# Stage 7: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 44 concepts ready. In the app: https://ai.page/roadmap/cambridge-stage-7 Part of: [Cambridge: Mathematics](https://ai.page/roadmap/cambridge.md) Goal: Cambridge Primary, Lower Secondary and IGCSE: Mathematics, Stage 7 ## 1. Statistics & Probability: Probability - [The Probability Scale](https://ai.page/c/the-probability-scale/index.md): Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible - [Experimental probability](https://ai.page/c/experimental-probability/index.md): Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability - [The 0-to-1 Probability Scale](https://ai.page/c/the-0-to-1-probability-scale/index.md): Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages - [Likelihood Language](https://ai.page/c/likelihood-language/index.md): Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible ## 2. Statistics & Probability: Statistics - [Statistical Analysis Vocabulary](https://ai.page/c/statistical-analysis-vocabulary/index.md): Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes - [Comparing measurements](https://ai.page/c/comparing-measurements/index.md): Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers ## 3. Geometry & Measure: Position and transformations - [Coordinate Transformations](https://ai.page/c/coordinate-transformations/index.md): Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original - [Transformations on a grid](https://ai.page/c/transformations-on-a-grid/index.md): Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size - [Transformations on a Grid](https://ai.page/c/transformations-on-a-grid-maths/index.md): Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed ## 4. Geometry & Measure: Geometrical reasoning, shapes and measurements - [Classifying shapes by properties](https://ai.page/c/classifying-shapes-by-properties/index.md): Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties - [Types of angles (age 11+)](https://ai.page/c/types-of-angles-age-11/index.md): Use conventional geometric terms and notation to describe, sketch, and draw points, lines, parallel and perpendicular lines, right angles, regular polygons, and reflectively/rotationally symmetric polygons - [Properties of triangles and quadrilaterals](https://ai.page/c/properties-of-triangles-and-quadrilaterals/index.md): Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths - [Angles with parallel lines](https://ai.page/c/angles-with-parallel-lines/index.md): Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles - [Lines, Rays & Angles](https://ai.page/c/lines-rays-and-angles/index.md): Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures - [Angle Sum Rules](https://ai.page/c/angle-sum-rules/index.md): Know that angles at a point sum to 360° (one whole turn), angles on a straight line sum to 180°, and vertically opposite angles are equal; use these facts to find missing angles - [Angles in triangles (age 10+)](https://ai.page/c/angles-in-triangles-age-10/index.md): Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties - [Angle sums in triangles and polygons](https://ai.page/c/angle-sums-in-triangles-and-polygons/index.md): Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons - [Parts of a circle](https://ai.page/c/parts-of-a-circle/index.md): Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius - [Circles: Circumference & Area](https://ai.page/c/circles-circumference-and-area/index.md): Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts - [3-D shapes (age 11+)](https://ai.page/c/3-d-shapes-age-11/index.md): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections - [Counting Unit Cubes](https://ai.page/c/counting-unit-cubes/index.md): Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units - [Using Simple Formulae](https://ai.page/c/using-simple-formulae/index.md): Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width)) - [Area of Triangles & Parallelograms](https://ai.page/c/area-of-triangles-and-parallelograms/index.md): Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles) - [Unit Conversions](https://ai.page/c/unit-conversions/index.md): Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate - [What Is an Angle?](https://ai.page/c/what-is-an-angle/index.md): Understand that an angle is a geometric shape formed by two rays sharing a common endpoint (vertex); recognise angles in real-life contexts and 2-D shapes ## 5. Algebra: Sequences, functions and graphs - [Algebraic Transformations](https://ai.page/c/algebraic-transformations/index.md): Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations - [Linear Function Graphs](https://ai.page/c/linear-function-graphs/index.md): Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context - [Plotting Linear Graphs](https://ai.page/c/plotting-linear-graphs/index.md): Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line - [Generating Sequences](https://ai.page/c/generating-sequences/index.md): Generate terms of a sequence from a term-to-term rule (e.g., 'add 3 each time') or a position-to-term rule (e.g., '2n + 1'), and identify whether a sequence is arithmetic, geometric, or neither - [Nth-Term Rules](https://ai.page/c/nth-term-rules/index.md): Find