: Natural selection"], "Community ecology: Ecology": ["Biodiversity: Ecology", "Disruptions to ecosystems: Ecology"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Chemistry", "course_url": "/science/ap-chemistry-beta", "page_contents": {"syllabus": {"topics": {"Unit 1: Atomic structure and properties": ["Moles and molar mass: Atomic structure and properties", "Mass spectrometry of elements: Atomic structure and properties", "Elemental composition of pure substances: Atomic structure and properties", "Composition of mixtures: Atomic structure and properties", "Periodic trends: Atomic structure and properties", "Valence electrons and ionic compounds: Atomic structure and properties", "Photoelectron spectroscopy: Atomic structure and properties"], "Unit 2: Molecular and ionic compound structure and properties": ["Types of chemical bonds: Molecular and ionic compound structure and properties", "Intramolecular force and potential energy: Molecular and ionic compound structure and properties", "Structure of ionic solids: Molecular and ionic compound structure and properties", "Structure of metals and alloys: Molecular and ionic compound structure and properties", "Lewis diagrams: Molecular and ionic compound structure and properties", "Resonance and formal charge: Molecular and ionic compound structure and properties", "VSEPR: Molecular and ionic compound structure and properties", "Bond hybridization: Molecular and ionic compound structure and properties"], "Unit 3: Intermolecular forces and properties": ["Intermolecular forces: Intermolecular forces and properties", "Properties of solids: Intermolecular forces and properties", "Solids, liquids, and gases: Intermolecular forces and properties", "Ideal gas law: Intermolecular forces and properties", "Kinetic molecular theory: Intermolecular forces and properties", "Deviation from ideal gas law: Intermolecular forces and properties", "Solutions and mixtures: Intermolecular forces and properties", "Representations of solutions: Intermolecular forces and properties", "Separation of solutions and mixtures chromatography: Intermolecular forces and properties", "Solubility: Intermolecular forces and properties", "Spectroscopy and the electromagnetic spectrum: Intermolecular forces and properties", "Electronic transitions in spectroscopy: Intermolecular forces and properties", "Beer\u2013Lambert law: Intermolecular forces and properties"], "Unit 4: Chemical reactions": ["Net ionic equations: Chemical reactions", "Representations of reactions: Chemical reactions", "Physical and chemical changes: Chemical reactions", "Introduction to acid\u2013base reactions: Chemical reactions", "Introduction to titration: Chemical reactions"], "Unit 5: Kinetics": ["Reaction rates: Kinetics", "Introduction to rate law: Kinetics", "Concentration changes over time: Kinetics", "Reaction mechanisms: Kinetics", "Activation energy and reaction rate: Kinetics", "Catalysis: Kinetics"], "Unit 6: Thermodynamics": ["Endothermic and exothermic processes: Thermodynamics", "Heat transfer and thermal equilibrium: Thermodynamics", "Heat capacity and calorimetry: Thermodynamics", "Energy of phase changes: Thermodynamics", "Introduction to enthalpy of reaction: Thermodynamics", "Hess's law: Thermodynamics", "Enthalpy of formation: Thermodynamics", "Bond enthalpies: Thermodynamics"], "Unit 7: Equilibrium": ["Introduction to equilibrium: Equilibrium", "Equilibrium constant and reaction quotient: Equilibrium", "Calculating the equilibrium constant: Equilibrium", "Magnitude and properties of the equilibrium constant: Equilibrium", "Calculating equilibrium concentrations: Equilibrium", "Using the reaction quotient: Equilibrium", "Le Ch\u00e2telier's principle: Equilibrium", "Solubility equilibria: Equilibrium"], "Unit 8: Acids and bases": ["Introduction to acids and bases: Acids and bases", "pH and pOH of strong acids and bases: Acids and bases", "Weak acid and base equilibria: Acids and bases", "Molecular structure of acids and bases: Acids and bases", "Acid\u2013base reactions: Acids and bases", "Buffers: Acids and bases", "Acid\u2013base titrations: Acids and bases"], "Unit 9: Applications of thermodynamics": ["Entropy: Applications of thermodynamics", "Gibbs free energy and thermodynamic favorability: Applications of thermodynamics", "Free energy of dissolution: Applications of thermodynamics", "Thermodynamics vs. kinetics: Applications of thermodynamics", "Free energy and equilibrium: Applications of thermodynamics", "Coupled reactions: Applications of thermodynamics", "Galvanic (voltaic) and electrolytic cells: Applications of thermodynamics", "Cell potential and free energy: Applications of thermodynamics", "Cell potential under nonstandard conditions: Applications of thermodynamics", "Electrolysis and Faraday's law: Applications of thermodynamics", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Environmental Science", "course_url": "/science/ap-college-environmental-science", "page_contents": {"syllabus": {"topics": {"Unit 1: The living world: ecosystems and biodiversity": ["Ecosystems and biomes: The living world: ecosystems and biodiversity", "Biogeochemical cycles: The living world: ecosystems and biodiversity", "Matter and energy flow: The living world: ecosystems and biodiversity", "Intro to biodiversity and biogeography: The living world: ecosystems and biodiversity", "Changes to ecosystems: The living world: ecosystems and biodiversity"], "Unit 2: Populations": ["Species growth: Populations", "Population growth: Populations", "Human populations: Populations"], "Unit 3: Earth systems and resources": ["Plate tectonics: Earth systems and resources", "Earth's climate: Earth systems and resources"], "Unit 4: Land and water use": ["Intro to land and water use: Land and water use", "Effects of land and water use I: Land and water use", "Effect of land and water use II: Land and water use", "Intro to sustainable practices: Land and water use", "Types of sustainable practices: Land and water use"], "Unit 5: Energy resources and consumption": ["Intro to energy resources and consumption: Energy resources and consumption", "Fuel types and uses II: Energy resources and consumption", "Energy conservation: Energy resources and consumption"], "Unit 6: Atmospheric pollution": ["Air pollution: Atmospheric pollution", "Reducing air pollution: Atmospheric pollution", "Other atmospheric pollution: Atmospheric pollution"], "Unit 7: Aquatic and terrestrial pollution": ["Sources of pollution: Aquatic and terrestrial pollution", "Types of aquatic and terrestrial pollution: Aquatic and terrestrial pollution", "Waste disposal, reduction, and treatment: Aquatic and terrestrial pollution", "Pollution and health: Aquatic and terrestrial pollution", "Pathogens: Aquatic and terrestrial pollution"], "Unit 8: Global change": ["Ozone: Global change", "Greenhouse effect: Global change", "Climate change: Global change", "Human impact on species: Global change", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Physics 1", "course_url": "/science/ap-college-physics-1", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Health and Medicine", "course_url": "/science/health-and-medicine", "page_contents": {"syllabus": {"topics": {"Unit 1: Introduction to human body systems": ["Circulatory system introduction: Introduction to human body systems", "Respiratory system introduction: Introduction to human body systems", "Hematologic system introduction: Introduction to human body systems", "Endocrine system introduction: Introduction to human body systems", "Nervous system introduction: Introduction to human body systems", "Gastrointestinal system introduction: Introduction to human body systems", "Musculoskeletal system introduction: Introduction to human body systems", "Reproductive system introduction: Introduction to human body systems", "Immunologic system introduction: Introduction to human body systems", "Urinary system introduction: Introduction to human body systems", "Integumentary system introduction: Introduction to human body systems", "Lymphatic system introduction: Introduction to human body systems"], "Unit 2: Circulatory system anatomy and physiology": ["Circulatory anatomy and blood flow: Circulatory system anatomy and physiology", "Heart muscle contraction: Circulatory system anatomy and physiology", "Heart depolarization: Circulatory system anatomy and physiology", "Blood pressure: Circulatory system anatomy and physiology", "Blood vessels: Circulatory system anatomy and physiology", "Blood pressure control by the kidney: Circulatory system anatomy and physiology", "Nerve regulation of the heart: Circulatory system anatomy and physiology", "Preload and afterload: Circulatory system anatomy and physiology", "Pressure volume loops: Circulatory system anatomy and physiology", "Changing the PV loop: Circulatory system anatomy and physiology", "Fetal circulation: Circulatory system anatomy and physiology"], "Unit 3: Circulatory system diseases": ["Heart disease and heart attacks: Circulatory system diseases", "Atherosclerosis, arteriosclerosis, and arteriolosclerosis: Circulatory system diseases", "Stroke diagnosis and management: Circulatory system diseases", "Aortic dissection and aneurysm: Circulatory system diseases", "Myocarditis and pericarditis : Circulatory system diseases", "Cardiomyopathy: Circulatory system diseases", "Cardiac dysrhythmias and tachycardias: Circulatory system diseases", "Heart valve diseases: Circulatory system diseases", "Acyanotic heart diseases: Circulatory system diseases", "Cyanotic heart diseases: Circulatory system diseases", "Shock: Circulatory system diseases", "Vasculitis: Circulatory system diseases"], "Unit 4: Respiratory system anatomy and physiology": ["Lung structure and function: Respiratory system anatomy and physiology", "Gas exchange: Respiratory system anatomy and physiology", "Breathing control: Respiratory system anatomy and physiology"], "Unit 5: Respiratory system diseases": ["Introduction to pulmonary diseases: Respiratory system diseases", "Asthma: Respiratory system diseases", "Emphysema (COPD): Respiratory system diseases", "Chronic Bronchitis (COPD): Respiratory system diseases", "Cystic fibrosis: Respiratory system diseases", "Occupational lung diseases: Respiratory system diseases", "Pulmonary hypertension: Respiratory system diseases", "Pneumonia: Respiratory system diseases", "Pleural Effusion: Respiratory system diseases", "Lung cancer: Respiratory system diseases", "Nose, sinus, and upper respiratory conditions: Respiratory system diseases", "Throat conditions: Respiratory system diseases", "Laryngeal conditions: Respiratory system diseases", "Bronchiolitis: Respiratory system diseases"], "Unit 6: Hematologic system physiology and disease": ["Blood and blood cells: Hematologic system physiology and disease", "Hemoglobin: Hematologic system physiology and disease", "Bleeding and impaired hemostasis: Hematologic system physiology and disease", "Leukemia: Hematologic system physiology and disease", "Iron deficiency anemia and anemia of chronic disease: Hematologic system physiology and disease", "Plasma cell dyscrasias: Hematologic system physiology and disease", "Myeloproliferative disorders: Hematologic system physiology and disease"], "Unit 7: Endocrine system physiology and disease": ["Intro to endocrine hormones: Endocrine system physiology and disease", "Biological basis of behavior: Endocrine system: Endocrine system physiology and disease"], "Unit 8: Nervous system physiology and disease": ["Structure and function of the nervous system: Nervous system physiology and disease", "Neural cell types: Nervous system physiology and disease", "Function of neurons and neurotransmitters: Nervous system physiology and disease", "Neuron membrane potentials: Nervous system physiology and disease", "Sensory perception: Nervous system physiology and disease", "Sight (vision): Nervous system physiology and disease", "Sound (Audition): Nervous system physiology and disease", "Somatosensation: Nervous system physiology and disease", "Taste (gustation) and smell (olfaction): Nervous system physiology and disease", "Multiple sclerosis: Nervous system physiology and disease", "Miscellaneous topics: Nervous system physiology and disease"], "Unit 9: Brain function and mental health": ["Cognition: Brain function and mental health", "Attention and language: Brain function and mental health", "Sleep and consciousness: Brain function and mental health", "Memory: Brain function and mental health", "Emotion: Brain function and mental health"], "Unit 10: Gastrointestinal system physiology and disease": ["Components of the GI tract: Gastrointestinal system physiology and disease", "Inflammatory bowel disease: Gastrointestinal system physiology and disease", "Celiac disease: Gastrointestinal system physiology and disease", "Colon diseases: Gastrointestinal system physiology and disease", "BMI and diet: Gastrointestinal system physiology and disease"], "Unit 11: Musculoskeletal system physiology and disease": ["Muscle contraction: Musculoskeletal system physiology and disease", "Muscle innervation : Musculoskeletal system physiology and disease", "Skeletal system introduction: Musculoskeletal system physiology and disease"], "Unit 12: Reproductive system and pregnancy": ["Female reproductive system: Reproductive system and pregnancy", "Male reproductive system: Reproductive system and pregnancy", "Pregnancy anatomy and physiology: Reproductive system and pregnancy", "Pregnancy complications: Reproductive system and pregnancy", "Fetal circulation: Reproductive system and pregnancy"], "Unit 13: Infectious diseases": ["Bacteria and viruses: Infectious diseases", "Pertussis: Infectious diseases", "Influenza: Infectious diseases"], "Unit 14: Other topics in health and medicine": ["Health care system: Other topics in health and medicine", "Lab values and concentrations : Other topics in health and medicine", "Child growth and development: Other topics in health and medicine", "Cancer: Other topics in health and medicine", "Inflammation and exposures: Other topics in health and medicine"]}}}}
{"course_title": "Computer programming", "course_url": "/computing/computer-programming", "page_contents": {"syllabus": {"topics": {"Unit 1: Intro to JS: Drawing & Animation": ["Intro to programming: Intro to JS: Drawing & Animation", "Drawing basics: Intro to JS: Drawing & Animation", "Coloring: Intro to JS: Drawing & Animation", "Variables: Intro to JS: Drawing & Animation", "Interactive programs: Intro to JS: Drawing & Animation", "Text and strings: Intro to JS: Drawing & Animation", "Functions: Intro to JS: Drawing & Animation", "Logic and if Statements: Intro to JS: Drawing & Animation", "Debugging programs: Intro to JS: Drawing & Animation", "Looping: Intro to JS: Drawing & Animation", "Writing clean code: Intro to JS: Drawing & Animation", "Arrays: Intro to JS: Drawing & Animation", "Objects: Intro to JS: Drawing & Animation", "Object-Oriented Design: Intro to JS: Drawing & Animation"], "Unit 2: Intro to HTML/CSS: Making webpages": ["Intro to HTML: Intro to HTML/CSS: Making webpages", "Intro to CSS: Intro to HTML/CSS: Making webpages", "More HTML tags: Intro to HTML/CSS: Making webpages", "CSS text properties: Intro to HTML/CSS: Making webpages", "CSS layout: Intro to HTML/CSS: Making webpages", "More CSS selectors: Intro to HTML/CSS: Making webpages", "Other ways to embed CSS: Intro to HTML/CSS: Making webpages"], "Unit 3: Intro to SQL: Querying and managing data": ["SQL basics: Intro to SQL: Querying and managing data", "More advanced SQL queries: Intro to SQL: Querying and managing data"], "Unit 6: HTML/JS: Making webpages interactive": ["Get ready to make your webpages interactive: HTML/JS: Making webpages interactive", "JS and the DOM: HTML/JS: Making webpages interactive", "DOM access methods: HTML/JS: Making webpages interactive", "DOM modification: HTML/JS: Making webpages interactive", "DOM events: HTML/JS: Making webpages interactive", "DOM animation: HTML/JS: Making webpages interactive"], "Unit 7: HTML/JS: Making webpages interactive with jQuery": ["Welcome to jQuery: HTML/JS: Making webpages interactive with jQuery", "DOM access with jQuery: HTML/JS: Making webpages interactive with jQuery", "DOM modification with jQuery: HTML/JS: Making webpages interactive with jQuery", "jQuery techniques: HTML/JS: Making webpages interactive with jQuery", "DOM events with jQuery: HTML/JS: Making webpages interactive with jQuery", "DOM animation & effects with jQuery: HTML/JS: Making webpages interactive with jQuery"], "Unit 8: Meet the professional": ["Meet the professional: Meet the professional", "Watch an introduction video0:5252 seconds", "Meet the professionals", "Meet the professionals", "Watch an introduction video0:5252 seconds", "Help requests", "Browse projects"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Computer Science Principles", "course_url": "/computing/ap-computer-science-principles", "page_contents": {"syllabus": {"topics": {"Unit 7: Online data security": ["Introduction to online data security: Online data security", "PII (Personally identifiable information): Online data security"]}}}}
