📐 Mathematics – Key Stage 3

Years 7-9

Aims

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programme of study for key stage 3 is organised into apparently distinct domains, but pupils should build on key stage 2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge in science, geography, computing and other subjects. Decisions about progression should be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for key stage 4. Those who are not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on.

Topics

Number16 objectives

Pupils should be taught to:

MA-KS3-N-01understand and use place value for decimals, measures and integers of any size
MA-KS3-N-02order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
MA-KS3-N-03use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property
MA-KS3-N-04use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
MA-KS3-N-05use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
MA-KS3-N-06recognise and use relationships between operations including inverse operations
MA-KS3-N-07use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations
MA-KS3-N-08interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or 0
MA-KS3-N-09work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and [Fraction:7/2] or 0.375 and [Fraction:3/8])
MA-KS3-N-10define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%
MA-KS3-N-11interpret fractions and percentages as operators
MA-KS3-N-12use standard units of mass, length, time, money and other measures, including with decimal quantities
MA-KS3-N-13round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
MA-KS3-N-14use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b
MA-KS3-N-15use a calculator and other technologies to calculate results accurately and then interpret them appropriately
MA-KS3-N-16appreciate the infinite nature of the sets of integers, real and rational numbers

Algebra16 objectives

Pupils should be taught to:

MA-KS3-A-01use and interpret algebraic notation, including: ab in place of a × b; 3y in place of y + y + y and 3 × y; a² in place of a × a, a³ in place of a × a × a; a²b in place of a × a × b; [Fraction:a/b] in place of a ÷ b; coefficients written as fractions rather than as decimals; brackets
MA-KS3-A-02substitute numerical values into formulae and expressions, including scientific formulae
MA-KS3-A-03understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
MA-KS3-A-04simplify and manipulate algebraic expressions to maintain equivalence by: collecting like terms; multiplying a single term over a bracket; taking out common factors; expanding products of 2 or more binomials
MA-KS3-A-05understand and use standard mathematical formulae; rearrange formulae to change the subject
MA-KS3-A-06model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
MA-KS3-A-07use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement)
MA-KS3-A-08work with coordinates in all 4 quadrants
MA-KS3-A-09recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane
MA-KS3-A-10interpret mathematical relationships both algebraically and graphically
MA-KS3-A-11reduce a given linear equation in 2 variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
MA-KS3-A-12use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
MA-KS3-A-13find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
MA-KS3-A-14generate terms of a sequence from either a term-to-term or a position-to-term rule
MA-KS3-A-15recognise arithmetic sequences and find the nth term
MA-KS3-A-16recognise geometric sequences and appreciate other sequences that arise

Ratio, proportion and rates of change10 objectives

Pupils should be taught to:

MA-KS3-R-01change freely between related standard units [for example time, length, area, volume/capacity, mass]
MA-KS3-R-02use scale factors, scale diagrams and maps
MA-KS3-R-03express 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1
MA-KS3-R-04use ratio notation, including reduction to simplest form
MA-KS3-R-05divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratio
MA-KS3-R-06understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction
MA-KS3-R-07relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
MA-KS3-R-08solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
MA-KS3-R-09solve problems involving direct and inverse proportion, including graphical and algebraic representations
MA-KS3-R-10use compound units such as speed, unit pricing and density to solve problems

Geometry and measures16 objectives

Pupils should be taught to:

MA-KS3-GM-01derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
MA-KS3-GM-02calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
MA-KS3-GM-03draw and measure line segments and angles in geometric figures, including interpreting scale drawings
MA-KS3-GM-04derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line
MA-KS3-GM-05describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
MA-KS3-GM-06use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
MA-KS3-GM-07derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
MA-KS3-GM-08identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
MA-KS3-GM-09identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
MA-KS3-GM-10apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
MA-KS3-GM-11understand and use the relationship between parallel lines and alternate and corresponding angles
MA-KS3-GM-12derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
MA-KS3-GM-13apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs
MA-KS3-GM-14use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
MA-KS3-GM-15use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
MA-KS3-GM-16interpret mathematical relationships both algebraically and geometrically

Probability4 objectives

Pupils should be taught to:

MA-KS3-P-01record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
MA-KS3-P-02understand that the probabilities of all possible outcomes sum to 1
MA-KS3-P-03enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
MA-KS3-P-04generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities

Statistics3 objectives

Pupils should be taught to:

MA-KS3-S-01describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)
MA-KS3-S-02construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
MA-KS3-S-03describe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs

Practise Mathematics with free games

These games are aligned to the Mathematics national curriculum objectives above.

Times Tables

Multiplication & Division

Maths Challenge

Number - Four Operations

Number Mage

Number

Fraction Pizza

Fractions

Coin Shop

Measurement - Money

Balance Lab

Number Bonds

Bubble Pop

Addition

Star Forge

Place Value

Clock Tower

Measurement - Time

Data Explorer

Statistics

Data Detective

Statistics

Decimal Diner

Decimals

Symmetry Mirror

Geometry - Symmetry

Algebra Arena

Algebra

Coordinate Raiders

Position & Direction

Content sourced from the Mathematics programmes of study, Department for Education, published September 2013. Crown copyright. Each objective carries a reference code (e.g. MA-KS3-...) for identification. Verify any objective by searching the GOV.UK source page linked above. Last verified against GOV.UK: April 2026. About this data