the nth-term expression for an arithmetic sequence by identifying the common difference and the zero-term, and use it to determine any term in the sequence or test whether a given number belongs to the sequence ## 6. Algebra: Expressions, equations and formulae - [Expressions & Equations Vocabulary](https://ai.page/c/expressions-and-equations-vocabulary/index.md): Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign) - [Collecting Like Terms](https://ai.page/c/collecting-like-terms/index.md): Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence - [Substituting into Formulae](https://ai.page/c/substituting-into-formulae/index.md): Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations ## 7. Number: Fractions, decimals, percentages, ratio and proportion - [Percentages as Fractions](https://ai.page/c/percentages-as-fractions/index.md): Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100% - [Proportional Reasoning Vocabulary](https://ai.page/c/proportional-reasoning-vocabulary/index.md): Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts - [Ratio Notation](https://ai.page/c/ratio-notation/index.md): Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations - [Percentages (age 9+)](https://ai.page/c/percentages-age-9/index.md): Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole) - [Decimal & Percent Notation](https://ai.page/c/decimal-and-percent-notation/index.md): Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value ## 8. Number: Place value, ordering and rounding - [Decimal place value](https://ai.page/c/decimal-place-value-3/index.md): Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy - [Decimal place value (age 11+)](https://ai.page/c/decimal-place-value-age-11/index.md): Round numbers and measures to an appropriate degree of accuracy including to a specified number of decimal places or significant figures ## 9. Number: Integers, powers and roots - [Ratio (age 11+)](https://ai.page/c/ratio-age-11/index.md): Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions - [Square and cube numbers](https://ai.page/c/square-and-cube-numbers-maths/index.md): Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations - [Factors, multiples, and primes](https://ai.page/c/factors-multiples-and-primes/index.md): Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems - [Positive and Negative Numbers](https://ai.page/c/positive-and-negative-numbers/index.md): Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances ## Health: 0 of 100 Of its 44 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version. Findings (each is a task for anyone's AI): - The Probability Scale has no explanation yet - Experimental probability has no explanation yet - The 0-to-1 Probability Scale has no explanation yet - Likelihood Language has no explanation yet - Statistical Analysis Vocabulary has no explanation yet - Comparing measurements has no explanation yet - Coordinate Transformations has no explanation yet - Transformations on a grid has no explanation yet - Transformations on a Grid has no explanation yet - Classifying shapes by properties has no explanation yet - Types of angles (age 11+) has no explanation yet - Properties of triangles and quadrilaterals has no explanation yet - Angles with parallel lines has no explanation yet - Lines, Rays & Angles has no explanation yet - Angle Sum Rules has no explanation yet - Angles in triangles (age 10+) has no explanation yet - Angle sums in triangles and polygons has no explanation yet - Parts of a circle has no explanation yet - Circles: Circumference & Area has no explanation yet - 3-D shapes (age 11+) has no explanation yet - Counting Unit Cubes has no explanation yet - Using Simple Formulae has no explanation yet - Area of Triangles & Parallelograms has no explanation yet - Unit Conversions has no explanation yet - What Is an Angle? has no explanation yet - Algebraic Transformations has no explanation yet - Linear Function Graphs comes before Substituting into Formulae, which it needs - Linear Function Graphs has no explanation yet - Plotting Linear Graphs has no explanation yet - Generating Sequences has no explanation yet - Nth-Term Rules has no explanation yet - Expressions & Equations Vocabulary has no explanation yet - Collecting Like Terms has no explanation yet - Substituting into Formulae has no explanation yet - Percentages as Fractions has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Ratio Notation comes before Factors, multiples, and primes, which it needs - Ratio Notation has no explanation yet - Percentages (age 9+) has no explanation yet - Decimal & Percent Notation has no explanation yet - Decimal place value has no explanation yet - Decimal place value (age 11+) has no explanation yet - Ratio (age 11+) has no explanation yet - Square and cube numbers has no explanation yet - Factors, multiples, and primes has no explanation yet - Positive and Negative Numbers has no explanation yet Credit: The structure of Cambridge Primary, Lower Secondary and IGCSE: Mathematics (https://www.cambridgeinternational.org/programmes-and-qualifications/cambridge-primary-and-lower-secondary/); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.