{"course_title": "Pixar in a Box", "course_url": "/computing/pixar", "page_contents": {"syllabus": {"topics": {"Unit 15Rendering": ["Video 2 minutes 5 seconds2:05", "Effects overview", "Introduction to particle systems", "Video 3 minutes 17 seconds3:17", "Introduction to virtual cameras", "How virtual cameras work", "Video 1 minute 48 seconds1:48", "Introduction to combinatorics", "Building crowds", "Video 2 minutes2:00", "Welcome to rigging", "Introduction to rigging", "Video 2 minutes 47 seconds2:47", "Math meets artistry", "Introduction to animation", "Watch an introduction video5:205 minutes 20 seconds", "Start here!", "Start here!", "Watch an introduction video5:205 minutes 20 seconds"], "Unit 2: The art of storytelling": ["We are all storytellers | 1: The art of storytelling", "Character | 2: The art of storytelling", "Story structure | 3: The art of storytelling", "Visual language | 4: The art of storytelling", "Film grammar | 5: The art of storytelling", "Pitching and feedback | 6: The art of storytelling"], "Unit 4: Simulation": ["Hair simulation 101: Simulation", "Code your own simulation: Simulation"], "Unit 5: Color science": ["Introduction to color: Color science", "Color spaces: Color science"], "Unit 6: Virtual cameras": ["How virtual cameras work: Virtual cameras", "Mathematics of depth of field: Virtual cameras"]}}}}
{"course_title": "US history", "course_url": "/humanities/us-history", "page_contents": {"syllabus": {"topics": {"Unit 1: Worlds collide (1491-1607)": ["Thinking like a historian: Worlds collide (1491-1607)", "Before contact: Worlds collide (1491-1607)", "Spanish colonization : Worlds collide (1491-1607)"], "Unit 2: Colonial America (1607-1754)": ["Early colonization projects: Colonial America (1607-1754)", "Chesapeake and Southern colonies: Colonial America (1607-1754)", "Colonial North America: Colonial America (1607-1754)"], "Unit 3: The road to revolution (1754-1800)": ["The American Revolution: The road to revolution (1754-1800)", "Creating a nation: The road to revolution (1754-1800)"], "Unit 4: The early republic (1800-1848)": ["The age of Jackson : The early republic (1800-1848)", "Culture and reform in the early nineteenth century: The early republic (1800-1848)"], "Unit 8: The postwar era (1945-1980)": ["The postwar era, 1945-1950: The postwar era (1945-1980)", "1950s America: The postwar era (1945-1980)"]}}}}
{"course_title": "AP\u00ae\ufe0e/College US History", "course_url": "/humanities/ap-us-history", "page_contents": {"syllabus": {"topics": {"Unit 11Unit 11: AP\u00ae\ufe0e US History standards mappings": ["Start Course challenge", "Watch an introduction video1:451 minute 45 seconds", "Learn more", "Learn more", "Watch an introduction video1:451 minute 45 seconds"], "Unit 1: Period 1: 1491-1607": ["Thinking like a historian: Period 1: 1491-1607", "Native American societies before contact: Period 1: 1491-1607", "Columbian Exchange, Spanish exploration, and conquest: Period 1: 1491-1607", "Labor, slavery, and caste in the Spanish colonial system : Period 1: 1491-1607", "Cultural interactions between Europeans, Native Americans, and Africans: Period 1: 1491-1607", "Causation in Period 1: Period 1: 1491-1607"], "Unit 2: Period 2: 1607-1754": ["European colonization: Period 2: 1607-1754", "Regions of British colonies: Period 2: 1607-1754", "Interactions between American Indians and Europeans: Period 2: 1607-1754", "Slavery in the British colonies: Period 2: 1607-1754", "Comparison in Period 2: Period 2: 1607-1754"], "Unit 3: Period 3: 1754-1800": ["The Seven Years' War (The French and Indian War): Period 3: 1754-1800", "The Articles of Confederation: Period 3: 1754-1800", "The Constitutional Convention and debates over ratification: Period 3: 1754-1800", "The Constitution: Period 3: 1754-1800", "Movement in the early republic: Period 3: 1754-1800", "Continuity and change in Period 3: Period 3: 1754-1800"], "Unit 4: Period 4: 1800-1848": ["America on the world stage: Period 4: 1800-1848", "Market Revolution: industrialization: Period 4: 1800-1848", "Market Revolution: society and culture: Period 4: 1800-1848", "Jackson and federal power: Period 4: 1800-1848", "The development of an American culture: Period 4: 1800-1848", "The Second Great Awakening: Period 4: 1800-1848", "An age of reform: Period 4: 1800-1848", "Causation in Period 4: Period 4: 1800-1848"], "Unit 5: Period 5: 1844-1877": ["Manifest Destiny: Period 5: 1844-1877", "The Compromise of 1850: Period 5: 1844-1877", "Election of 1860 and secession: Period 5: 1844-1877", "Military conflict in the Civil War: Period 5: 1844-1877", "Comparison in Period 5: Period 5: 1844-1877"], "Unit 6: Period 6: 1865-1898": ["Technological innovation: Period 6: 1865-1898", "The rise of industrial capitalism: Period 6: 1865-1898", "Reform in the Gilded Age: Period 6: 1865-1898", "Continuity and change in Period 6: Period 6: 1865-1898"], "Unit 7: Period 7: 1890-1945": ["Imperialism: debates: Period 7: 1890-1945", "The Progressives: Period 7: 1890-1945", "1920s: cultural and political controversies: Period 7: 1890-1945", "Interwar foreign policy: Period 7: 1890-1945", "World War II: military: Period 7: 1890-1945", "Comparison in Period 7: Period 7: 1890-1945"], "Unit 8: Period 8: 1945-1980": ["The Cold War from 1945 to 1980: Period 8: 1945-1980", "The Vietnam War : Period 8: 1945-1980", "Continuity and change in Period 8: Period 8: 1945-1980"]}}}}
{"course_title": "US government and civics", "course_url": "/humanities/us-government-and-civics", "page_contents": {"syllabus": {"topics": {"Unit 10Unit 10: Primary documents": ["Start Course challenge", "Watch an introduction video2:332 minutes 33 seconds", "Start learning", "Start learning", "Watch an introduction video2:332 minutes 33 seconds"], "Unit 1: Foundations of American democracy": ["Welcome to US government and civics!: Foundations of American democracy", "Ideals of democracy: Foundations of American democracy", "Types of democracy: Foundations of American democracy", "Challenges of the Articles of Confederation: Foundations of American democracy", "Government power and individual rights: Foundations of American democracy", "Ratification of the US Constitution: Foundations of American democracy", "Principles of American government: Foundations of American democracy", "The relationship between the states and the federal government: Foundations of American democracy", "Constitutional interpretations of federalism : Foundations of American democracy", "Federalism in action: Foundations of American democracy"], "Unit 2: Interactions among branches of government": ["Congress: The Senate and the House of Representatives: Interactions among branches of government", "Structures, powers, and functions of Congress: Interactions among branches of government", "Congressional behavior: Interactions among branches of government", "Roles and powers of the president: Interactions among branches of government", "Checks on the presidency: Interactions among branches of government", "Expansion of presidential power: Interactions among branches of government", "Presidential communication: Interactions among branches of government", "The judicial branch: Interactions among branches of government", "Legitimacy of the judicial branch: Interactions among branches of government", "Checks on the judicial branch: Interactions among branches of government", "The bureaucracy: functions and responsibilities: Interactions among branches of government", "The bureaucracy: authority and accountability: Interactions among branches of government"], "Unit 3: Civil liberties and civil rights": ["The Bill of Rights: Civil liberties and civil rights", "The First Amendment: freedom of religion: Civil liberties and civil rights", "The Second Amendment: Civil liberties and civil rights", "Balancing individual freedom with public order and safety: Civil liberties and civil rights", "Selective incorporation: Civil liberties and civil rights", "Due process and the rights of the accused: Civil liberties and civil rights", "Social movements and equal protection: Civil liberties and civil rights", "Government responses to social movements: Civil liberties and civil rights", "Balancing minority and majority rights: Civil liberties and civil rights", "Affirmative action: Civil liberties and civil rights"], "Unit 4: Citizenship": ["What does it mean to be a citizen?: Citizenship", "What are the rights and responsibilities of citizenship?: Citizenship", "How has the definition of citizenship changed over time?: Citizenship", "What is the pathway to citizenship?: Citizenship", "How can citizens change a democracy?: Citizenship"], "Unit 5: American political ideologies and beliefs": ["American attitudes about government and politics: American political ideologies and beliefs", "Political socialization: American political ideologies and beliefs", "Influences on ideology: American political ideologies and beliefs", "Ideologies of political parties: American political ideologies and beliefs", "Ideology and economic policy: American political ideologies and beliefs", "Ideology and social policy: American political ideologies and beliefs"], "Unit 6: Political participation": ["Voting rights and models of voter behavior: Political participation", "Voter turnout: Political participation", "Political parties: Political participation", "How and why political parties change and adapt: Political participation", "Third-party politics: Political participation", "Groups influencing policymaking and policy outcomes: Political participation", "Electing a president: Political participation", "Congressional elections: Political participation", "Modern campaigns: Political participation", "Campaign finance: Political participation", "The media: Political participation", "Changing media: Political participation"], "Unit 7: Government & civics with CBS's John Dickerson": ["Why it matters: Government & civics with CBS's John Dickerson", "What has changed: Government & civics with CBS's John Dickerson", "Presidential history: Government & civics with CBS's John Dickerson"], "Unit 8: The National Constitution Center": ["The Constitution: The National Constitution Center", "The Bill of Rights: The National Constitution Center", "Landmark Supreme Court cases: The National Constitution Center"]}}}}
{"course_title": "AP\u00ae\ufe0e/College US Government & Politics", "course_url": "/humanities/ap-us-government-and-politics", "page_contents": {"syllabus": {"topics": {"Unit 1: Foundations of American democracy": ["Ideals of democracy: Foundations of American democracy", "Types of democracy: Foundations of American democracy", "Challenges of the Articles of Confederation: Foundations of American democracy", "Government power and individual rights: Foundations of American democracy", "Ratification of the US Constitution: Foundations of American democracy", "Principles of American government: Foundations of American democracy", "The relationship between the states and the federal government: Foundations of American democracy", "Constitutional interpretations of federalism : Foundations of American democracy", "Federalism in action: Foundations of American democracy"], "Unit 2: Interactions among branches of government": ["Congress: The Senate and the House of Representatives: Interactions among branches of government", "Structures, powers, and functions of Congress: Interactions among branches of government", "Congressional behavior: Interactions among branches of government", "Roles and powers of the president: Interactions among branches of government", "Checks on the presidency: Interactions among branches of government", "Expansion of presidential power: Interactions among branches of government", "Presidential communication: Interactions among branches of government", "The judicial branch: Interactions among branches of government", "Legitimacy of the judicial branch: Interactions among branches of government", "The Court in action: Interactions among branches of government", "Checks on the judicial branch: Interactions among branches of government", "The bureaucracy: Interactions among branches of government", "Discretionary and rule-making authority: Interactions among branches of government", "Holding the bureaucracy accountable: Interactions among branches of government", "Policy and the branches of government: Interactions among branches of government"], "Unit 3: Civil liberties and civil rights": ["The Bill of Rights: Civil liberties and civil rights", "The First Amendment: freedom of religion: Civil liberties and civil rights", "The Second Amendment: Civil liberties and civil rights", "Balancing individual freedom with public order and safety: Civil liberties and civil rights", "Selective incorporation: Civil liberties and civil rights", "Due process and the rights of the accused: Civil liberties and civil rights", "Social movements and equal protection: Civil liberties and civil rights", "Government responses to social movements: Civil liberties and civil rights", "Balancing minority and majority rights: Civil liberties and civil rights", "Affirmative action: Civil liberties and civil rights"], "Unit 4: American political ideologies and beliefs": ["American attitudes about government and politics: American political ideologies and beliefs", "Political socialization: American political ideologies and beliefs", "Changes in ideology: American political ideologies and beliefs", "Influence of political events on ideology: American political ideologies and beliefs", "Measuring public opinion: American political ideologies and beliefs", "Evaluating public opinion data: American political ideologies and beliefs", "Ideologies of political parties: American political ideologies and beliefs", "Ideology and policymaking: American political ideologies and beliefs", "Ideology and economic policy: American political ideologies and beliefs", "Ideology and social policy: American political ideologies and beliefs"], "Unit 5: Political participation": ["Voting rights and models of voter behavior: Political participation", "Voter turnout: Political participation", "Political parties: Political participation", "How and why political parties change and adapt: Political participation", "Third-party politics: Political participation", "Interest groups influencing policymaking : Political participation", "Groups influencing policy outcomes: Political participation", "Electing a president: Political participation", "Congressional elections: Political participation", "Modern campaigns: Political participation", "Campaign finance: Political participation", "The media: Political participation", "Changing media: Political participation"]}}}}
{"course_title": "World History Project - Origins to the Present", "course_url": "/humanities/whp-origins", "page_contents": {"syllabus": {"topics": {"Unit 7: Era 7 - The Great Convergence and Divergence (1880 CE to the future)": ["Other Materials: Era 7 - The Great Convergence and Divergence (1880 CE to the future)", "Start Course challenge"]}}}}
