During key stage 3 pupils take increasing responsibility for planning and executing their work.   They extend their calculating skills for fractions, percentages and decimals, and begin to understand the importance of proportional reasoning.   They are beginning to use algebraic techniques and symbols. They generate and solve simple equations and study linear and quadratic functions with their corresponding graphs.   They begin to use deduction to manipulate algebraic expressions. Pupils progress from a simple understanding of the features of shape and space to using definitions and reasoning to understand geometrical objects. As they encounter simple algebraic and geometric proofs, they should begin to understand reasoned arguments.   They communicate mathematics in speech and a variety of written forms, explaining their reasoning.   They study handling data through practical activities and are introduced to a quantitative approach to probability.   Pupils should begin to make connections between different aspects of mathematics.   While it is still essential to show an ability for mental working the use of a calculator is now used for more difficulty arithmetic.   Some computer work may also be used to help demonstrate mathematical principles.

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	Integers		To increse understanding of integers and place value to deal with arbitrarily large positive numbers. Use the concepts and vocabulary of factor, multiple, common factor, highest common factor, least common multiple.
	fractions		To understand equivalent fractions, simplifying a fraction by cancelling all common factors; order fractions by rewriting them with a common denominator
	Decimals		Use decimal notation and recognise that each terminating decimal is a fraction, order decimals
	Percentages		To understand what percentage means and use this to compare proportions, interpret percentage as an operator .
	Rounding		To round to powers of ten, a set number of decimal places.
	Estimates and checking calculations		To make estimates of calculations on multiplication, divsion. To use these to rough check answers to calculations.
	Ratio		Use ratio notation, including reduction to its simplest form and its links to fraction notation recognise where fractions or percentages are needed to compare proportions. Identify problems that call for proportional reasoning, and choose the correct numbers to take as 100%, or as a whole.
	Powers and roots		Use the terms square, positive and negative square root, cube, cube root; use index notation for small integer powers and index laws for multiplication and division of positive integer powers.
	Algebra basic understanding		To understand the concept of an algebraic variable.
	Algebra simple equations		Set up simple equations, solve simple equations in one variable, by using inverse operations or by transforming both sides in the same way.
	Equations forming simple expressions		The use of fractions of variables and brackets in equations.
	Number patterns and sequences		Generate common integer sequences integers, squared integers, powers of 2, powers of 10, triangular numbers, to describe the Nth term of a sequence, justifying its form by referring to the activity or context from which it was generated
	Coordinates and liner graphs		From a simple liner equation calculate the X-Y pairs and plot them. To find gradients and intercepts.
	Graphs in higher powers		Curve recognition, sketching and relate data set to quadratic and qubic equations.
	Using linear graphs		Introdution of curves in higher powers of and to to sketch them.
	Shapes		The names of types of triangles and names of polygons.
	Solids		Names of simple three dimensional bodies. Relate volumes and suface areas.
	Symmetry		To determine the number of lines and order of rotational symmetry of 2D shapes. The plane of symmetry of simple 3D shapes
	Constructions and LOGO		To draw 2D shapes from known angles and lengths by using a ruler and compass. to understand a set of instructions that define a shape.
	Angles and tessellations		To know the names of angles to calculate unknown angles in shapes and crossing lines.
	Bearings and scale drawings		Relating angles to compass bearings and scale drawings from measurements and compass bearings.
	Transformations		The rotation, translation, reflection or rotation of an object in two dimensional space.
	Measures and measurement weights and lengths		Relating weights to every day objects and simple conversions of weights and lengths.
	Measures of time		The units of time and calculating time of arrival of journeys of known start time and length.
	Area and perimeter of 2D shapes		Calculation of areas and perimeters of regular and irregular shapes.
	Volume of 3D solids		Calculation of volumes and surface areas and relate cross sections to volumes.
	Collecting data		Freqency tables and dections from them, the differnces between primary and secondary data, stem and leaf diagrams.
	Representing data		Various pictograms including histograms and pie charts.
	Scatter diagrams		Simple deductions from linear scatter diagrams plotting from a data set.
	Averages		Calculations of means, modes, medians and range for a set of data. understand hoe these change with changes in the data set.
	Probability		True or false statements and simple probabilities using coins and spinners. Tables of probabilities and deductions from them.
	Numerical methods		Use systematic trial and improvement methods with ICT tools to find approximate solutions of equations where there is no simple analytical method.
	Inequalities		Solve simple linear inequalities in one variable, and represent the solution set on a number line