# Number -Subject content

### Structure and calculation

1. order positive and negative integers, decimals and fractions; use the symbols =. ≠, <, ≤, ≥
2.  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)
3. 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
4. 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
5. apply systematic listing strategies including use of the product rule for counting
6. 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
7. calculate with roots, and with integer and fractional indices
8. calculate exactly with fractions, surds and multiples of π; simplify surd expressions involving squares and rationalise denominators
9. calculate with and interpret standard form A × 10n, where 1A < 10 and n is an integer.

### Fractions, decimals and percentages

10. work interchangeably with terminating decimals and their corresponding fractions; change recurring decimals into their corresponding fractions and vice versa
11. identify and work with fractions in problems
12. interpret fractions and percentages as operators

### Measures and accuracy

13. use standard units of mass, length, time, money and other measures (standard compound measures) using decimal quantities where appropriate
14. estimate answers;check calculataions using approximation and estimation, including answers obtained by technology (calculators and computing software)
15. 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)
16. apply and interpret limits of accuracy, including upper and lower bounds