{"course_title": "World History Project - 1750 to the Present", "course_url": "/humanities/whp-1750", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "AP\u00ae\ufe0e/College World HistoryNEW", "course_url": "/humanities/world-history-project-ap", "page_contents": {"syllabus": {"topics": {"Unit 10Review \u2014 Introduction to World History": ["Watch an introduction video1:351 minute 35 seconds", "Looking for a review on ancient World History before you dive into this course? Click here!", "Looking for a review on ancient World History before you dive into this course? Click here!", "Watch an introduction video1:351 minute 35 seconds"]}}}}
{"course_title": "Big history", "course_url": "/humanities/big-history-project", "page_contents": {"syllabus": {"topics": {"Unit 2: The Big Bang": ["The Big Bang | 2.0 : The Big Bang", "Other Materials: The Big Bang"], "Unit 9: Acceleration": ["Transitions, Thresholds, and Turning Points in History | 9.0: Acceleration", "The Anthropocene | 9.2: Acceleration"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Art History", "course_url": "/humanities/ap-art-history", "page_contents": {"syllabus": {"topics": {"Unit 1: Start here": ["Why art matters: Start here", "The language of art history: Start here", "Current issues in art history: Start here"], "Unit 4: Ancient Mediterranean: 3500 B.C.E.-300 C.E.": ["Ancient Greece : Ancient Mediterranean: 3500 B.C.E.-300 C.E.", "Ancient Rome: Ancient Mediterranean: 3500 B.C.E.-300 C.E."]}}}}
{"course_title": "Macroeconomics", "course_url": "/economics-finance-domain/macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Markets: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["Gross Domestic Product: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal v. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The market for loanable funds: Financial sector", "Interest rates and the time value of money: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Real interest rates and international capital flows: Open economy: international trade and finance"], "Unit 7: Keynesian approaches and IS-LM": ["The consumption function: Keynesian approaches and IS-LM", "The Keynesian cross: Keynesian approaches and IS-LM", "IS-LM: Keynesian approaches and IS-LM", "Keynesian economics and its critiques: Keynesian approaches and IS-LM"], "Analysis of income inequality in the United States (in partnership with the New York Times): Contemporary macroeconomic issues": ["National income and inequality: Contemporary macroeconomic issues", "The 2008 Financial Crisis: Contemporary macroeconomic issues"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Macroeconomics", "course_url": "/economics-finance-domain/ap-macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Market equilibrium, disequilibrium, and changes in equilibrium: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["The Circular Flow and GDP: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Price Indices and inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal vs. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The Market for loanable funds: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies", "Public policy and economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Changes in the foreign exchange markets and net exports: Open economy: international trade and finance", "Real Interest Rates and International Capital Flows: Open economy: international trade and finance"]}}}}
{"course_title": "Microeconomics", "course_url": "/economics-finance-domain/microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic economic concepts": ["Introduction to economics: Basic economic concepts", "Economic systems: Basic economic concepts", "Production possibilities frontier: Basic economic concepts", "Comparative advantage and the terms of trade : Basic economic concepts"], "Unit 2: Supply, demand, and market equilibrium": ["Demand: Supply, demand, and market equilibrium", "Supply: Supply, demand, and market equilibrium", "Market equilibrium and changes in equilibrium: Supply, demand, and market equilibrium"], "Unit 3: Elasticity": ["Price elasticity of demand: Elasticity", "Price elasticity of supply: Elasticity", "Income elasticity of demand and cross-price elasticity of demand: Elasticity"], "Unit 4: Consumer and producer surplus, market interventions, and international trade": ["Consumer and producer surplus: Consumer and producer surplus, market interventions, and international trade", "Market interventions and deadweight loss: Consumer and producer surplus, market interventions, and international trade", "International trade: Consumer and producer surplus, market interventions, and international trade"], "Unit 5: Consumer theory": ["Introduction to consumer theory: total utility and marginal utility: Consumer theory", "Utility maximization using marginal utility per dollar spent: Consumer theory", "Utility maximization with indifference curves: Consumer theory"], "Unit 6: Production decisions and economic profit": ["Introduction to production and costs: Production decisions and economic profit", "Production and costs in the short run: Production decisions and economic profit", "Production and costs in the long run: Production decisions and economic profit", "Types of profit: Production decisions and economic profit", "Profit maximization: Production decisions and economic profit", "Firm entry, exit, and the shut-down rule: Production decisions and economic profit"], "Unit 7: Forms of competition": ["Perfect competition: Forms of competition", "Monopoly: Forms of competition", "Price discrimination: Forms of competition", "Monopolistic competition: Forms of competition", "Oligopoly and game theory: Forms of competition"], "Unit 8: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Optimal choice of factors in perfectly competitive factor markets : Factor markets", "Choosing inputs when factor markets are monopolistically competitive: Factor markets"], "Unit 9: Market failure and the role of government": ["Externalities: Market failure and the role of government", "The four types of goods: private goods, public goods, common resources, and natural monopolies: Market failure and the role of government", "Start Course challenge"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Microeconomics", "course_url": "/economics-finance-domain/ap-microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic Economic Concepts": ["Resource Allocation and Economic Systems: Basic Economic Concepts", "Production possibilities curve (PPC): Basic Economic Concepts", "Comparative advantage and trade: Basic Economic Concepts", "Cost-benefit analysis: Basic Economic Concepts", "Marginal analysis and consumer choice: Basic Economic Concepts"], "Unit 2: Supply and Demand": ["Demand: Supply and Demand", "Supply: Supply and Demand", "Price elasticity of demand: Supply and Demand", "Price elasticity of supply: Supply and Demand", "Other elasticities: Supply and Demand", "Market equilibrium and consumer and producer surplus: Supply and Demand", "Disequilibrium and changes in equilibrium: Supply and Demand", "The effects of government interventions in markets: Supply and Demand", "International trade and public policy: Supply and Demand"], "Unit 3: Production, cost, and the perfect competition model": ["The production function: Production, cost, and the perfect competition model", "Short-run production costs: Production, cost, and the perfect competition model", "Long-run production costs: Production, cost, and the perfect competition model", "Types of profit: Production, cost, and the perfect competition model", "Profit maximization: Production, cost, and the perfect competition model", "Firms\u2019 Short-run Decisions to Produce and Long-Run Decisions to Enter or Exit a Market: Production, cost, and the perfect competition model", "Perfect competition: Production, cost, and the perfect competition model"], "Unit 4: Imperfect competition": ["Introduction to imperfect competition: Imperfect competition", "Monopoly: Imperfect competition", "Price discrimination: Imperfect competition", "Monopolistic competition: Imperfect competition", "Oligopoly and game theory: Imperfect competition"], "Unit 5: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Profit-maximizing behavior in perfectly competitive factor markets: Factor markets", "Monopsonistic markets: Factor markets"], "Unit 6: Market failure and the role of government": ["Socially efficient and inefficient market outcomes: Market failure and the role of government", "Externalities: Market failure and the role of government", "Public and private goods: Market failure and the role of government", "The effects of government intervention in different market structures: Market failure and the role of government", "Inequality: Market failure and the role of government"]}}}}
{"course_title": "2nd grade", "course_url": "/ela/cc-2nd-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Fairy Tales Retold": ["Close reading: fiction; Little Red Riding Hood: Fairy Tales Retold", "Close reading: fiction; Granny the Hero: Fairy Tales Retold", "Applying vocabulary knowledge: Fairy Tales Retold", "Reading for understanding: drama: Fairy Tales Retold", "Reading for understanding: poetry and drama: Fairy Tales Retold"], "Unit 2: The Moon": ["Close reading: informational text: The Moon", "Close reading: fiction: The Moon", "Applying vocabulary knowledge: The Moon", "Reading for understanding: poetry: The Moon", "Reading for understanding: informational text: The Moon"], "Unit 3: Rural, Suburban, Urban": ["Close reading: informational text: Rural, Suburban, Urban", "Close reading: fiction: Rural, Suburban, Urban", "Applying vocabulary knowledge: Rural, Suburban, Urban", "Reading for understanding: informational text: Rural, Suburban, Urban", "Reading for understanding: fiction: Rural, Suburban, Urban"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Art History", "course_url": "/humanities/ap-art-history", "page_contents": {"syllabus": {"topics": {"Unit 1: Start here": ["Why art matters: Start here", "The language of art history: Start here", "Current issues in art history: Start here"], "Unit 4: Ancient Mediterranean: 3500 B.C.E.-300 C.E.": ["Ancient Greece : Ancient Mediterranean: 3500 B.C.E.-300 C.E.", "Ancient Rome: Ancient Mediterranean: 3500 B.C.E.-300 C.E."]}}}}
{"course_title": "Macroeconomics", "course_url": "/economics-finance-domain/macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Markets: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["Gross Domestic Product: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal v. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The market for loanable funds: Financial sector", "Interest rates and the time value of money: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Real interest rates and international capital flows: Open economy: international trade and finance"], "Unit 7: Keynesian approaches and IS-LM": ["The consumption function: Keynesian approaches and IS-LM", "The Keynesian cross: Keynesian approaches and IS-LM", "IS-LM: Keynesian approaches and IS-LM", "Keynesian economics and its critiques: Keynesian approaches and IS-LM"], "Analysis of income inequality in the United States (in partnership with the New York Times): Contemporary macroeconomic issues": ["National income and inequality: Contemporary macroeconomic issues", "The 2008 Financial Crisis: Contemporary macroeconomic issues"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Macroeconomics", "course_url": "/economics-finance-domain/ap-macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Market equilibrium, disequilibrium, and changes in equilibrium: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["The Circular Flow and GDP: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Price Indices and inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal vs. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The Market for loanable funds: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies", "Public policy and economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Changes in the foreign exchange markets and net exports: Open economy: international trade and finance", "Real Interest Rates and International Capital Flows: Open economy: international trade and finance"]}}}}
{"course_title": "Microeconomics", "course_url": "/economics-finance-domain/microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic economic concepts": ["Introduction to economics: Basic economic concepts", "Economic systems: Basic economic concepts", "Production possibilities frontier: Basic economic concepts", "Comparative advantage and the terms of trade : Basic economic concepts"], "Unit 2: Supply, demand, and market equilibrium": ["Demand: Supply, demand, and market equilibrium", "Supply: Supply, demand, and market equilibrium", "Market equilibrium and changes in equilibrium: Supply, demand, and market equilibrium"], "Unit 3: Elasticity": ["Price elasticity of demand: Elasticity", "Price elasticity of supply: Elasticity", "Income elasticity of demand and cross-price elasticity of demand: Elasticity"], "Unit 4: Consumer and producer surplus, market interventions, and international trade": ["Consumer and producer surplus: Consumer and producer surplus, market interventions, and international trade", "Market interventions and deadweight loss: Consumer and producer surplus, market interventions, and international trade", "International trade: Consumer and producer surplus, market interventions, and international trade"], "Unit 5: Consumer theory": ["Introduction to consumer theory: total utility and marginal utility: Consumer theory", "Utility maximization using marginal utility per dollar spent: Consumer theory", "Utility maximization with indifference curves: Consumer theory"], "Unit 6: Production decisions and economic profit": ["Introduction to production and costs: Production decisions and economic profit", "Production and costs in the short run: Production decisions and economic profit", "Production and costs in the long run: Production decisions and economic profit", "Types of profit: Production decisions and economic profit", "Profit maximization: Production decisions and economic profit", "Firm entry, exit, and the shut-down rule: Production decisions and economic profit"], "Unit 7: Forms of competition": ["Perfect competition: Forms of competition", "Monopoly: Forms of competition", "Price discrimination: Forms of competition", "Monopolistic competition: Forms of competition", "Oligopoly and game theory: Forms of competition"], "Unit 8: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Optimal choice of factors in perfectly competitive factor markets : Factor markets", "Choosing inputs when factor markets are monopolistically competitive: Factor markets"], "Unit 9: Market failure and the role of government": ["Externalities: Market failure and the role of government", "The four types of goods: private goods, public goods, common resources, and natural monopolies: Market failure and the role of government"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Microeconomics", "course_url": "/economics-finance-domain/ap-microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic Economic Concepts": ["Resource Allocation and Economic Systems: Basic Economic Concepts", "Production possibilities curve (PPC): Basic Economic Concepts", "Comparative advantage and trade: Basic Economic Concepts", "Cost-benefit analysis: Basic Economic Concepts", "Marginal analysis and consumer choice: Basic Economic Concepts"], "Unit 2: Supply and Demand": ["Demand: Supply and Demand", "Supply: Supply and Demand", "Price elasticity of demand: Supply and Demand", "Price elasticity of supply: Supply and Demand", "Other elasticities: Supply and Demand", "Market equilibrium and consumer and producer surplus: Supply and Demand", "Disequilibrium and changes in equilibrium: Supply and Demand", "The effects of government interventions in markets: Supply and Demand", "International trade and public policy: Supply and Demand"], "Unit 3: Production, cost, and the perfect competition model": ["The production function: Production, cost, and the perfect competition model", "Short-run production costs: Production, cost, and the perfect competition model", "Long-run production costs: Production, cost, and the perfect competition model", "Types of profit: Production, cost, and the perfect competition model", "Profit maximization: Production, cost, and the perfect competition model", "Firms\u2019 Short-run Decisions to Produce and Long-Run Decisions to Enter or Exit a Market: Production, cost, and the perfect competition model", "Perfect competition: Production, cost, and the perfect competition model"], "Unit 4: Imperfect competition": ["Introduction to imperfect competition: Imperfect competition", "Monopoly: Imperfect competition", "Price discrimination: Imperfect competition", "Monopolistic competition: Imperfect competition", "Oligopoly and game theory: Imperfect competition"], "Unit 5: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Profit-maximizing behavior in perfectly competitive factor markets: Factor markets", "Monopsonistic markets: Factor markets"], "Unit 6: Market failure and the role of government": ["Socially efficient and inefficient market outcomes: Market failure and the role of government", "Externalities: Market failure and the role of government", "Public and private goods: Market failure and the role of government", "The effects of government intervention in different market structures: Market failure and the role of government", "Inequality: Market failure and the role of government"]}}}}
