#### NUMBER

– Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

– Interpret and compare numbers in standard form A × 10^{n} 1 ≤ A < 10, where n is a positive or negative integer or zero

– Appreciate the infinite nature of the sets of integers, real and rational numbers

#### ALGEBRA

– Use and interpret algebraic notation, including: coefficients written as fractions rather than as decimals

– Simplify and manipulate algebraic expressions to maintain equivalence by expanding products of two or more binomials

– Understand and use standard mathematical formulae;

– rearrange formulae to change the subject

– Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

– Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

– Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

– Interpret mathematical relationships both algebraically and graphically

– Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

– Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

– Recognise geometric sequences and appreciate other sequences that arise.

#### Ratio, proportion and rates of change

– Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction ½ × 3 = 3 over 2

– Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

– Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

– Solve problems involving direct ( ∝) and inverse proportion (1/∝) including graphical and algebraic representations

– Use compound units such as speed, unit pricing and density to solve problems.

#### Geometry and measures

– Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

– Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs

– Use Pythagoras’ Theorem (a² = b² + c² ) and trigonometric ratios (SOHCAHTOA) in similar triangles to solve problems involving right-angled triangles

#### PROBABILITY

– Enumerate sets and unions/ intersections of sets systematically, using tables, grids and Venn diagrams

– Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities

#### STATISTICS

– Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

– Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

– Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs