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English National Curriculum
Programme Of Study For Key Stage 3 Mathematics

Printable Cards - Landscape!

These are the statements, each one preceeded with the words "Pupils should be taught to:". Print onto card (landscape) then cut them out for your sorting or grouping activities.

Number (01)

...understand and use place value for decimals, measures and integers of any size

Number (02)

...order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

Number (03)

...use 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

Number (04)

...use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Number (05)

...use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

Number (06)

...recognise and use relationships between operations including inverse operations

Number (07)

...use 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

Number (08)

...interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or zero

Number (09) interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 72 or 0.375 and 38 )

Number (10)

...define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

Number (11)

...interpret fractions and percentages as operators

Number (12)

...use standard units of mass, length, time, money and other measures, including with decimal quantities

Number (13)

...round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

Number (14)

...use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b

Number (15)

...use a calculator and other technologies to calculate results accurately and then interpret them appropriately

Number (16)

...appreciate the infinite nature of the sets of integers, real and rational numbers.

Algebra (01)

...use 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
- ab in place of a ÷ b
- coefficients written as fractions rather than as decimals
- brackets

Algebra (02)

...substitute numerical values into formulae and expressions, including scientific formulae

Algebra (03)

...understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

Algebra (04)

...simplify 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 two or more binomials

Algebra (05)

...understand and use standard mathematical formulae; rearrange formulae to change the subject

Algebra (06)

...model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

Algebra (07)

...use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

Algebra (08) with coordinates in all four quadrants

Algebra (09)

...recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

Algebra (10)

...interpret mathematical relationships both algebraically and graphically

Algebra (11)

...reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

Algebra (12)

...use 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

Algebra (13)

...find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

Algebra (14)

...generate terms of a sequence from either a term-to-term or a position-to-term rule

Algebra (15)

...recognise arithmetic sequences and find the nth term

Algebra (16)

...recognise geometric sequences and appreciate other sequences that arise.

Ratio and Proportion (01)

...change freely between related standard units [for example time, length, area, volume/capacity, mass]

Ratio and Proportion (02)

...use scale factors, scale diagrams and maps

Ratio and Proportion (03) one quantity as a fraction of another, where the fraction is less than 1 and greater than 1

Ratio and Proportion (04)

...use ratio notation, including reduction to simplest form

Ratio and Proportion (05)

...divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio

Ratio and Proportion (06)

...understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

Ratio and Proportion (07)

...relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

Ratio and Proportion (08)

...solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

Ratio and Proportion (09)

...solve problems involving direct and inverse proportion, including graphical and algebraic representations

Ratio and Proportion (10)

...use compound units such as speed, unit pricing and density to solve problems.

Geometry and measures (01)

...derive 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)

Geometry and measures (02)

...calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

Geometry and measures (03)

...draw and measure line segments and angles in geometric figures, including interpreting scale drawings

Geometry and measures (04)

...derive 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

Geometry and measures (05)

...describe, 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

Geometry and measures (06)

...use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

Geometry and measures (07)

...derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

Geometry and measures (08)

...identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

Geometry and measures (09)

...identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

Geometry and measures (10)

...apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

Geometry and measures (11)

...understand and use the relationship between parallel lines and alternate and corresponding angles

Geometry and measures (12)

...derive 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

Geometry and measures (13)

...apply 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

Geometry and measures (14)

...use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

Geometry and measures (15)

...use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

Geometry and measures (16)

...interpret mathematical relationships both algebraically and geometrically.

Probability (01)

...record, 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

Probability (02)

...understand that the probabilities of all possible outcomes sum to 1

Probability (03)

...enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams

Probability (04)

...generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities

Statistics (01)

...describe, 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)

Statistics (02)

...construct 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

Statistics (03)

...describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.


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