openfreebooks-bookgenerator/data/math-curriculum.json

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{
"title": "Mathematics",
"intro": "Topic units across three strands, shaped for learners worldwide. The map shows required prerequisites; the list follows a readable teaching order; Compare explains how chapters relate to popular curricula.",
"graph": {
"edges": [
{
"from": "zero-and-one",
"to": "counting-and-numbers"
},
{
"from": "counting-and-numbers",
"to": "basic-math-notation"
},
{
"from": "basic-math-notation",
"to": "properties-of-operations"
},
{
"from": "properties-of-operations",
"to": "written-calculation"
},
{
"from": "written-calculation",
"to": "integer-foundations"
},
{
"from": "written-calculation",
"to": "rational-number-operations"
},
{
"from": "integer-foundations",
"to": "integer-arithmetic"
},
{
"from": "rational-number-operations",
"to": "percentage-applications"
},
{
"from": "rational-number-operations",
"to": "ratios-and-rates-foundation"
},
{
"from": "percentage-applications",
"to": "ratios-and-rates-foundation"
},
{
"from": "integer-arithmetic",
"to": "directed-numbers-rates"
},
{
"from": "ratios-and-rates-foundation",
"to": "directed-numbers-rates"
},
{
"from": "directed-numbers-rates",
"to": "polynomials-expansion-factorisation"
},
{
"from": "polynomials-expansion-factorisation",
"to": "algebraic-fractions-formulas"
},
{
"from": "polynomials-expansion-factorisation",
"to": "linear-equations-two-unknowns"
},
{
"from": "linear-equations-two-unknowns",
"to": "linear-inequalities-one-unknown"
},
{
"from": "polynomials-expansion-factorisation",
"to": "laws-of-indices"
},
{
"from": "laws-of-indices",
"to": "quadratic-equations"
},
{
"from": "polynomials-expansion-factorisation",
"to": "factor-remainder-theorems"
},
{
"from": "quadratic-equations",
"to": "factor-remainder-theorems"
},
{
"from": "quadratic-equations",
"to": "complex-numbers"
},
{
"from": "quadratic-equations",
"to": "functions-graphs"
},
{
"from": "quadratic-equations",
"to": "sequences-series"
},
{
"from": "functions-graphs",
"to": "exponential-logarithmic"
},
{
"from": "functions-graphs",
"to": "variations"
},
{
"from": "functions-graphs",
"to": "sequences-series"
},
{
"from": "functions-graphs",
"to": "linear-programming"
},
{
"from": "sequences-series",
"to": "linear-programming"
},
{
"from": "polynomials-expansion-factorisation",
"to": "coordinate-geometry-foundations"
},
{
"from": "quadratic-equations",
"to": "coordinate-circles"
},
{
"from": "functions-graphs",
"to": "advanced-trigonometry"
},
{
"from": "coordinate-geometry-foundations",
"to": "deductive-geometry"
},
{
"from": "coordinate-geometry-foundations",
"to": "coordinate-circles"
},
{
"from": "deductive-geometry",
"to": "congruence-similarity"
},
{
"from": "congruence-similarity",
"to": "pythagoras-theorem"
},
{
"from": "pythagoras-theorem",
"to": "introduction-trigonometry"
},
{
"from": "introduction-trigonometry",
"to": "mensuration-3d"
},
{
"from": "introduction-trigonometry",
"to": "advanced-trigonometry"
},
{
"from": "coordinate-circles",
"to": "circle-properties"
},
{
"from": "deductive-geometry",
"to": "circle-properties"
},
{
"from": "coordinate-circles",
"to": "loci"
},
{
"from": "circle-properties",
"to": "loci"
},
{
"from": "directed-numbers-rates",
"to": "statistical-charts-averages"
},
{
"from": "statistical-charts-averages",
"to": "measures-dispersion"
},
{
"from": "statistical-charts-averages",
"to": "basic-probability"
},
{
"from": "basic-probability",
"to": "permutations-combinations-probability"
},
{
"from": "measures-dispersion",
"to": "normal-distribution-z-scores"
},
{
"from": "measures-dispersion",
"to": "statistical-literacy"
},
{
"from": "basic-probability",
"to": "statistical-literacy"
},
{
"from": "permutations-combinations-probability",
"to": "statistical-literacy"
}
]
},
"strands": [
{
"id": "number-algebra",
"title": "Number & Algebra",
"chapters": [
{
"slug": "zero-and-one",
"title": "Zero and one",
"description": "0 is nothing; 1 is one. Learn to tell them apart — the same skill as telling false from true — before counting larger amounts.",
"status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"DSE": "related",
"IB": "related",
"A-Level": "related",
"AP": "related",
"Gaokao": "related"
}
},
{
"slug": "counting-and-numbers",
"title": "Counting and numbers",
"description": "Count objects, spot patterns, add, multiply, and divide; then meet place value and big numbers from hundreds to billions.",
"status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"DSE": "related",
"IB": "related",
"A-Level": "related",
"AP": "related",
"Gaokao": "related"
}
},
{
"slug": "basic-math-notation",
"title": "Basic math notation",
"description": "Learn the names and meanings of plus, minus, times, divide, equals, brackets, and other signs used in number sentences.",