{"course_title": "2nd grade", "course_url": "/ela/cc-2nd-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Fairy Tales Retold": ["Close reading: fiction; Little Red Riding Hood: Fairy Tales Retold", "Close reading: fiction; Granny the Hero: Fairy Tales Retold", "Applying vocabulary knowledge: Fairy Tales Retold", "Reading for understanding: drama: Fairy Tales Retold", "Reading for understanding: poetry and drama: Fairy Tales Retold"], "Unit 2: The Moon": ["Close reading: informational text: The Moon", "Close reading: fiction: The Moon", "Applying vocabulary knowledge: The Moon", "Reading for understanding: poetry: The Moon", "Reading for understanding: informational text: The Moon"], "Unit 3: Rural, Suburban, Urban": ["Close reading: informational text: Rural, Suburban, Urban", "Close reading: fiction: Rural, Suburban, Urban", "Applying vocabulary knowledge: Rural, Suburban, Urban", "Reading for understanding: informational text: Rural, Suburban, Urban", "Reading for understanding: fiction: Rural, Suburban, Urban"]}}}}
{"course_title": "3rd grade", "course_url": "/ela/cc-3rd-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Pets": ["Close reading: informational text: Pets", "Close reading: opinions: Pets", "Applying vocabulary knowledge: Pets", "Reading for understanding: fiction: Pets", "Reading for understanding: poetry: Pets"], "Unit 2: Homes": ["Close reading: informational text: Homes", "Close reading: fiction: Homes", "Applying vocabulary knowledge: Homes", "Reading for understanding: informational text: Homes", "Reading for understanding: fiction: Homes"], "Unit 3: Extreme Environments": ["Close reading: informational text: Extreme Environments", "Close reading: fiction: Extreme Environments", "Applying vocabulary knowledge: Extreme Environments", "Reading for understanding: informational text; Antarctica: Extreme Environments", "Reading for understanding: informational text; The Arctic Circle: Extreme Environments"]}}}}
{"course_title": "4th grade", "course_url": "/ela/cc-4th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Superheroes": ["Close reading: informational text: Superheroes", "Close reading: fiction: Superheroes", "Applying vocabulary knowledge: Superheroes", "Reading for understanding: drama and fiction: Superheroes", "Reading for understanding: informational text: Superheroes"], "Unit 2: Growth Mindset": ["Close reading: informational text: Growth Mindset", "Close reading: fiction: Growth Mindset", "Applying vocabulary knowledge: Growth Mindset", "Reading for understanding: fiction: Growth Mindset", "Reading for understanding: informational text: Growth Mindset"], "Unit 3: Journeys West": ["Close reading: informational text: Journeys West", "Close reading: poetry: Journeys West", "Applying vocabulary knowledge: Journeys West", "Reading for understanding: fiction and informational text: Journeys West", "Reading for understanding: informational text: Journeys West"]}}}}
{"course_title": "5th grade", "course_url": "/ela/cc-5th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Imaginative Worlds": ["Close reading: fiction: Imaginative Worlds", "Close reading: informational text: Imaginative Worlds", "Applying vocabulary knowledge: Imaginative Worlds", "Reading for understanding: fiction; The Boy in the Painting: Imaginative Worlds", "Reading for understanding: fiction; The Dawning: Imaginative Worlds"], "Unit 2: Athletes in Action": ["Close reading: informational text; Title IX: Athletes in Action", "Close reading: informational text; Fast and Female: Athletes in Action", "Applying vocabulary knowledge: Athletes in Action", "Reading for understanding: informational text: Athletes in Action", "Reading for understanding: poetry: Athletes in Action"], "Unit 3: Inventing Progress": ["Close reading: informational text: Inventing Progress", "Close reading: argumentative text: Inventing Progress", "Applying vocabulary knowledge: Inventing Progress", "Reading for understanding: fiction; The Ingenuity Fair: Inventing Progress", "Reading for understanding: fiction; Robots and Turtles: Inventing Progress"]}}}}
{"course_title": "6th grade", "course_url": "/ela/cc-6th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Banning Behavior": ["Close reading: informational text: Banning Behavior", "Close reading: argumentative text: Banning Behavior", "Applying vocabulary knowledge: Banning Behavior", "Reading for understanding: fiction: Banning Behavior", "Reading for understanding: drama: Banning Behavior"], "Unit 2: Identity": ["Close reading: informational text: Identity", "Close reading: fiction: Identity", "Applying vocabulary knowledge: Identity", "Reading for understanding: fiction: Identity", "Reading for understanding: drama: Identity"], "Unit 3: Ocean Conservation": ["Close reading: informational text: Ocean Conservation", "Close reading: poetry: Ocean Conservation", "Applying vocabulary knowledge: Ocean Conservation", "Reading for understanding: informational text; Boyan Slat: Ocean Conservation", "Reading for understanding: informational text; The Underwater Sea Train: Ocean Conservation"]}}}}
{"course_title": "7th grade", "course_url": "/ela/cc-7th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Trailblazing Women": ["Close reading: informational text: Trailblazing Women", "Close reading: speech and drama: Trailblazing Women", "Applying vocabulary knowledge: Trailblazing Women", "Reading for understanding: informational text; Mae Jemison: Trailblazing Women"], "Unit 2: Mysteries of the Past": ["Close reading: informational text: Mysteries of the Past", "Close reading: argumentative text: Mysteries of the Past", "Applying vocabulary knowledge: Mysteries of the Past", "Reading for understanding: informational text: Mysteries of the Past", "Reading for understanding: fiction: Mysteries of the Past"], "Unit 3: Living Tongues": ["Close reading: informational text: Living Tongues", "Close reading: poetry: Living Tongues", "Applying vocabulary knowledge: Living Tongues", "Reading for understanding: informational text: Living Tongues", "Reading for understanding: fiction: Living Tongues"]}}}}
{"course_title": "8th grade", "course_url": "/ela/cc-8th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Funny Business": ["Close reading: drama: Funny Business", "Close reading: informational text: Funny Business", "Applying vocabulary knowledge: Funny Business", "Reading for understanding: fiction; Use What You Have: Funny Business", "Reading for understanding: fiction; An Uncomfortable Bed: Funny Business"], "Unit 2: Obscuring the Truth": ["Close reading: informational text; Why Do We Lie?: Obscuring the Truth", "Close reading: informational text; The Science of Lying: Obscuring the Truth", "Applying vocabulary knowledge: Obscuring the Truth", "Reading for understanding: fiction; One Big Mess: Obscuring the Truth", "Reading for understanding: fiction; The Open Window: Obscuring the Truth"], "Unit 3: Crossing the Line": ["Close reading: informational text: Crossing the Line", "Close reading: fiction: Crossing the Line", "Applying vocabulary knowledge: Crossing the Line", "Reading for understanding: informational text: Crossing the Line", "Reading for understanding: fiction: Crossing the Line"]}}}}
{"course_title": "9th grade", "course_url": "/ela/cc-9th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Borders": ["Close reading: poetry: Borders", "Close reading: argumentative text: Borders", "Applying vocabulary knowledge: Borders", "Reading for understanding: informational text: Borders", "Reading for understanding: speech: Borders"], "Unit 2: Social Psychology": ["Close reading: informational text: Social Psychology", "Close reading: fiction: Social Psychology", "Applying vocabulary knowledge: Social Psychology", "Reading for understanding: informational text: Social Psychology", "Reading for understanding: fiction: Social Psychology"], "Unit 3: The Apocalypse": ["Close reading: informational text: The Apocalypse", "Close reading: fiction: The Apocalypse", "Applying vocabulary knowledge: The Apocalypse", "Reading for understanding: fiction; The War of the Worlds: The Apocalypse"]}}}}
{"course_title": "Grammar", "course_url": "/humanities/grammar", "page_contents": {"syllabus": {"topics": {"Usage and style: Unit test": ["Watch an introduction video2:462 minutes 46 seconds", "Start learning", "Start learning", "Watch an introduction video2:462 minutes 46 seconds"], "Unit 1: Parts of speech: the noun": ["Welcome to grammar!: Parts of speech: the noun", "Introduction to nouns: Parts of speech: the noun", "Types of nouns: Parts of speech: the noun", "Irregular plural nouns: base plurals and irregular endings: Parts of speech: the noun", "Irregular plural nouns: mutant and foreign plurals: Parts of speech: the noun"], "Unit 2: Parts of speech: the verb": ["Introduction to verbs: Parts of speech: the verb", "Verb tenses: Parts of speech: the verb", "Linking and helping verbs: Parts of speech: the verb", "Irregular verbs: Parts of speech: the verb", "Verb aspect: simple, progressive, and perfect: Parts of speech: the verb", "Verb aspect and modal verbs: Parts of speech: the verb"], "Unit 3: Parts of speech: the pronoun": ["Introduction to pronouns: Parts of speech: the pronoun", "Possessive and reflexive pronouns: Parts of speech: the pronoun", "Relative pronouns: Parts of speech: the pronoun", "Subject, object, person, and number: Parts of speech: the pronoun", "Indefinite pronouns, pronoun vagueness, and emphatic pronouns: Parts of speech: the pronoun"], "Unit 4: Parts of speech: the modifier": ["Introduction to adjectives and articles: Parts of speech: the modifier", "Introduction to adverbs: Parts of speech: the modifier", "Adjective order and commas with adjectives: Parts of speech: the modifier", "Comparative, superlative, intensifiers, and adverbs of degree: Parts of speech: the modifier"], "Unit 5: Parts of speech: the preposition and the conjunction": ["Introduction to prepositions: Parts of speech: the preposition and the conjunction", "Introduction to conjunctions: Parts of speech: the preposition and the conjunction", "Correlative conjunctions and starting sentences: Parts of speech: the preposition and the conjunction"], "Unit 6: Punctuation: the comma and the apostrophe": ["Introduction to commas: Punctuation: the comma and the apostrophe", "Commas in space and time: Punctuation: the comma and the apostrophe", "More ways to use commas: Punctuation: the comma and the apostrophe", "Apostrophes and contractions: Punctuation: the comma and the apostrophe", "Introduction to the possessive: Punctuation: the comma and the apostrophe", "\"Its\" versus \"it's\": Punctuation: the comma and the apostrophe"], "Unit 7: Punctuation: the colon, semicolon, and more": ["Introduction to colons: Punctuation: the colon, semicolon, and more", "Introduction to semicolons: Punctuation: the colon, semicolon, and more", "Formatting styles: Punctuation: the colon, semicolon, and more", "Hyphens, dashes, and ellipses: Punctuation: the colon, semicolon, and more"], "Unit 8: Syntax: sentences and clauses": ["Introduction to sentences: Syntax: sentences and clauses", "Types of sentences: Syntax: sentences and clauses", "Subjects and predicates: Syntax: sentences and clauses", "Phrases and clauses: Syntax: sentences and clauses"], "Unit 9: Syntax: conventions of standard English": ["Subject-verb agreement and pronoun-antecedent agreement : Syntax: conventions of standard English", "Fragments and run-ons: Syntax: conventions of standard English", "Dangling modifiers and parallel structure: Syntax: conventions of standard English"], "Unit 10: Usage and style": ["Frequently confused words: Usage and style", "Style!: Usage and style"]}}}}
{"course_title": "AI for educationNEW", "course_url": "/college-careers-more/ai-for-education", "page_contents": {"syllabus": {"topics": {"Unit 1: What is AI and how does it work?": ["How AI works: What is AI and how does it work?", "Video series: Practical AI for instructors and students: What is AI and how does it work?", "Ethics and AI : What is AI and how does it work?"]}}}}
{"course_title": "Financial literacyNEW", "course_url": "/college-careers-more/financial-literacy", "page_contents": {"syllabus": {"topics": {"Unit 11Unit 11: Additional resources": ["Watch an introduction video2:082 minutes 8 seconds", "Learn more", "Learn more", "Watch an introduction video2:082 minutes 8 seconds"], "Unit 2: Budgeting and saving": ["Reducing expenses: Budgeting and saving", "Saving money: Budgeting and saving"], "Unit 3: Consumer credit": ["Credit score: Consumer credit", "Payment methods: Consumer credit"], "Unit 4: Financial goals": ["Money personality: Financial goals", "Charitable giving: Financial goals", "SMART goals: Financial goals", "Short, medium, and long term goals: Financial goals"], "Unit 5: Loans and debt": ["Borrowing money: Loans and debt", "Types of loans: Loans and debt", "Terms of borrowing: Loans and debt", "Debt: Loans and debt", "Bankruptcy: Loans and debt"], "Unit 6: Insurance": ["What is risk and how to manage it: Insurance", "Insurance basics and terminology: Insurance", "Health insurance options and costs: Insurance", "Disability and long-term care insurance: Insurance", "Life insurance: Insurance", "Property insurance options and costs: Insurance", "Car insurance options and cost: Insurance", "Supplemental insurance and warranties: Insurance", "Estate planning and legal instruments: Insurance"], "Unit 7: Investments and retirement": ["Introduction to saving and investing: Investments and retirement", "Risk and return of investment options: Investments and retirement", "Planning for retirement: Investments and retirement"], "Unit 8: Scams & fraud": ["How to protect your personal information: Scams & fraud", "Common scams: Scams & fraud", "Consumer protection agencies: Scams & fraud"], "Unit 9: Careers and education": ["Education and earnings: Careers and education", "College, post-secondary education, and training: Careers and education", "Cost of post-secondary education and training: Careers and education", "Choosing where to go: Careers and education"], "Unit 10: Taxes and tax forms": ["What are taxes?: Taxes and tax forms", "Tax forms: Taxes and tax forms"], "Unit 11: Additional resources": ["Saving and budgeting: Additional resources", "Investments and retirement: Additional resources", "Pay & benefits: Additional resources", "Housing: Additional resources", "Car buying/leasing: Additional resources"]}}}}
