Year 7 maths - New Curriculum, 2015

This is what children aged 10 to 11 in year 7, should know for Maths, key stage 3.

Strand Ref Know how to

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


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


Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple(LCM), prime factorisation, including using product notation and the unique factorisation property


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


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


Recognise and use relationships between operations including inverse operations


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


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


Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and ⅜)


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%


Interpret fractions and percentages as operators


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


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


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


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


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


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
  • fraction in place of a ÷ b
  • coefficients written as fractions rather than as decimals
  • brackets

Substitute numerical values into formulae and expressions, including scientific formulae


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


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

Understand and use standard mathematical formulae; rearrange formulae to change the subject


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


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


Work with coordinates in all four quadrants


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


Interpret mathematical relationships both algebraically and graphically


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


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


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


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


Recognise arithmetic sequences and find the nth term


Recognise geometric sequences and appreciate other sequences that arise.

Ratio, proportion and rates of change 7R1

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


Use scale factors, scale diagrams and maps


Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1


Use ratio notation, including reduction to simplest form


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


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


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


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


Solve problems involving direct and inverse proportion, including graphical and algebraic representations


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

Strand Ref Know how to
Geometry and measures 7G1

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)


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


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


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


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


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


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


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


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


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


Understand and use the relationship between parallel lines and alternate and corresponding angles


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


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


Use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles


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


Interpret mathematical relationships both algebraically and geometrically.


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


Understand that the probabilities of all possible outcomes sum to 1


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


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


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)


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


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