### 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
NUMBER 7N1

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

7N2

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

7N3

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

7N4

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

7N5

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

7N6

Recognise and use relationships between operations including inverse operations

7N7

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

7N8

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

7N9

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

7N10

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%

7N11

Interpret fractions and percentages as operators

7N12

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

7N13

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

7N14

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

7N15

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

7N16

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

ALGEBRA 7A1

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
• in place of a ÷ b
• coefficients written as fractions rather than as decimals
• brackets
7A2

Substitute numerical values into formulae and expressions, including scientific formulae

7A3

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

7A4

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
7A5

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

7A6

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

7A7

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

7A8

Work with coordinates in all four quadrants

7A9

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

7A10

Interpret mathematical relationships both algebraically and graphically

7A11

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

7A12

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

7A13

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

7A14

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

7A15

Recognise arithmetic sequences and find the nth term

7A16

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]

7R2

Use scale factors, scale diagrams and maps

7R3

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

7R4

Use ratio notation, including reduction to simplest form

7R5

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

7R6

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

7R

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

7R8

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

7R9

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

7R10

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)

7G2

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

7G3

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

7G4

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

7G5

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

7G6

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

7G7

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

7G8

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

7G9

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

7G10

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

7G11

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

7G12

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

7G13

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

7G14

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

7G15

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

7G16

Interpret mathematical relationships both algebraically and geometrically.

PROBABILITY 7P1

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

7P2

Understand that the probabilities of all possible outcomes sum to 1

7P3

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

7P4

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

STATISTICS 7S1

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)

7S2

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

7S3

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