"status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"DSE": "related",
"IB": "related",
"A-Level": "related",
"AP": "related",
"Gaokao": "related"
}
},
{
"slug": "properties-of-operations",
"title": "Properties of operations",
"description": "See why order, grouping, and distribution can change how you write a sum or product without changing the result — with interactive area and dot models.",
"status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"DSE": "related",
"IB": "related",
"A-Level": "related",
"AP": "related",
"Gaokao": "related"
}
},
{
"slug": "written-calculation",
"title": "Written calculation",
"description": "Add, subtract, multiply, and divide whole numbers using vertical written form: align columns, regroup, and read the result.",
"status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"DSE": "related",
"IB": "related",
"A-Level": "related",
"AP": "related",
"Gaokao": "related"
}
},
{
"slug": "integer-foundations",
"title": "Integer foundations",
"description": "Model directed magnitude on number lines; use the zero principle and tiles to add and subtract integers, and see subtraction as adding an opposite.",
"status": "planned",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"IB": "related",
"A-Level": "related",
"AP": "related",
"DSE": "related",
"Gaokao": "related"
}
},
{
"slug": "integer-arithmetic",
"title": "Integer arithmetic",
"description": "Multiply and divide integers from models to symbolic rules; apply order of operations with signed numbers in multi-step expressions.",
"status": "planned",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"IB": "related",
"A-Level": "related",
"AP": "related",
"DSE": "related",
"Gaokao": "related"
}
},
{
"slug": "rational-number-operations",
"title": "Fractions and decimals",
"description": "Convert between fractions, terminating decimals, and repeating decimals; add, subtract, multiply, and divide rational numbers and mixed numbers.",
"status": "planned",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"IB": "related",
"A-Level": "related",
"AP": "related",
"DSE": "related",
"Gaokao": "related"
}
},
{
"slug": "percentage-applications",
"title": "Percentage applications",
"description": "Relate fractions and decimals to base-100 ratios; calculate percent increase and decrease in financial and real-world contexts.",
"status": "planned",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"IB": "related",
"A-Level": "related",
"AP": "related",
"DSE": "related",
"Gaokao": "related"
}
},
{
"slug": "ratios-and-rates-foundation",
"title": "Ratios & rates foundations",
"description": "Formulate part-to-part and part-to-whole ratios, find equivalent ratios, compute unit rates, and graph proportional relationships.",
"status": "planned",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"IB": "related",
"A-Level": "related",
"AP": "related",
"DSE": "related",
"Gaokao": "related"
}
},
{
"slug": "directed-numbers-rates",
"title": "Directed numbers, rates & ratios",
"description": "Operate with negative numbers and solve ratio, rate, and proportion problems in context.",
"status": "live",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"Foundation": "related",
"IB": "related",
"A-Level": "related",
"AP": "related",
"Gaokao": "related"
}
},
{
"slug": "polynomials-expansion-factorisation",
"title": "Polynomials: expansion & factorisation",
"description": "Expand products, collect like terms, and factorise expressions using common factors and identities.",
"status": "live",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"A-Level": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"Gaokao": "core",
"Foundation": "related",
"AP": "related"
}
},
{
"slug": "algebraic-fractions-formulas",
"title": "Algebraic fractions & formulas",
"description": "Simplify algebraic fractions and change the subject of formulas in applied contexts.",
"status": "live",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"A-Level": "core",
"Common Core": "related",
"Singapore": "related",
"UK GCSE": "core",
"Gaokao": "related",
"Foundation": "related",
"AP": "related"
}
},
{
"slug": "linear-equations-two-unknowns",
"title": "Linear equations in two unknowns",
"description": "Solve simultaneous linear equations by substitution, elimination, and graphical interpretation; classify unique, parallel, and coincident cases.",
"status": "live",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"A-Level": "core",
"Common Core": "core",
"Singapore": "core",
"UK GCSE": "core",
"Gaokao": "core",
"AP": "related",
"Foundation": "related"
}
},
{
"slug": "linear-inequalities-one-unknown",
"title": "Linear inequalities in one unknown",
"description": "Solve and represent linear inequalities on the number line and in word problems.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"Common Core": "core",