{"course_title": "Internet safetyNEW", "course_url": "/college-careers-more/internet-safety", "page_contents": {"syllabus": {"topics": {"Online data security: Unit test": ["Watch an introduction video1:481 minute 48 seconds", "Start Learning", "Start Learning", "Watch an introduction video1:481 minute 48 seconds"], "Unit 1: Online data security": ["Welcome to the Internet Safety Course!: Online data security", "Ask Google: How do I keep my account safe?: Online data security", "Going deeper with personally identifiable information: Online data security", "Ask Google: How can I be sure I\u2019m surfing the web safely?: Online data security", "Going deeper with safe browsing: Online data security", "Ask Google: How can I keep my devices safe?: Online data security", "Ask Google: How can I recognize online scams?: Online data security", "Going deeper with recognizing and avoiding online scams: Online data security", "Data encryption techniques: Online data security", "Secure internet protocols: Online data security"]}}}}
{"course_title": "Social mediaNEW", "course_url": "/college-careers-more/social-media-challenges-and-opportunities", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "Growth mindset", "course_url": "/partner-content/learnstorm-growth-mindset-activities-us", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "College admissions", "course_url": "/college-careers-more/college-admissions", "page_contents": {"syllabus": {"topics": {"Unit 7Life after college": ["Watch an introduction video1:551 minute 55 seconds", "Start learning", "Start learning", "Watch an introduction video1:551 minute 55 seconds"], "Unit 1: Getting started": ["Introduction: College admissions: Getting started", "Importance of college: Getting started", "Access to college: Getting started"], "Unit 2: Making high school count": ["Introduction: Making high school count: Making high school count", "High school classes: Making high school count", "Extracurricular and leadership activities: Making high school count"], "Unit 3: Exploring college options": ["Introduction: Exploring college options: Exploring college options", "College search: Other important choices: Exploring college options", "Campus visit: Exploring college options"], "Unit 4: Applying to college": ["Introduction: Applying to college: Applying to college", "College application process: Applying to college", "Admissions essays: Applying to college", "Letters of recommendation: Applying to college", "Admissions interviews: Applying to college"], "Unit 5: Paying for college": ["Introduction: Paying for college: Paying for college", "Financial aid application process: Paying for college", "Grants and scholarships: Paying for college", "Work study: Paying for college", "Loans: Paying for college", "Financial aid packages: Paying for college"], "Unit 6: Wrapping up": ["Introduction: Wrapping up: Wrapping up", "Post college acceptance: Wrapping up"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Art History", "course_url": "/humanities/ap-art-history", "page_contents": {"syllabus": {"topics": {"Unit 1: Start here": ["Why art matters: Start here", "The language of art history: Start here", "Current issues in art history: Start here"], "Unit 4: Ancient Mediterranean: 3500 B.C.E.-300 C.E.": ["Ancient Greece : Ancient Mediterranean: 3500 B.C.E.-300 C.E.", "Ancient Rome: Ancient Mediterranean: 3500 B.C.E.-300 C.E."]}}}}
{"course_title": "Macroeconomics", "course_url": "/economics-finance-domain/macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Markets: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["Gross Domestic Product: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal v. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The market for loanable funds: Financial sector", "Interest rates and the time value of money: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Real interest rates and international capital flows: Open economy: international trade and finance"], "Unit 7: Keynesian approaches and IS-LM": ["The consumption function: Keynesian approaches and IS-LM", "The Keynesian cross: Keynesian approaches and IS-LM", "IS-LM: Keynesian approaches and IS-LM", "Keynesian economics and its critiques: Keynesian approaches and IS-LM"], "Analysis of income inequality in the United States (in partnership with the New York Times): Contemporary macroeconomic issues": ["National income and inequality: Contemporary macroeconomic issues", "The 2008 Financial Crisis: Contemporary macroeconomic issues"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Macroeconomics", "course_url": "/economics-finance-domain/ap-macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Market equilibrium, disequilibrium, and changes in equilibrium: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["The Circular Flow and GDP: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Price Indices and inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal vs. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The Market for loanable funds: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies", "Public policy and economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Changes in the foreign exchange markets and net exports: Open economy: international trade and finance", "Real Interest Rates and International Capital Flows: Open economy: international trade and finance"]}}}}
{"course_title": "Microeconomics", "course_url": "/economics-finance-domain/microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic economic concepts": ["Introduction to economics: Basic economic concepts", "Economic systems: Basic economic concepts", "Production possibilities frontier: Basic economic concepts", "Comparative advantage and the terms of trade : Basic economic concepts"], "Unit 2: Supply, demand, and market equilibrium": ["Demand: Supply, demand, and market equilibrium", "Supply: Supply, demand, and market equilibrium", "Market equilibrium and changes in equilibrium: Supply, demand, and market equilibrium"], "Unit 3: Elasticity": ["Price elasticity of demand: Elasticity", "Price elasticity of supply: Elasticity", "Income elasticity of demand and cross-price elasticity of demand: Elasticity"], "Unit 4: Consumer and producer surplus, market interventions, and international trade": ["Consumer and producer surplus: Consumer and producer surplus, market interventions, and international trade", "Market interventions and deadweight loss: Consumer and producer surplus, market interventions, and international trade", "International trade: Consumer and producer surplus, market interventions, and international trade"], "Unit 5: Consumer theory": ["Introduction to consumer theory: total utility and marginal utility: Consumer theory", "Utility maximization using marginal utility per dollar spent: Consumer theory", "Utility maximization with indifference curves: Consumer theory"], "Unit 6: Production decisions and economic profit": ["Introduction to production and costs: Production decisions and economic profit", "Production and costs in the short run: Production decisions and economic profit", "Production and costs in the long run: Production decisions and economic profit", "Types of profit: Production decisions and economic profit", "Profit maximization: Production decisions and economic profit", "Firm entry, exit, and the shut-down rule: Production decisions and economic profit"], "Unit 7: Forms of competition": ["Perfect competition: Forms of competition", "Monopoly: Forms of competition", "Price discrimination: Forms of competition", "Monopolistic competition: Forms of competition", "Oligopoly and game theory: Forms of competition"], "Unit 8: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Optimal choice of factors in perfectly competitive factor markets : Factor markets", "Choosing inputs when factor markets are monopolistically competitive: Factor markets"], "Unit 9: Market failure and the role of government": ["Externalities: Market failure and the role of government", "The four types of goods: private goods, public goods, common resources, and natural monopolies: Market failure and the role of government"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Microeconomics", "course_url": "/economics-finance-domain/ap-microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic Economic Concepts": ["Resource Allocation and Economic Systems: Basic Economic Concepts", "Production possibilities curve (PPC): Basic Economic Concepts", "Comparative advantage and trade: Basic Economic Concepts", "Cost-benefit analysis: Basic Economic Concepts", "Marginal analysis and consumer choice: Basic Economic Concepts"], "Unit 2: Supply and Demand": ["Demand: Supply and Demand", "Supply: Supply and Demand", "Price elasticity of demand: Supply and Demand", "Price elasticity of supply: Supply and Demand", "Other elasticities: Supply and Demand", "Market equilibrium and consumer and producer surplus: Supply and Demand", "Disequilibrium and changes in equilibrium: Supply and Demand", "The effects of government interventions in markets: Supply and Demand", "International trade and public policy: Supply and Demand"], "Unit 3: Production, cost, and the perfect competition model": ["The production function: Production, cost, and the perfect competition model", "Short-run production costs: Production, cost, and the perfect competition model", "Long-run production costs: Production, cost, and the perfect competition model", "Types of profit: Production, cost, and the perfect competition model", "Profit maximization: Production, cost, and the perfect competition model", "Firms\u2019 Short-run Decisions to Produce and Long-Run Decisions to Enter or Exit a Market: Production, cost, and the perfect competition model", "Perfect competition: Production, cost, and the perfect competition model"], "Unit 4: Imperfect competition": ["Introduction to imperfect competition: Imperfect competition", "Monopoly: Imperfect competition", "Price discrimination: Imperfect competition", "Monopolistic competition: Imperfect competition", "Oligopoly and game theory: Imperfect competition"], "Unit 5: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Profit-maximizing behavior in perfectly competitive factor markets: Factor markets", "Monopsonistic markets: Factor markets"], "Unit 6: Market failure and the role of government": ["Socially efficient and inefficient market outcomes: Market failure and the role of government", "Externalities: Market failure and the role of government", "Public and private goods: Market failure and the role of government", "The effects of government intervention in different market structures: Market failure and the role of government", "Inequality: Market failure and the role of government"]}}}}
{"course_title": "2nd grade", "course_url": "/ela/cc-2nd-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Fairy Tales Retold": ["Close reading: fiction; Little Red Riding Hood: Fairy Tales Retold", "Close reading: fiction; Granny the Hero: Fairy Tales Retold", "Applying vocabulary knowledge: Fairy Tales Retold", "Reading for understanding: drama: Fairy Tales Retold", "Reading for understanding: poetry and drama: Fairy Tales Retold"], "Unit 2: The Moon": ["Close reading: informational text: The Moon", "Close reading: fiction: The Moon", "Applying vocabulary knowledge: The Moon", "Reading for understanding: poetry: The Moon", "Reading for understanding: informational text: The Moon"], "Unit 3: Rural, Suburban, Urban": ["Close reading: informational text: Rural, Suburban, Urban", "Close reading: fiction: Rural, Suburban, Urban", "Applying vocabulary knowledge: Rural, Suburban, Urban", "Reading for understanding: informational text: Rural, Suburban, Urban", "Reading for understanding: fiction: Rural, Suburban, Urban"]}}}}
{"course_title": "3rd grade", "course_url": "/ela/cc-3rd-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Pets": ["Close reading: informational text: Pets", "Close reading: opinions: Pets", "Applying vocabulary knowledge: Pets", "Reading for understanding: fiction: Pets", "Reading for understanding: poetry: Pets"], "Unit 2: Homes": ["Close reading: informational text: Homes", "Close reading: fiction: Homes", "Applying vocabulary knowledge: Homes", "Reading for understanding: informational text: Homes", "Reading for understanding: fiction: Homes"], "Unit 3: Extreme Environments": ["Close reading: informational text: Extreme Environments", "Close reading: fiction: Extreme Environments", "Applying vocabulary knowledge: Extreme Environments", "Reading for understanding: informational text; Antarctica: Extreme Environments", "Reading for understanding: informational text; The Arctic Circle: Extreme Environments"]}}}}
{"course_title": "4th grade", "course_url": "/ela/cc-4th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Superheroes": ["Close reading: informational text: Superheroes", "Close reading: fiction: Superheroes", "Applying vocabulary knowledge: Superheroes", "Reading for understanding: drama and fiction: Superheroes", "Reading for understanding: informational text: Superheroes"], "Unit 2: Growth Mindset": ["Close reading: informational text: Growth Mindset", "Close reading: fiction: Growth Mindset", "Applying vocabulary knowledge: Growth Mindset", "Reading for understanding: fiction: Growth Mindset", "Reading for understanding: informational text: Growth Mindset"], "Unit 3: Journeys West": ["Close reading: informational text: Journeys West", "Close reading: poetry: Journeys West", "Applying vocabulary knowledge: Journeys West", "Reading for understanding: fiction and informational text: Journeys West", "Reading for understanding: informational text: Journeys West"]}}}}
{"course_title": "5th grade", "course_url": "/ela/cc-5th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Imaginative Worlds": ["Close reading: fiction: Imaginative Worlds", "Close reading: informational text: Imaginative Worlds", "Applying vocabulary knowledge: Imaginative Worlds", "Reading for understanding: fiction; The Boy in the Painting: Imaginative Worlds", "Reading for understanding: fiction; The Dawning: Imaginative Worlds"], "Unit 2: Athletes in Action": ["Close reading: informational text; Title IX: Athletes in Action", "Close reading: informational text; Fast and Female: Athletes in Action", "Applying vocabulary knowledge: Athletes in Action", "Reading for understanding: informational text: Athletes in Action", "Reading for understanding: poetry: Athletes in Action"], "Unit 3: Inventing Progress": ["Close reading: informational text: Inventing Progress", "Close reading: argumentative text: Inventing Progress", "Applying vocabulary knowledge: Inventing Progress", "Reading for understanding: fiction; The Ingenuity Fair: Inventing Progress", "Reading for understanding: fiction; Robots and Turtles: Inventing Progress"]}}}}
{"course_title": "6th grade", "course_url": "/ela/cc-6th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Banning Behavior": ["Close reading: informational text: Banning Behavior", "Close reading: argumentative text: Banning Behavior", "Applying vocabulary knowledge: Banning Behavior", "Reading for understanding: fiction: Banning Behavior", "Reading for understanding: drama: Banning Behavior"], "Unit 2: Identity": ["Close reading: informational text: Identity", "Close reading: fiction: Identity", "Applying vocabulary knowledge: Identity", "Reading for understanding: fiction: Identity", "Reading for understanding: drama: Identity"], "Unit 3: Ocean Conservation": ["Close reading: informational text: Ocean Conservation", "Close reading: poetry: Ocean Conservation", "Applying vocabulary knowledge: Ocean Conservation", "Reading for understanding: informational text; Boyan Slat: Ocean Conservation", "Reading for understanding: informational text; The Underwater Sea Train: Ocean Conservation"]}}}}
