1 Numbers and the number system

understand and use integers (positive, negative and zero)

understand place value

use directed numbers in practical situations e.g. temperatures

order integers

use the four rules of addition, subtraction, multiplication and division

use brackets and the hierarchy of operations

use the terms ‘odd’, ‘even’, ’prime numbers’, ‘factors’ and ‘multiples’

identify prime factors, common factors and common multiples

understand and use equivalent fractions, simplifying a fraction by cancelling common factors and expressing it in its simplest form (lowest terms)

understand and use mixed numbers and vulgar fractions

identify common denominators

order fractions and calculate a given fraction of a given quantity

express a given number as a fraction of another number

use common denominators to add and subtract fractions and mixed numbers

convert a fraction to a decimal or a percentage

understand and use unit fractions as multiplicative inverses

multiply and divide fractions and mixed numbers

use decimal notation

understand place value

order decimals

convert a decimal to a fraction or a percentage Terminating decimals only

recognise that a terminating decimal is a fraction

convert recurring decimals into fractions

identify square numbers and cube numbers

calculate squares, square roots, cubes and cube roots

use index notation and index laws for multiplication and division of positive and negative integer powers including zero

express integers as a product of powers of prime factors

find highest common factors (HCF) and lowest common multiples (LCM)

understand the meaning of surds

manipulate surds, including rationalising a denominator

use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers

understand the definition of a set

use the set notation ∪, ∩, ∈ and ∉, with E for the universal set and ∅ for the empty set

understand the concept of the universal set and the empty set and the symbols for these sets

understand and use the complement of a set, using the notation A'

use Venn diagrams to represent sets

understand sets defined in algebraic terms, and understand and use subsets; if A is a subset of B, use A ⊂ B

use Venn diagrams to represent sets and the number of elements in sets

use the notation n(A) for the number of elements in the set A

use sets in practical situations

Understand that a percentage is a number of parts per 100.

express a given number as a percentage of another number

express a percentage as a fraction and as a decimal

understand the multiplicative nature of percentages as operators

solve simple percentage problems, including percentage increase and decrease

use reverse percentages In a sale, prices were reduced by 30%. The sale price of an item was £17.50 Calculate the original price of the item

use compound interest and depreciation

use repeated percentage change Calculate the total percentage increase when an increase of 30% is followed by a decrease of 20%

solve compound interest problems

use ratio notation, including reduction to its simplest form and its various links to fraction notation Express in the form 1 : n

divide a quantity in a given ratio or ratios Share £416 in the ratio 5 : 3 or 4 : 3 : 1

use the process of proportionality to evaluate unknown quantities

Calculate an unknown quantity when quantities vary in direct proportion, including completing a value table.

solve word problems about ratio and proportion Including maps and scale diagrams

round integers to a given power of 10

round to a given number of significant figures or decimal places

identify upper and lower bounds where values are given to a degree of accuracy

Use estimation, including rounding values to one significant figure, to evaluate numerical approximations.

Solve upper- and lower-bound problems when values are given to a stated degree of accuracy.

calculate with and interpret numbers in the form a × 10ⁿ, where n is an integer and 1 ≤ a < 10

solve problems involving standard form

use and apply number in everyday personal, domestic or community life

Carry out calculations using metric units of mass, length, area, volume and capacity.

Carry out calculations with time and money, including currency conversion.

Use a scientific electronic calculator to determine numerical results.