"UK GCSE": "core",
"IB": "related",
"A-Level": "related",
"AP": "related",
"Singapore": "related",
"Gaokao": "related"
}
},
{
"slug": "laws-of-indices",
"title": "Laws of indices",
"description": "Apply index laws to simplify expressions with integer and rational exponents.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"A-Level": "core",
"AP": "core",
"Common Core": "core",
"UK GCSE": "core",
"Singapore": "core",
"Gaokao": "core",
"Foundation": "related"
}
},
{
"slug": "quadratic-equations",
"title": "Quadratic equations",
"description": "Solve quadratics by factorising, completing the square, and the formula. Model real problems with parabolas and roots.",
"status": "live",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"A-Level": "core",
"AP": "core",
"Common Core": "core",
"UK GCSE": "core",
"Singapore": "core",
"Gaokao": "core",
"Foundation": "related"
}
},
{
"slug": "factor-remainder-theorems",
"title": "Factor & remainder theorems",
"description": "Use the factor and remainder theorems to factorise higher-degree polynomials and solve related equations.",
"status": "planned",
"tier": "non-foundation",
"curriculumCoverage": {
"DSE": "extension",
"IB": "extension",
"A-Level": "extension",
"IGCSE": "related",
"Gaokao": "related",
"AP": "related"
}
},
{
"slug": "complex-numbers",
"title": "Complex numbers",
"description": "Represent complex numbers in Cartesian form and perform operations including conjugates and division.",
"status": "planned",
"tier": "non-foundation",
"curriculumCoverage": {
"DSE": "extension",
"IB": "extension",
"A-Level": "extension",
"Gaokao": "related",
"IGCSE": "related",
"AP": "related"
}
},
{
"slug": "functions-graphs",
"title": "Functions & graphs",
"description": "Study domains, ranges, transformations, and graphs of common functions including quadratics and rationals.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"A-Level": "core",
"AP": "core",
"Common Core": "core",
"UK GCSE": "core",
"Singapore": "core",
"Gaokao": "core",
"Foundation": "related"
}
},
{
"slug": "exponential-logarithmic",
"title": "Exponential & logarithmic functions",
"description": "Explore laws of logarithms, exponential growth and decay, and sketch related graphs.",
"status": "planned",
"tier": "non-foundation",
"curriculumCoverage": {
"DSE": "extension",
"IGCSE": "core",
"IB": "core",
"A-Level": "core",
"AP": "core",
"Common Core": "core",
"UK GCSE": "core",
"Gaokao": "core",
"Singapore": "related",
"Foundation": "related"
}
},
{
"slug": "sequences-series",
"title": "Sequences & series",
"description": "Work with arithmetic and geometric sequences, sigma notation, and finite summation formulas.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"A-Level": "core",
"Common Core": "related",
"UK GCSE": "core",
"AP": "related",
"Gaokao": "core",
"Singapore": "related",
"Foundation": "related"
}
},
{
"slug": "variations",
"title": "Variations",
"description": "Model direct, inverse, joint, and partial variation and solve combined variation problems.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IB": "related",
"A-Level": "related",
"IGCSE": "related",
"Common Core": "related",
"Singapore": "related"
}
},
{
"slug": "linear-programming",
"title": "Linear programming",
"description": "Graph linear inequalities, identify feasible regions, and optimise objective functions in two variables.",
"status": "planned",
"tier": "non-foundation",
"curriculumCoverage": {
"DSE": "extension",
"IB": "extension",
"A-Level": "related",
"AP": "related",
"IGCSE": "related"
}
}
]
},
{
"id": "measures-shape-space",
"title": "Measures, Shape & Space",
"chapters": [
{
"slug": "coordinate-geometry-foundations",
"title": "Coordinate geometry foundations",
"description": "Plot points, find distances and midpoints, and work with slopes of lines in the Cartesian plane.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"Common Core": "core",
"UK GCSE": "core",
"IB": "core",
"A-Level": "related",
"Singapore": "core",
"AP": "related",
"Gaokao": "related"
}
},
{
"slug": "deductive-geometry",
"title": "Deductive geometry",
"description": "Prove angle and side relationships for intersecting lines, triangles, and polygons.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"UK GCSE": "core",
"Common Core": "core",
"Singapore": "core",
"IB": "related",
"A-Level": "related",
"Gaokao": "related"
}
},
{
"slug": "congruence-similarity",
"title": "Congruence & similarity",
"description": "Apply congruence and similarity criteria to justify properties of triangles and scale figures.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"UK GCSE": "core",
"Common Core": "core",
"Singapore": "core",
"IB": "related",
"A-Level": "related",
"Gaokao": "related"
}
},
{
"slug": "pythagoras-theorem",
"title": "Pythagoras' theorem",
"description": "Use Pythagoras' theorem and its converse in 2D problems and coordinate settings.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"UK GCSE": "core",
"Common Core": "core",
"Singapore": "core",
"IB": "core",
"A-Level": "related",
"Gaokao": "core",
"AP": "related"
}
},
{
"slug": "introduction-trigonometry",
"title": "Introduction to trigonometry",
"description": "Define sine, cosine, and tangent ratios and solve right-angled triangle problems.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"UK GCSE": "core",
"Common Core": "core",
"Singapore": "core",
"IB": "core",
"A-Level": "related",
"Gaokao": "core",
"AP": "related"
}
},
{
"slug": "mensuration-3d",
"title": "Mensuration in 3D",
"description": "Find volumes and surface areas of prisms, cylinders, pyramids, cones, and spheres.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"UK GCSE": "core",
"Common Core": "core",
"Singapore": "core",
"IB": "related",
"A-Level": "related",
"Gaokao": "related"
}
},
{
"slug": "coordinate-circles",
"title": "Coordinate geometry of circles",
"description": "Find equations of circles, tangents, and intersections using coordinate methods and distance.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "related",
"IB": "extension",
"A-Level": "extension",
"Gaokao": "related",
"UK GCSE": "related",
"AP": "related"
}
},
{
"slug": "advanced-trigonometry",
"title": "Advanced trigonometry",
"description": "Use sine and cosine rules, radians, and trigonometric graphs in 2D and 3D applications.",
"status": "planned",
"tier": "non-foundation",
"curriculumCoverage": {
"DSE": "extension",
"IGCSE": "core",
"IB": "core",
"A-Level": "core",
"AP": "core",
"UK GCSE": "core",
"Gaokao": "core",
"Common Core": "related",
"Singapore": "related"
}
},
{
"slug": "circle-properties",
"title": "Properties of circles",
"description": "Apply chord, tangent, and angle theorems in circles to prove results and solve geometry problems.",
"status": "planned",
"tier": "non-foundation",
"curriculumCoverage": {
"DSE": "extension",
"IGCSE": "core",
"UK GCSE": "core",
"IB": "related",
"A-Level": "related",
"Gaokao": "related",
"Singapore": "related"
}
},
{
"slug": "loci",
"title": "Loci",
"description": "Describe and construct loci in the plane, linking geometric constraints to algebraic equations.",
"status": "planned",
"tier": "non-foundation",
"curriculumCoverage": {
"DSE": "extension",
"IGCSE": "related",
"A-Level": "related",
"IB": "related",
"UK GCSE": "related"
}
}
]
},
{
"id": "data-handling",
"title": "Data Handling",
"chapters": [
{
"slug": "statistical-charts-averages",
"title": "Charts & averages",
"description": "Organise data with tables and charts and calculate mean, median, and mode.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"Common Core": "core",
"UK GCSE": "core",
"Singapore": "core",
"AP": "related",
"Gaokao": "related",
"A-Level": "related"
}
},
{
"slug": "measures-dispersion",
"title": "Measures of dispersion",
"description": "Interpret range, interquartile range, variance, and standard deviation for comparing data sets.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"A-Level": "related",
"AP": "related",
"Common Core": "core",
"UK GCSE": "core",
"Singapore": "related",
"Gaokao": "related"
}
},
{
"slug": "basic-probability",
"title": "Basic probability",
"description": "Calculate theoretical and experimental probabilities for simple events and complements.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IGCSE": "core",
"IB": "core",
"Common Core": "core",
"UK GCSE": "core",
"Singapore": "core",
"AP": "related",
"A-Level": "related",
"Gaokao": "related"
}
},
{
"slug": "permutations-combinations-probability",
"title": "Permutations, combinations & probability",
"description": "Count outcomes with permutations and combinations, then compute probabilities in finite sample spaces.",
"status": "planned",
"tier": "non-foundation",
"curriculumCoverage": {
"DSE": "extension",
"IGCSE": "extension",
"IB": "core",
"A-Level": "core",
"AP": "related",
"Gaokao": "related",
"Common Core": "related"
}
},
{
"slug": "normal-distribution-z-scores",
"title": "Normal distribution & z-scores",
"description": "Model continuous data with the normal curve, standardise with z-scores, and read probabilities from tables.",
"status": "planned",
"tier": "non-foundation",
"curriculumCoverage": {
"DSE": "extension",
"IB": "core",
"A-Level": "core",
"AP": "related",
"IGCSE": "related",
"Gaokao": "related",
"Common Core": "related"
}
},
{
"slug": "statistical-literacy",
"title": "Statistical literacy",
"description": "Evaluate claims in media and research: sampling bias, correlation versus causation, and misleading charts.",
"status": "planned",
"curriculumCoverage": {
"DSE": "core",
"IB": "related",
"Common Core": "related",
"IGCSE": "related",
"AP": "related",
"A-Level": "related",
"Singapore": "related"
}
}
]
}
]
}