{"course_title": "7th grade", "course_url": "/ela/cc-7th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Trailblazing Women": ["Close reading: informational text: Trailblazing Women", "Close reading: speech and drama: Trailblazing Women", "Applying vocabulary knowledge: Trailblazing Women", "Reading for understanding: informational text; Mae Jemison: Trailblazing Women"], "Unit 2: Mysteries of the Past": ["Close reading: informational text: Mysteries of the Past", "Close reading: argumentative text: Mysteries of the Past", "Applying vocabulary knowledge: Mysteries of the Past", "Reading for understanding: informational text: Mysteries of the Past", "Reading for understanding: fiction: Mysteries of the Past"], "Unit 3: Living Tongues": ["Close reading: informational text: Living Tongues", "Close reading: poetry: Living Tongues", "Applying vocabulary knowledge: Living Tongues", "Reading for understanding: informational text: Living Tongues", "Reading for understanding: fiction: Living Tongues"]}}}}
{"course_title": "8th grade", "course_url": "/ela/cc-8th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Funny Business": ["Close reading: drama: Funny Business", "Close reading: informational text: Funny Business", "Applying vocabulary knowledge: Funny Business", "Reading for understanding: fiction; Use What You Have: Funny Business", "Reading for understanding: fiction; An Uncomfortable Bed: Funny Business"], "Unit 2: Obscuring the Truth": ["Close reading: informational text; Why Do We Lie?: Obscuring the Truth", "Close reading: informational text; The Science of Lying: Obscuring the Truth", "Applying vocabulary knowledge: Obscuring the Truth", "Reading for understanding: fiction; One Big Mess: Obscuring the Truth", "Reading for understanding: fiction; The Open Window: Obscuring the Truth"], "Unit 3: Crossing the Line": ["Close reading: informational text: Crossing the Line", "Close reading: fiction: Crossing the Line", "Applying vocabulary knowledge: Crossing the Line", "Reading for understanding: informational text: Crossing the Line", "Reading for understanding: fiction: Crossing the Line"]}}}}
{"course_title": "9th grade", "course_url": "/ela/cc-9th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Borders": ["Close reading: poetry: Borders", "Close reading: argumentative text: Borders", "Applying vocabulary knowledge: Borders", "Reading for understanding: informational text: Borders", "Reading for understanding: speech: Borders"], "Unit 2: Social Psychology": ["Close reading: informational text: Social Psychology", "Close reading: fiction: Social Psychology", "Applying vocabulary knowledge: Social Psychology", "Reading for understanding: informational text: Social Psychology", "Reading for understanding: fiction: Social Psychology"], "Unit 3: The Apocalypse": ["Close reading: informational text: The Apocalypse", "Close reading: fiction: The Apocalypse", "Applying vocabulary knowledge: The Apocalypse", "Reading for understanding: fiction; The War of the Worlds: The Apocalypse"]}}}}
{"course_title": "Grammar", "course_url": "/humanities/grammar", "page_contents": {"syllabus": {"topics": {"Usage and style: Unit test": ["Watch an introduction video2:462 minutes 46 seconds", "Start learning", "Start learning", "Watch an introduction video2:462 minutes 46 seconds"], "Unit 1: Parts of speech: the noun": ["Welcome to grammar!: Parts of speech: the noun", "Introduction to nouns: Parts of speech: the noun", "Types of nouns: Parts of speech: the noun", "Irregular plural nouns: base plurals and irregular endings: Parts of speech: the noun", "Irregular plural nouns: mutant and foreign plurals: Parts of speech: the noun"], "Unit 2: Parts of speech: the verb": ["Introduction to verbs: Parts of speech: the verb", "Verb tenses: Parts of speech: the verb", "Linking and helping verbs: Parts of speech: the verb", "Irregular verbs: Parts of speech: the verb", "Verb aspect: simple, progressive, and perfect: Parts of speech: the verb", "Verb aspect and modal verbs: Parts of speech: the verb"], "Unit 3: Parts of speech: the pronoun": ["Introduction to pronouns: Parts of speech: the pronoun", "Possessive and reflexive pronouns: Parts of speech: the pronoun", "Relative pronouns: Parts of speech: the pronoun", "Subject, object, person, and number: Parts of speech: the pronoun", "Indefinite pronouns, pronoun vagueness, and emphatic pronouns: Parts of speech: the pronoun"], "Unit 4: Parts of speech: the modifier": ["Introduction to adjectives and articles: Parts of speech: the modifier", "Introduction to adverbs: Parts of speech: the modifier", "Adjective order and commas with adjectives: Parts of speech: the modifier", "Comparative, superlative, intensifiers, and adverbs of degree: Parts of speech: the modifier"], "Unit 5: Parts of speech: the preposition and the conjunction": ["Introduction to prepositions: Parts of speech: the preposition and the conjunction", "Introduction to conjunctions: Parts of speech: the preposition and the conjunction", "Correlative conjunctions and starting sentences: Parts of speech: the preposition and the conjunction"], "Unit 6: Punctuation: the comma and the apostrophe": ["Introduction to commas: Punctuation: the comma and the apostrophe", "Commas in space and time: Punctuation: the comma and the apostrophe", "More ways to use commas: Punctuation: the comma and the apostrophe", "Apostrophes and contractions: Punctuation: the comma and the apostrophe", "Introduction to the possessive: Punctuation: the comma and the apostrophe", "\"Its\" versus \"it's\": Punctuation: the comma and the apostrophe"], "Unit 7: Punctuation: the colon, semicolon, and more": ["Introduction to colons: Punctuation: the colon, semicolon, and more", "Introduction to semicolons: Punctuation: the colon, semicolon, and more", "Formatting styles: Punctuation: the colon, semicolon, and more", "Hyphens, dashes, and ellipses: Punctuation: the colon, semicolon, and more"], "Unit 8: Syntax: sentences and clauses": ["Introduction to sentences: Syntax: sentences and clauses", "Types of sentences: Syntax: sentences and clauses", "Subjects and predicates: Syntax: sentences and clauses", "Phrases and clauses: Syntax: sentences and clauses"], "Unit 9: Syntax: conventions of standard English": ["Subject-verb agreement and pronoun-antecedent agreement : Syntax: conventions of standard English", "Fragments and run-ons: Syntax: conventions of standard English", "Dangling modifiers and parallel structure: Syntax: conventions of standard English"], "Unit 10: Usage and style": ["Frequently confused words: Usage and style", "Style!: Usage and style"]}}}}
{"course_title": "Growth mindset", "course_url": "/partner-content/learnstorm-growth-mindset-activities-us", "page_contents": {"syllabus": {"topics": {}}}}
{"course_title": "AP\u00ae\ufe0e/College Art History", "course_url": "/humanities/ap-art-history", "page_contents": {"syllabus": {"topics": {"Unit 1: Start here": ["Why art matters: Start here", "The language of art history: Start here", "Current issues in art history: Start here"], "Unit 4: Ancient Mediterranean: 3500 B.C.E.-300 C.E.": ["Ancient Greece : Ancient Mediterranean: 3500 B.C.E.-300 C.E.", "Ancient Rome: Ancient Mediterranean: 3500 B.C.E.-300 C.E."]}}}}
{"course_title": "Macroeconomics", "course_url": "/economics-finance-domain/macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Markets: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["Gross Domestic Product: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal v. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The market for loanable funds: Financial sector", "Interest rates and the time value of money: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Real interest rates and international capital flows: Open economy: international trade and finance"], "Unit 7: Keynesian approaches and IS-LM": ["The consumption function: Keynesian approaches and IS-LM", "The Keynesian cross: Keynesian approaches and IS-LM", "IS-LM: Keynesian approaches and IS-LM", "Keynesian economics and its critiques: Keynesian approaches and IS-LM"], "Analysis of income inequality in the United States (in partnership with the New York Times): Contemporary macroeconomic issues": ["National income and inequality: Contemporary macroeconomic issues", "The 2008 Financial Crisis: Contemporary macroeconomic issues"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Macroeconomics", "course_url": "/economics-finance-domain/ap-macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Market equilibrium, disequilibrium, and changes in equilibrium: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["The Circular Flow and GDP: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Price Indices and inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal vs. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The Market for loanable funds: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies", "Public policy and economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Changes in the foreign exchange markets and net exports: Open economy: international trade and finance", "Real Interest Rates and International Capital Flows: Open economy: international trade and finance"]}}}}
{"course_title": "Microeconomics", "course_url": "/economics-finance-domain/microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic economic concepts": ["Introduction to economics: Basic economic concepts", "Economic systems: Basic economic concepts", "Production possibilities frontier: Basic economic concepts", "Comparative advantage and the terms of trade : Basic economic concepts"], "Unit 2: Supply, demand, and market equilibrium": ["Demand: Supply, demand, and market equilibrium", "Supply: Supply, demand, and market equilibrium", "Market equilibrium and changes in equilibrium: Supply, demand, and market equilibrium"], "Unit 3: Elasticity": ["Price elasticity of demand: Elasticity", "Price elasticity of supply: Elasticity", "Income elasticity of demand and cross-price elasticity of demand: Elasticity"], "Unit 4: Consumer and producer surplus, market interventions, and international trade": ["Consumer and producer surplus: Consumer and producer surplus, market interventions, and international trade", "Market interventions and deadweight loss: Consumer and producer surplus, market interventions, and international trade", "International trade: Consumer and producer surplus, market interventions, and international trade"], "Unit 5: Consumer theory": ["Introduction to consumer theory: total utility and marginal utility: Consumer theory", "Utility maximization using marginal utility per dollar spent: Consumer theory", "Utility maximization with indifference curves: Consumer theory"], "Unit 6: Production decisions and economic profit": ["Introduction to production and costs: Production decisions and economic profit", "Production and costs in the short run: Production decisions and economic profit", "Production and costs in the long run: Production decisions and economic profit", "Types of profit: Production decisions and economic profit", "Profit maximization: Production decisions and economic profit", "Firm entry, exit, and the shut-down rule: Production decisions and economic profit"], "Unit 7: Forms of competition": ["Perfect competition: Forms of competition", "Monopoly: Forms of competition", "Price discrimination: Forms of competition", "Monopolistic competition: Forms of competition", "Oligopoly and game theory: Forms of competition"], "Unit 8: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Optimal choice of factors in perfectly competitive factor markets : Factor markets", "Choosing inputs when factor markets are monopolistically competitive: Factor markets"], "Unit 9: Market failure and the role of government": ["Externalities: Market failure and the role of government", "The four types of goods: private goods, public goods, common resources, and natural monopolies: Market failure and the role of government"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Microeconomics", "course_url": "/economics-finance-domain/ap-microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic Economic Concepts": ["Resource Allocation and Economic Systems: Basic Economic Concepts", "Production possibilities curve (PPC): Basic Economic Concepts", "Comparative advantage and trade: Basic Economic Concepts", "Cost-benefit analysis: Basic Economic Concepts", "Marginal analysis and consumer choice: Basic Economic Concepts"], "Unit 2: Supply and Demand": ["Demand: Supply and Demand", "Supply: Supply and Demand", "Price elasticity of demand: Supply and Demand", "Price elasticity of supply: Supply and Demand", "Other elasticities: Supply and Demand", "Market equilibrium and consumer and producer surplus: Supply and Demand", "Disequilibrium and changes in equilibrium: Supply and Demand", "The effects of government interventions in markets: Supply and Demand", "International trade and public policy: Supply and Demand"], "Unit 3: Production, cost, and the perfect competition model": ["The production function: Production, cost, and the perfect competition model", "Short-run production costs: Production, cost, and the perfect competition model", "Long-run production costs: Production, cost, and the perfect competition model", "Types of profit: Production, cost, and the perfect competition model", "Profit maximization: Production, cost, and the perfect competition model", "Firms\u2019 Short-run Decisions to Produce and Long-Run Decisions to Enter or Exit a Market: Production, cost, and the perfect competition model", "Perfect competition: Production, cost, and the perfect competition model"], "Unit 4: Imperfect competition": ["Introduction to imperfect competition: Imperfect competition", "Monopoly: Imperfect competition", "Price discrimination: Imperfect competition", "Monopolistic competition: Imperfect competition", "Oligopoly and game theory: Imperfect competition"], "Unit 5: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Profit-maximizing behavior in perfectly competitive factor markets: Factor markets", "Monopsonistic markets: Factor markets"], "Unit 6: Market failure and the role of government": ["Socially efficient and inefficient market outcomes: Market failure and the role of government", "Externalities: Market failure and the role of government", "Public and private goods: Market failure and the role of government", "The effects of government intervention in different market structures: Market failure and the role of government", "Inequality: Market failure and the role of government"]}}}}
{"course_title": "2nd grade", "course_url": "/ela/cc-2nd-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Fairy Tales Retold": ["Close reading: fiction; Little Red Riding Hood: Fairy Tales Retold", "Close reading: fiction; Granny the Hero: Fairy Tales Retold", "Applying vocabulary knowledge: Fairy Tales Retold", "Reading for understanding: drama: Fairy Tales Retold", "Reading for understanding: poetry and drama: Fairy Tales Retold"], "Unit 2: The Moon": ["Close reading: informational text: The Moon", "Close reading: fiction: The Moon", "Applying vocabulary knowledge: The Moon", "Reading for understanding: poetry: The Moon", "Reading for understanding: informational text: The Moon"], "Unit 3: Rural, Suburban, Urban": ["Close reading: informational text: Rural, Suburban, Urban", "Close reading: fiction: Rural, Suburban, Urban", "Applying vocabulary knowledge: Rural, Suburban, Urban", "Reading for understanding: informational text: Rural, Suburban, Urban", "Reading for understanding: fiction: Rural, Suburban, Urban"]}}}}
{"course_title": "3rd grade", "course_url": "/ela/cc-3rd-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Pets": ["Close reading: informational text: Pets", "Close reading: opinions: Pets", "Applying vocabulary knowledge: Pets", "Reading for understanding: fiction: Pets", "Reading for understanding: poetry: Pets"], "Unit 2: Homes": ["Close reading: informational text: Homes", "Close reading: fiction: Homes", "Applying vocabulary knowledge: Homes", "Reading for understanding: informational text: Homes", "Reading for understanding: fiction: Homes"], "Unit 3: Extreme Environments": ["Close reading: informational text: Extreme Environments", "Close reading: fiction: Extreme Environments", "Applying vocabulary knowledge: Extreme Environments", "Reading for understanding: informational text; Antarctica: Extreme Environments", "Reading for understanding: informational text; The Arctic Circle: Extreme Environments"]}}}}
