3.1 Number

3.1.1 Structure and calculation

N1

Basic foundation content	Additional foundation content	Higher content only
order positive and negative integers, decimals and fractions use the symbols =, ≠, <, >, ≤, ≥

Basic foundation content

Additional foundation content

Higher content only

order positive and negative integers, decimals and fractions

use the symbols =, ≠, <, >, ≤, ≥

Notes: including use of a number line. See also A22

N2

Basic foundation content	Additional foundation content	Higher content only
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)

Basic foundation content

Additional foundation content

Higher content only

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)

Notes: including questions set in context.

Knowledge and understanding of terms used in household finance, for example profit, loss, cost price, selling price, debit, credit, balance, income tax, VAT and interest rate. See also R9

N3

Basic foundation content	Additional foundation content	Higher content only
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

Basic foundation content

Additional foundation content

Higher content only

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

N4

Basic foundation content	Additional foundation content	Higher content only
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

Notes: prime factor decomposition including product of prime factors written in index form.

N5

Basic foundation content	Additional foundation content	Higher content only
apply systematic listing strategies		including use of the product rule for counting

Notes: including using lists, tables and diagrams.

N6

Basic foundation content	Additional foundation content	Higher content only
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

Notes: including square numbers up to $15 \times 15$

Students should know that $1000 = 10^{3}$ and 1 million = $10^{6}$

N7

Basic foundation content	Additional foundation content	Higher content only
	calculate with roots, and with integer indices	calculate with fractional indices

N8

Basic foundation content	Additional foundation content	Higher content only
calculate exactly with fractions	calculate exactly with multiples of $π$	calculate exactly with surds simplify surd expressions involving squares (eg $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2 \sqrt{3}$ ) and rationalise denominators

Basic foundation content

Additional foundation content

Higher content only

calculate exactly with fractions

calculate exactly with multiples of $π$

calculate exactly with surds

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

Notes: see also G17 and G18

N9

Basic foundation content	Additional foundation content	Higher content only
calculate with and interpret standard form $A \times 10^{n}$ , where $1 \leq A < 10$ and $n$ is an integer

Notes: with and without a calculator.

Interpret calculator displays.

3.1.2 Fractions, decimals and percentages

N10

Basic foundation content	Additional foundation content	Higher content only
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

Notes: including ordering.

N11

Basic foundation content	Additional foundation content	Higher content only
identify and work with fractions in ratio problems

Notes: See also R8

N12

Basic foundation content	Additional foundation content	Higher content only
interpret fractions and percentages as operators

Notes: including interpreting percentage problems using a multiplier. See also R9

3.1.3 Measures and accuracy

N13

Basic foundation content	Additional foundation content	Higher content only
use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate

Notes: know and use metric conversion factors for length, area, volume and capacity.

Imperial/metric conversions will be given in the question.

N14

Basic foundation content	Additional foundation content	Higher content only
estimate answers check calculations using approximation and estimation, including answers obtained using technology

Basic foundation content

Additional foundation content

Higher content only

estimate answers

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

Notes: including evaluation of results obtained. See also N15

N15

Basic foundation content	Additional foundation content	Higher content only
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

Notes: including appropriate rounding for questions set in context.

Students should know not to round values during intermediate steps of a calculation. See also N14

N16

Basic foundation content	Additional foundation content	Higher content only
	apply and interpret limits of accuracy	including upper and lower bounds

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3.2 Algebra