Year 7 and 8

Children will learn 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 real numbers; use the symbols <, >, ≤, ≥

• 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

• round numbers and measures to an appropriate degree of accuracy, including significant figures

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

Children will learn to:

• 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

• use standard units of time

• recognise and use relationships between operations including inverse operations

• use integer powers and associated real roots, recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

• use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation

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

Children will learn to:

• work interchangeably with terminating decimals and their corresponding fractions

• interpret fractions and percentages as operators

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

• define percentage as 'number of parts per hundred'

• interpret percentage change 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%

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

Children will learn to:

• use and interpret algebraic notation, including:

  • • • ab in place of a x b

      • 3y in place of y+y+y and 3 x y

      • a² in place of a x a, a³ in place of a x a x a, a²b in place a x a x b

      • in place of a ÷ b

      • coefficients written as fractions rather than decimals

      • brackets

• substitute numerical values into formulae and expressions

• simplify and manipulate algebraic expressions to maintain equivalence by

  • • • collecting like terms

      • multiplying a single term over a bracket (the term outside the bracket will be restricted to a single integer such as 3(x-1))

      • taking out common factors

      • expanding products of two or more binomials

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

• understand and use standard mathematical formulae, rearrange formulae to change the subject

• use algebraic methods to solve linear equations in one variable

• model situations or procedures by translating them into algebraic expressions or formulae and by using graphs (linear equations only)

• work with coordinates in all four quadrants

• recognise, sketch and produce graphs of linear functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane (x = ± c, y = ± c, y = ± x only)

• 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 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 conversion graphs or distance-time graphs

• generate terms of a sequence either from 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 which arise

Children will learn to:

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

• use scale factors, scale diagrams and maps (scale factors may be either in the form ‘1:50000’ or ‘1 cm represents 500m’)

• express 1 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 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratio

• understand that a multiplicative relationship between 2 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 and decrease and simple interest in financial mathematics

• solve problems involving direct and inverse proportion, including graphical representations

• use compound units such as the relationship between distance, time and speed

Children will learn to:

• 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

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

• 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 point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

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

• describe, sketch and draw, using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons which are reflectively and rotationally symmetric

• use the standard conventions for labelling the sides and angles of triangle ABC

• derive and illustrate properties of triangles, quadrilaterals 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 (translations will be described in terms of units moved left/right and up/down)

• identify and construct congruent triangles, and construct similar shapes by enlargement, with coordinate grids (enlargements will be by a positive, integral scale factor)

• know and use the criteria for congruence of triangles

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

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

• solve angle problems with algebra

• derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon with up to 4 sides, and to derive properties of regular polygons

• apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides.

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

• use Pythagoras' Theorem to solve problems involving right-angled triangles

• interpret mathematical relationships bot algebraically and geometrically

• calculate surface area and volume of cubes, cuboids, prisms and cylinders

• understand and represent bearings

Children will learn to:

• 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 up to 2 events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities

Children will learn to:

• describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

• 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)

• describe simple mathematical relationships between two variables in observational and experimental contexts and illustrate using scatter graphs.