{"course_title": "4th grade", "course_url": "/ela/cc-4th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Superheroes": ["Close reading: informational text: Superheroes", "Close reading: fiction: Superheroes", "Applying vocabulary knowledge: Superheroes", "Reading for understanding: drama and fiction: Superheroes", "Reading for understanding: informational text: Superheroes"], "Unit 2: Growth Mindset": ["Close reading: informational text: Growth Mindset", "Close reading: fiction: Growth Mindset", "Applying vocabulary knowledge: Growth Mindset", "Reading for understanding: fiction: Growth Mindset", "Reading for understanding: informational text: Growth Mindset"], "Unit 3: Journeys West": ["Close reading: informational text: Journeys West", "Close reading: poetry: Journeys West", "Applying vocabulary knowledge: Journeys West", "Reading for understanding: fiction and informational text: Journeys West", "Reading for understanding: informational text: Journeys West"]}}}}
{"course_title": "5th grade", "course_url": "/ela/cc-5th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Imaginative Worlds": ["Close reading: fiction: Imaginative Worlds", "Close reading: informational text: Imaginative Worlds", "Applying vocabulary knowledge: Imaginative Worlds", "Reading for understanding: fiction; The Boy in the Painting: Imaginative Worlds", "Reading for understanding: fiction; The Dawning: Imaginative Worlds"], "Unit 2: Athletes in Action": ["Close reading: informational text; Title IX: Athletes in Action", "Close reading: informational text; Fast and Female: Athletes in Action", "Applying vocabulary knowledge: Athletes in Action", "Reading for understanding: informational text: Athletes in Action", "Reading for understanding: poetry: Athletes in Action"], "Unit 3: Inventing Progress": ["Close reading: informational text: Inventing Progress", "Close reading: argumentative text: Inventing Progress", "Applying vocabulary knowledge: Inventing Progress", "Reading for understanding: fiction; The Ingenuity Fair: Inventing Progress", "Reading for understanding: fiction; Robots and Turtles: Inventing Progress"]}}}}
{"course_title": "6th grade", "course_url": "/ela/cc-6th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Banning Behavior": ["Close reading: informational text: Banning Behavior", "Close reading: argumentative text: Banning Behavior", "Applying vocabulary knowledge: Banning Behavior", "Reading for understanding: fiction: Banning Behavior", "Reading for understanding: drama: Banning Behavior"], "Unit 2: Identity": ["Close reading: informational text: Identity", "Close reading: fiction: Identity", "Applying vocabulary knowledge: Identity", "Reading for understanding: fiction: Identity", "Reading for understanding: drama: Identity"], "Unit 3: Ocean Conservation": ["Close reading: informational text: Ocean Conservation", "Close reading: poetry: Ocean Conservation", "Applying vocabulary knowledge: Ocean Conservation", "Reading for understanding: informational text; Boyan Slat: Ocean Conservation", "Reading for understanding: informational text; The Underwater Sea Train: Ocean Conservation"]}}}}
{"course_title": "7th grade", "course_url": "/ela/cc-7th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Trailblazing Women": ["Close reading: informational text: Trailblazing Women", "Close reading: speech and drama: Trailblazing Women", "Applying vocabulary knowledge: Trailblazing Women", "Reading for understanding: informational text; Mae Jemison: Trailblazing Women"], "Unit 2: Mysteries of the Past": ["Close reading: informational text: Mysteries of the Past", "Close reading: argumentative text: Mysteries of the Past", "Applying vocabulary knowledge: Mysteries of the Past", "Reading for understanding: informational text: Mysteries of the Past", "Reading for understanding: fiction: Mysteries of the Past"], "Unit 3: Living Tongues": ["Close reading: informational text: Living Tongues", "Close reading: poetry: Living Tongues", "Applying vocabulary knowledge: Living Tongues", "Reading for understanding: informational text: Living Tongues", "Reading for understanding: fiction: Living Tongues"]}}}}
{"course_title": "8th grade", "course_url": "/ela/cc-8th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Funny Business": ["Close reading: drama: Funny Business", "Close reading: informational text: Funny Business", "Applying vocabulary knowledge: Funny Business", "Reading for understanding: fiction; Use What You Have: Funny Business", "Reading for understanding: fiction; An Uncomfortable Bed: Funny Business"], "Unit 2: Obscuring the Truth": ["Close reading: informational text; Why Do We Lie?: Obscuring the Truth", "Close reading: informational text; The Science of Lying: Obscuring the Truth", "Applying vocabulary knowledge: Obscuring the Truth", "Reading for understanding: fiction; One Big Mess: Obscuring the Truth", "Reading for understanding: fiction; The Open Window: Obscuring the Truth"], "Unit 3: Crossing the Line": ["Close reading: informational text: Crossing the Line", "Close reading: fiction: Crossing the Line", "Applying vocabulary knowledge: Crossing the Line", "Reading for understanding: informational text: Crossing the Line", "Reading for understanding: fiction: Crossing the Line"]}}}}
{"course_title": "9th grade", "course_url": "/ela/cc-9th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Borders": ["Close reading: poetry: Borders", "Close reading: argumentative text: Borders", "Applying vocabulary knowledge: Borders", "Reading for understanding: informational text: Borders", "Reading for understanding: speech: Borders"], "Unit 2: Social Psychology": ["Close reading: informational text: Social Psychology", "Close reading: fiction: Social Psychology", "Applying vocabulary knowledge: Social Psychology", "Reading for understanding: informational text: Social Psychology", "Reading for understanding: fiction: Social Psychology"], "Unit 3: The Apocalypse": ["Close reading: informational text: The Apocalypse", "Close reading: fiction: The Apocalypse", "Applying vocabulary knowledge: The Apocalypse", "Reading for understanding: fiction; The War of the Worlds: The Apocalypse"]}}}}
{"course_title": "Grammar", "course_url": "/humanities/grammar", "page_contents": {"syllabus": {"topics": {"Usage and style: Unit test": ["Watch an introduction video2:462 minutes 46 seconds", "Start learning", "Start learning", "Watch an introduction video2:462 minutes 46 seconds"], "Unit 1: Parts of speech: the noun": ["Welcome to grammar!: Parts of speech: the noun", "Introduction to nouns: Parts of speech: the noun", "Types of nouns: Parts of speech: the noun", "Irregular plural nouns: base plurals and irregular endings: Parts of speech: the noun", "Irregular plural nouns: mutant and foreign plurals: Parts of speech: the noun"], "Unit 2: Parts of speech: the verb": ["Introduction to verbs: Parts of speech: the verb", "Verb tenses: Parts of speech: the verb", "Linking and helping verbs: Parts of speech: the verb", "Irregular verbs: Parts of speech: the verb", "Verb aspect: simple, progressive, and perfect: Parts of speech: the verb", "Verb aspect and modal verbs: Parts of speech: the verb"], "Unit 3: Parts of speech: the pronoun": ["Introduction to pronouns: Parts of speech: the pronoun", "Possessive and reflexive pronouns: Parts of speech: the pronoun", "Relative pronouns: Parts of speech: the pronoun", "Subject, object, person, and number: Parts of speech: the pronoun", "Indefinite pronouns, pronoun vagueness, and emphatic pronouns: Parts of speech: the pronoun"], "Unit 4: Parts of speech: the modifier": ["Introduction to adjectives and articles: Parts of speech: the modifier", "Introduction to adverbs: Parts of speech: the modifier", "Adjective order and commas with adjectives: Parts of speech: the modifier", "Comparative, superlative, intensifiers, and adverbs of degree: Parts of speech: the modifier"], "Unit 5: Parts of speech: the preposition and the conjunction": ["Introduction to prepositions: Parts of speech: the preposition and the conjunction", "Introduction to conjunctions: Parts of speech: the preposition and the conjunction", "Correlative conjunctions and starting sentences: Parts of speech: the preposition and the conjunction"], "Unit 6: Punctuation: the comma and the apostrophe": ["Introduction to commas: Punctuation: the comma and the apostrophe", "Commas in space and time: Punctuation: the comma and the apostrophe", "More ways to use commas: Punctuation: the comma and the apostrophe", "Apostrophes and contractions: Punctuation: the comma and the apostrophe", "Introduction to the possessive: Punctuation: the comma and the apostrophe", "\"Its\" versus \"it's\": Punctuation: the comma and the apostrophe"], "Unit 7: Punctuation: the colon, semicolon, and more": ["Introduction to colons: Punctuation: the colon, semicolon, and more", "Introduction to semicolons: Punctuation: the colon, semicolon, and more", "Formatting styles: Punctuation: the colon, semicolon, and more", "Hyphens, dashes, and ellipses: Punctuation: the colon, semicolon, and more"], "Unit 8: Syntax: sentences and clauses": ["Introduction to sentences: Syntax: sentences and clauses", "Types of sentences: Syntax: sentences and clauses", "Subjects and predicates: Syntax: sentences and clauses", "Phrases and clauses: Syntax: sentences and clauses"], "Unit 9: Syntax: conventions of standard English": ["Subject-verb agreement and pronoun-antecedent agreement : Syntax: conventions of standard English", "Fragments and run-ons: Syntax: conventions of standard English", "Dangling modifiers and parallel structure: Syntax: conventions of standard English"], "Unit 10: Usage and style": ["Frequently confused words: Usage and style", "Style!: Usage and style"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Art History", "course_url": "/humanities/ap-art-history", "page_contents": {"syllabus": {"topics": {"Unit 1: Start here": ["Why art matters: Start here", "The language of art history: Start here", "Current issues in art history: Start here"], "Unit 4: Ancient Mediterranean: 3500 B.C.E.-300 C.E.": ["Ancient Greece : Ancient Mediterranean: 3500 B.C.E.-300 C.E.", "Ancient Rome: Ancient Mediterranean: 3500 B.C.E.-300 C.E."]}}}}
{"course_title": "Macroeconomics", "course_url": "/economics-finance-domain/macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Markets: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["Gross Domestic Product: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal v. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The market for loanable funds: Financial sector", "Interest rates and the time value of money: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Real interest rates and international capital flows: Open economy: international trade and finance"], "Unit 7: Keynesian approaches and IS-LM": ["The consumption function: Keynesian approaches and IS-LM", "The Keynesian cross: Keynesian approaches and IS-LM", "IS-LM: Keynesian approaches and IS-LM", "Keynesian economics and its critiques: Keynesian approaches and IS-LM"], "Analysis of income inequality in the United States (in partnership with the New York Times): Contemporary macroeconomic issues": ["National income and inequality: Contemporary macroeconomic issues", "The 2008 Financial Crisis: Contemporary macroeconomic issues"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Macroeconomics", "course_url": "/economics-finance-domain/ap-macroeconomics", "page_contents": {"syllabus": {"topics": {"Opportunity cost and the Production Possibilities Curve: Basic economics concepts": ["Comparative advantage and the gains from trade: Basic economics concepts", "Demand: Basic economics concepts", "Supply: Basic economics concepts", "Market equilibrium, disequilibrium, and changes in equilibrium: Basic economics concepts"], "Unit 2: Economic indicators and the business cycle": ["The Circular Flow and GDP: Economic indicators and the business cycle", "Limitations of GDP: Economic indicators and the business cycle", "Unemployment: Economic indicators and the business cycle", "Price Indices and inflation: Economic indicators and the business cycle", "Costs of Inflation: Economic indicators and the business cycle", "Real vs. nominal GDP: Economic indicators and the business cycle", "Business cycles: Economic indicators and the business cycle"], "Unit 3: National income and price determination": ["Aggregate demand: National income and price determination", "Multipliers: National income and price determination", "Short-run aggregate supply: National income and price determination", "Long-run aggregate supply: National income and price determination", "Equilibrium in the AD-AS Model: National income and price determination", "Changes in the AD-AS model in the short run: National income and price determination", "Long run self-adjustment: National income and price determination", "Fiscal policy: National income and price determination", "Automatic stabilizers: National income and price determination"], "Unit 4: Financial sector": ["Financial assets: Financial sector", "Nominal vs. real interest rates: Financial sector", "Definition, measurement, and functions of money: Financial sector", "Banking and the expansion of the money supply: Financial sector", "The money market: Financial sector", "Monetary policy: Financial sector", "The Market for loanable funds: Financial sector"], "Unit 5: Long-run consequences of stabilization policies": ["Fiscal and Monetary Policy Actions in the Short Run: Long-run consequences of stabilization policies", "The Phillips curve: Long-run consequences of stabilization policies", "Money growth and inflation: Long-run consequences of stabilization policies", "Crowding out: Long-run consequences of stabilization policies", "Deficits and debts: Long-run consequences of stabilization policies", "Economic growth: Long-run consequences of stabilization policies", "Public policy and economic growth: Long-run consequences of stabilization policies"], "Unit 6: Open economy: international trade and finance": ["The balance of payments: Open economy: international trade and finance", "Exchange rates: Open economy: international trade and finance", "The foreign exchange market: Open economy: international trade and finance", "Effect of changes in policies and economic conditions on the foreign exchange market: Open economy: international trade and finance", "Changes in the foreign exchange markets and net exports: Open economy: international trade and finance", "Real Interest Rates and International Capital Flows: Open economy: international trade and finance"]}}}}
