**use and interpret algebraic notation**, including:

ab in place of a × b

3y in place of y + y + y and 3 × y

a2 in place of a × a,

a3 in place of a × a × a;

a2 b in place of a × a × b

b a in place of a ÷ b

coefficients written as fractions rather than as decimals

brackets

**substitute numerical values into formulae and expressions, including scientific formulae **

**understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors **

**simplify and manipulate algebraic expressions to maintain equivalence by: **

**collecting like terms **

**multiplying a single term over a bracket **

**taking out common factors**

**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)

- work with coordinates in all four quadrants

- 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

- reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

- 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

- generate terms of a sequence from either a term-to-term or a position-to-term rule

- recognise arithmetic sequences and find the nth term

- recognise geometric sequences and appreciate other sequences that arise.