### Structure and calculation

**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(e.g. when working with very large or very small numbers, and when calculating with decimals) - recognise and use relationships between operations, including inverse operations (example 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 facto**r,**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
- 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 π;**simplify surd****expressions involving squares and rationalise denominators** - calculate with and interpret standard form
*A*× 10^{n}, where 1 ≤*A*< 10 and*n*is an integer.

### Fractions, decimals and percentages

- work interchangeably with terminating decimals and their corresponding fractions;
**change recurring decimals into their corresponding fractions and vice versa** - identify and work with fractions in problems
**interpret fractions**and percentages**as operators**

### Measures and accuracy

- use standard units of mass, length, time, money and other measures (standard compound measures) using decimal quantities where appropriate
- estimate answers;check calculataions using approximation and estimation, including answers obtained by technology (calculators and computing software)
- round numbersround numbers and measures to an appropriate degree of accuracy ( e.g. 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**