{"course_title": "Microeconomics", "course_url": "/economics-finance-domain/microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic economic concepts": ["Introduction to economics: Basic economic concepts", "Economic systems: Basic economic concepts", "Production possibilities frontier: Basic economic concepts", "Comparative advantage and the terms of trade : Basic economic concepts"], "Unit 2: Supply, demand, and market equilibrium": ["Demand: Supply, demand, and market equilibrium", "Supply: Supply, demand, and market equilibrium", "Market equilibrium and changes in equilibrium: Supply, demand, and market equilibrium"], "Unit 3: Elasticity": ["Price elasticity of demand: Elasticity", "Price elasticity of supply: Elasticity", "Income elasticity of demand and cross-price elasticity of demand: Elasticity"], "Unit 4: Consumer and producer surplus, market interventions, and international trade": ["Consumer and producer surplus: Consumer and producer surplus, market interventions, and international trade", "Market interventions and deadweight loss: Consumer and producer surplus, market interventions, and international trade", "International trade: Consumer and producer surplus, market interventions, and international trade"], "Unit 5: Consumer theory": ["Introduction to consumer theory: total utility and marginal utility: Consumer theory", "Utility maximization using marginal utility per dollar spent: Consumer theory", "Utility maximization with indifference curves: Consumer theory"], "Unit 6: Production decisions and economic profit": ["Introduction to production and costs: Production decisions and economic profit", "Production and costs in the short run: Production decisions and economic profit", "Production and costs in the long run: Production decisions and economic profit", "Types of profit: Production decisions and economic profit", "Profit maximization: Production decisions and economic profit", "Firm entry, exit, and the shut-down rule: Production decisions and economic profit"], "Unit 7: Forms of competition": ["Perfect competition: Forms of competition", "Monopoly: Forms of competition", "Price discrimination: Forms of competition", "Monopolistic competition: Forms of competition", "Oligopoly and game theory: Forms of competition"], "Unit 8: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Optimal choice of factors in perfectly competitive factor markets : Factor markets", "Choosing inputs when factor markets are monopolistically competitive: Factor markets"], "Unit 9: Market failure and the role of government": ["Externalities: Market failure and the role of government", "The four types of goods: private goods, public goods, common resources, and natural monopolies: Market failure and the role of government"]}}}}
{"course_title": "AP\u00ae\ufe0e/College Microeconomics", "course_url": "/economics-finance-domain/ap-microeconomics", "page_contents": {"syllabus": {"topics": {"Unit 1: Basic Economic Concepts": ["Resource Allocation and Economic Systems: Basic Economic Concepts", "Production possibilities curve (PPC): Basic Economic Concepts", "Comparative advantage and trade: Basic Economic Concepts", "Cost-benefit analysis: Basic Economic Concepts", "Marginal analysis and consumer choice: Basic Economic Concepts"], "Unit 2: Supply and Demand": ["Demand: Supply and Demand", "Supply: Supply and Demand", "Price elasticity of demand: Supply and Demand", "Price elasticity of supply: Supply and Demand", "Other elasticities: Supply and Demand", "Market equilibrium and consumer and producer surplus: Supply and Demand", "Disequilibrium and changes in equilibrium: Supply and Demand", "The effects of government interventions in markets: Supply and Demand", "International trade and public policy: Supply and Demand"], "Unit 3: Production, cost, and the perfect competition model": ["The production function: Production, cost, and the perfect competition model", "Short-run production costs: Production, cost, and the perfect competition model", "Long-run production costs: Production, cost, and the perfect competition model", "Types of profit: Production, cost, and the perfect competition model", "Profit maximization: Production, cost, and the perfect competition model", "Firms\u2019 Short-run Decisions to Produce and Long-Run Decisions to Enter or Exit a Market: Production, cost, and the perfect competition model", "Perfect competition: Production, cost, and the perfect competition model"], "Unit 4: Imperfect competition": ["Introduction to imperfect competition: Imperfect competition", "Monopoly: Imperfect competition", "Price discrimination: Imperfect competition", "Monopolistic competition: Imperfect competition", "Oligopoly and game theory: Imperfect competition"], "Unit 5: Factor markets": ["Introduction to factor markets: Factor markets", "Changes in factor demand and supply: Factor markets", "Profit-maximizing behavior in perfectly competitive factor markets: Factor markets", "Monopsonistic markets: Factor markets"], "Unit 6: Market failure and the role of government": ["Socially efficient and inefficient market outcomes: Market failure and the role of government", "Externalities: Market failure and the role of government", "Public and private goods: Market failure and the role of government", "The effects of government intervention in different market structures: Market failure and the role of government", "Inequality: Market failure and the role of government"]}}}}
{"course_title": "2nd grade", "course_url": "/ela/cc-2nd-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Fairy Tales Retold": ["Close reading: fiction; Little Red Riding Hood: Fairy Tales Retold", "Close reading: fiction; Granny the Hero: Fairy Tales Retold", "Applying vocabulary knowledge: Fairy Tales Retold", "Reading for understanding: drama: Fairy Tales Retold", "Reading for understanding: poetry and drama: Fairy Tales Retold"], "Unit 2: The Moon": ["Close reading: informational text: The Moon", "Close reading: fiction: The Moon", "Applying vocabulary knowledge: The Moon", "Reading for understanding: poetry: The Moon", "Reading for understanding: informational text: The Moon"], "Unit 3: Rural, Suburban, Urban": ["Close reading: informational text: Rural, Suburban, Urban", "Close reading: fiction: Rural, Suburban, Urban", "Applying vocabulary knowledge: Rural, Suburban, Urban", "Reading for understanding: informational text: Rural, Suburban, Urban", "Reading for understanding: fiction: Rural, Suburban, Urban"]}}}}
{"course_title": "3rd grade", "course_url": "/ela/cc-3rd-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Pets": ["Close reading: informational text: Pets", "Close reading: opinions: Pets", "Applying vocabulary knowledge: Pets", "Reading for understanding: fiction: Pets", "Reading for understanding: poetry: Pets"], "Unit 2: Homes": ["Close reading: informational text: Homes", "Close reading: fiction: Homes", "Applying vocabulary knowledge: Homes", "Reading for understanding: informational text: Homes", "Reading for understanding: fiction: Homes"], "Unit 3: Extreme Environments": ["Close reading: informational text: Extreme Environments", "Close reading: fiction: Extreme Environments", "Applying vocabulary knowledge: Extreme Environments", "Reading for understanding: informational text; Antarctica: Extreme Environments", "Reading for understanding: informational text; The Arctic Circle: Extreme Environments"]}}}}
{"course_title": "4th grade", "course_url": "/ela/cc-4th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Superheroes": ["Close reading: informational text: Superheroes", "Close reading: fiction: Superheroes", "Applying vocabulary knowledge: Superheroes", "Reading for understanding: drama and fiction: Superheroes", "Reading for understanding: informational text: Superheroes"], "Unit 2: Growth Mindset": ["Close reading: informational text: Growth Mindset", "Close reading: fiction: Growth Mindset", "Applying vocabulary knowledge: Growth Mindset", "Reading for understanding: fiction: Growth Mindset", "Reading for understanding: informational text: Growth Mindset"], "Unit 3: Journeys West": ["Close reading: informational text: Journeys West", "Close reading: poetry: Journeys West", "Applying vocabulary knowledge: Journeys West", "Reading for understanding: fiction and informational text: Journeys West", "Reading for understanding: informational text: Journeys West"]}}}}
{"course_title": "5th grade", "course_url": "/ela/cc-5th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Imaginative Worlds": ["Close reading: fiction: Imaginative Worlds", "Close reading: informational text: Imaginative Worlds", "Applying vocabulary knowledge: Imaginative Worlds", "Reading for understanding: fiction; The Boy in the Painting: Imaginative Worlds", "Reading for understanding: fiction; The Dawning: Imaginative Worlds"], "Unit 2: Athletes in Action": ["Close reading: informational text; Title IX: Athletes in Action", "Close reading: informational text; Fast and Female: Athletes in Action", "Applying vocabulary knowledge: Athletes in Action", "Reading for understanding: informational text: Athletes in Action", "Reading for understanding: poetry: Athletes in Action"], "Unit 3: Inventing Progress": ["Close reading: informational text: Inventing Progress", "Close reading: argumentative text: Inventing Progress", "Applying vocabulary knowledge: Inventing Progress", "Reading for understanding: fiction; The Ingenuity Fair: Inventing Progress", "Reading for understanding: fiction; Robots and Turtles: Inventing Progress"]}}}}
{"course_title": "6th grade", "course_url": "/ela/cc-6th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Banning Behavior": ["Close reading: informational text: Banning Behavior", "Close reading: argumentative text: Banning Behavior", "Applying vocabulary knowledge: Banning Behavior", "Reading for understanding: fiction: Banning Behavior", "Reading for understanding: drama: Banning Behavior"], "Unit 2: Identity": ["Close reading: informational text: Identity", "Close reading: fiction: Identity", "Applying vocabulary knowledge: Identity", "Reading for understanding: fiction: Identity", "Reading for understanding: drama: Identity"], "Unit 3: Ocean Conservation": ["Close reading: informational text: Ocean Conservation", "Close reading: poetry: Ocean Conservation", "Applying vocabulary knowledge: Ocean Conservation", "Reading for understanding: informational text; Boyan Slat: Ocean Conservation", "Reading for understanding: informational text; The Underwater Sea Train: Ocean Conservation"]}}}}
{"course_title": "7th grade", "course_url": "/ela/cc-7th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Trailblazing Women": ["Close reading: informational text: Trailblazing Women", "Close reading: speech and drama: Trailblazing Women", "Applying vocabulary knowledge: Trailblazing Women", "Reading for understanding: informational text; Mae Jemison: Trailblazing Women"], "Unit 2: Mysteries of the Past": ["Close reading: informational text: Mysteries of the Past", "Close reading: argumentative text: Mysteries of the Past", "Applying vocabulary knowledge: Mysteries of the Past", "Reading for understanding: informational text: Mysteries of the Past", "Reading for understanding: fiction: Mysteries of the Past"], "Unit 3: Living Tongues": ["Close reading: informational text: Living Tongues", "Close reading: poetry: Living Tongues", "Applying vocabulary knowledge: Living Tongues", "Reading for understanding: informational text: Living Tongues", "Reading for understanding: fiction: Living Tongues"]}}}}
{"course_title": "8th grade", "course_url": "/ela/cc-8th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Funny Business": ["Close reading: drama: Funny Business", "Close reading: informational text: Funny Business", "Applying vocabulary knowledge: Funny Business", "Reading for understanding: fiction; Use What You Have: Funny Business", "Reading for understanding: fiction; An Uncomfortable Bed: Funny Business"], "Unit 2: Obscuring the Truth": ["Close reading: informational text; Why Do We Lie?: Obscuring the Truth", "Close reading: informational text; The Science of Lying: Obscuring the Truth", "Applying vocabulary knowledge: Obscuring the Truth", "Reading for understanding: fiction; One Big Mess: Obscuring the Truth", "Reading for understanding: fiction; The Open Window: Obscuring the Truth"], "Unit 3: Crossing the Line": ["Close reading: informational text: Crossing the Line", "Close reading: fiction: Crossing the Line", "Applying vocabulary knowledge: Crossing the Line", "Reading for understanding: informational text: Crossing the Line", "Reading for understanding: fiction: Crossing the Line"]}}}}
{"course_title": "9th grade", "course_url": "/ela/cc-9th-reading-vocab", "page_contents": {"syllabus": {"topics": {"Unit 1: Borders": ["Close reading: poetry: Borders", "Close reading: argumentative text: Borders", "Applying vocabulary knowledge: Borders", "Reading for understanding: informational text: Borders", "Reading for understanding: speech: Borders"], "Unit 2: Social Psychology": ["Close reading: informational text: Social Psychology", "Close reading: fiction: Social Psychology", "Applying vocabulary knowledge: Social Psychology", "Reading for understanding: informational text: Social Psychology", "Reading for understanding: fiction: Social Psychology"], "Unit 3: The Apocalypse": ["Close reading: informational text: The Apocalypse", "Close reading: fiction: The Apocalypse", "Applying vocabulary knowledge: The Apocalypse", "Reading for understanding: fiction; The War of the Worlds: The Apocalypse"]}}}}
{"course_title": "Grammar", "course_url": "/humanities/grammar", "page_contents": {"syllabus": {"topics": {"Usage and style: Unit test": ["Watch an introduction video2:462 minutes 46 seconds", "Start learning", "Start learning", "Watch an introduction video2:462 minutes 46 seconds"], "Unit 1: Parts of speech: the noun": ["Welcome to grammar!: Parts of speech: the noun", "Introduction to nouns: Parts of speech: the noun", "Types of nouns: Parts of speech: the noun", "Irregular plural nouns: base plurals and irregular endings: Parts of speech: the noun", "Irregular plural nouns: mutant and foreign plurals: Parts of speech: the noun"], "Unit 2: Parts of speech: the verb": ["Introduction to verbs: Parts of speech: the verb", "Verb tenses: Parts of speech: the verb", "Linking and helping verbs: Parts of speech: the verb", "Irregular verbs: Parts of speech: the verb", "Verb aspect: simple, progressive, and perfect: Parts of speech: the verb", "Verb aspect and modal verbs: Parts of speech: the verb"], "Unit 3: Parts of speech: the pronoun": ["Introduction to pronouns: Parts of speech: the pronoun", "Possessive and reflexive pronouns: Parts of speech: the pronoun", "Relative pronouns: Parts of speech: the pronoun", "Subject, object, person, and number: Parts of speech: the pronoun", "Indefinite pronouns, pronoun vagueness, and emphatic pronouns: Parts of speech: the pronoun"], "Unit 4: Parts of speech: the modifier": ["Introduction to adjectives and articles: Parts of speech: the modifier", "Introduction to adverbs: Parts of speech: the modifier", "Adjective order and commas with adjectives: Parts of speech: the modifier", "Comparative, superlative, intensifiers, and adverbs of degree: Parts of speech: the modifier"], "Unit 5: Parts of speech: the preposition and the conjunction": ["Introduction to prepositions: Parts of speech: the preposition and the conjunction", "Introduction to conjunctions: Parts of speech: the preposition and the conjunction", "Correlative conjunctions and starting sentences: Parts of speech: the preposition and the conjunction"], "Unit 6: Punctuation: the comma and the apostrophe": ["Introduction to commas: Punctuation: the comma and the apostrophe", "Commas in space and time: Punctuation: the comma and the apostrophe", "More ways to use commas: Punctuation: the comma and the apostrophe", "Apostrophes and contractions: Punctuation: the comma and the apostrophe", "Introduction to the possessive: Punctuation: the comma and the apostrophe", "\"Its\" versus \"it's\": Punctuation: the comma and the apostrophe"], "Unit 7: Punctuation: the colon, semicolon, and more": ["Introduction to colons: Punctuation: the colon, semicolon, and more", "Introduction to semicolons: Punctuation: the colon, semicolon, and more", "Formatting styles: Punctuation: the colon, semicolon, and more", "Hyphens, dashes, and ellipses: Punctuation: the colon, semicolon, and more"], "Unit 8: Syntax: sentences and clauses": ["Introduction to sentences: Syntax: sentences and clauses", "Types of sentences: Syntax: sentences and clauses", "Subjects and predicates: Syntax: sentences and clauses", "Phrases and clauses: Syntax: sentences and clauses"], "Unit 9: Syntax: conventions of standard English": ["Subject-verb agreement and pronoun-antecedent agreement : Syntax: conventions of standard English", "Fragments and run-ons: Syntax: conventions of standard English", "Dangling modifiers and parallel structure: Syntax: conventions of standard English"], "Unit 10: Usage and style": ["Frequently confused words: Usage and style", "Style!: Usage and style"]}}}}
