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Key Stage 3 - Algebra

Use and interpret algebraic notation, including:

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:

<Simplify expressions>    <Expand brackets like 3(x + 2)>   <Expand brackets like (x + 3)(x - 2)>

Understand and use standard mathematical formulae; rearrange formulae to change the subject

<Formulae for hiring tools, etc>

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

Use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement)

<Equations 1>   <Equations 2>   <Equations 3>   <Equations 4>   

Work with coordinates in all 4 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

<Draw a linear graph>   <Drawing y = mx + c graphs>

Interpret mathematical relationships both algebraically and graphically

Reduce a given linear equation in 2 variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

<Finding gradients>   <Identify a linear equation from the graph’s gradient and y intercept>

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

<Introduction to simultaneous equations>   <Graphical solutions for simultaneous equations>

<Solving simultaneous equations with substitution>   <Solving simultaneous equations with elimination part 1>

<Solving simultaneous equations with elimination part 2>

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

<Recap of sequences>   <Sequences and the term-to-term rule>   <Sequences and the position rule>

Recognise arithmetic sequences and find the nth term

Recognise geometric sequences and appreciate other sequences that arise

<Identify linear and quadratic sequences>    <Finding the position rule for a linear sequence>

<Using the nth term rule with quadratic sequences>   <Finding the nth term rule for a quadratic sequence>

The National Curriculum KS3 requirements are shown below in blue text. Underneath each of these requirements work helping to address ideas involved can be viewed by clicking on the bold underlined titles.