order positive and negative integers, decimals and fractions;

use the symbols =, ≠, <, >, ≤, ≥

apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative;

understand and use place value (eg when working with very large or very small numbers, and when calculating with decimals)

recognise and use relationships between operations, including inverse operations (eg cancellation to simplify calculations and expressions);

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

use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem

apply systematic listing strategies;

including use of the product rule for counting (i.e. if there are \(m\) ways of doing one task and for each of these, there are \(n\) ways of doing another task, then the total number of ways the two tasks can be done is \(m×n\) ways)

use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5;

estimate powers and roots of any given positive number

calculate with roots, and with integer and fractional indices

calculate exactly with fractions, surds and multiples of \(\pi\);

simplify surd expressions involving squares (eg \(\sqrt{12} = \sqrt{4×3} = \sqrt{4}×\sqrt{3} = 2\sqrt{3} \)) and rationalise denominators

calculate with and interpret standard form \(A × 10^n\), where \(1 ≤ A < 10\) and \(n\) is an integer

work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and \(\frac{7}{2}\) or 0.375 and \(\frac{3}{8}\));

change recurring decimals into their corresponding fractions and vice versa

identify and work with fractions in ratio problems

interpret fractions and percentages as operators

use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate

estimate answers;

check calculations using approximation and estimation, including answers obtained using technology

round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures);

use inequality notation to specify simple error intervals due to truncation or rounding

apply and interpret limits of accuracy, including upper and lower bounds