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KS4 Maths – Foundation

Please click on the links below to find out more about each unit.

Year Long Term Objective: To Build upon the foundation laid in KS3 to prepare students for the rigours of the GCSE. Students should be stretched with challenging GCSE style questions routinely.
Year Autumn 1 Autumn 2 Spring 1  Spring 2 Summer 1 Summer 2
Medium Term Objective: Autumn: Recap and extend students on fundamental number and algebra work. Spring: Work on geometry, while stretching students by interleaving with number and algebra exam problems. Summer: Enhance students proportional reasoning skills and develop ability at harder exam questions.
Number Fractions and Percentages Angles Graphs Ratio and Proportion Multiplicative Reasoning

Algebra Equations, Inequalities and sequences Averages and Range Transformations Right Angled Triangles



– Calculations

– Decimals

– Place value

– Bounds (To include safety in carrying goods in a lorry)

– Primes

– Factors and Multiples

– Squares and Cubes

– Index notation

Example Key Words


The result when two or more numbers are mutiplied together


The opposite operation


A whole number, positive, negative or zero

Significant figure

The first non zero digits of a number


A number that divides exactly into another number


A value in the number’s time table

Fractions and Percentages


– Working with fractions

– Calculating with fractions

– Fractions, decimals and percentages

– Calculating percentages 1

Example Key Words


The top number of a fraction


The bottom number of a fraction

Equivalent fraction

Fractions that are equal in size but are written differently

Simplest terms

A fraction in its simplest terms cannot be cancelled down


Out of one hundred

Percentages and fractions

Percentages are fractions with a denominator of 100



– Properties of shapes

– Angles in parallel lines

– Angles in triangles

– Exterior and interior angles

– Geometrical patterns

Example Key Words

Properties of a shape

A character that defines a shape. E.g the number of sides, total sum of angles.


Two or more straight lines that do not intersect and remain the same distance apart


A shape that has a minimum of three sides

Interior angles

One of the angles inside a polygon

Exterior angle

An angle formed on the outside of a polygon by extending one of its sides.


A four sided shape.



– Coordinates

– Linear graphs

– Gradient and y = mx + c

– Real-life graphs (To include phone bills and taxi charges)

– Distance-time graphs

Example Key Words


A pair of numbers that describe the position of a point on a graph using the horizontal and vertical distances from the two reference axes.

Linear graph

A straight line graph


The measure of the steepness of a curve.

Y intercept

The point where the line crosses the y axis

Distance- time graph

A graph that plots the distance traveled by an object on a vertical axis against the time taken

Ratio and Proportion


– Writing and using ratios

– Ratios and measures

– Comparing ratios

– Using proportion

– Proportion and graphs

– Proportion problems

Example Key Words


This compares two or more values. They are written in the form a:b

Simplify a ratio

Reducing a ratio to its simplest form

Unit ratio

Writing a raio in the form n:1 or 1:n


Describes a relationship between two variables.

Multiplicative Reasoning


– Percentages

– Growth and decay (To include loan sharks and exponential growth in diseases)

– Compound measures

– Distance, speed and time

– Direct and inverse proportion

Example Key Words

Compound Interest

The amount of interest earned each year is added onto the original capital and included in the following year’s calculation

Simple interest

The total amount of interest is added on at the end the term


The reduction in value of an asset over time.

Growth and decay

Using a compound interest type formula to calculate the growth of a population or depeciation of an asset

Direct Proportion

A direct relationship between the increase or decrease of two variables.

Inverse proportion

The relationship between one variable is directly proportional to the reciprocal of another.



– Algebraic expressions

– Simplifying expressions

– Substitution

– Formulae

– Expanding brackets

– Factorising

Example Key Words


A mathematical expression uses letters to represent numbers. It does not contain an equals sign


An unknown quantity, usually shown by a letter. Variables can take different values

Term (of an expression)

Each of the ‘bits’ in an expression, separated by plus or minus signs is called a term


Multiply out brackets to remove them from an expression


Rewrite an expressions by putting it in brackets with a factor on the outside


Make something simpler by dividing by common factors or collecting like terms

Equations, Inequalities and sequences


– Solving equations 1

– Introducing inequalities

– Formulae

– Generating sequences

– Using the nth term of a sequence

Example Key Words


A symbol that stands for an unknown quantity


A mathematics statement that uses an equals sign to show that two expressions are equal.


A relationship between two expressions that are not equal, often written with the symbols >, >, <, and 


An equation that expresses a mathematical relationship between two or more variables


A number in a sequence


A set of numbers or objects arranged according to a specific rule or pattern.

Averages and Range


– Mean and range

– Mode and median

– Estimating the mean

– Sampling

Example Key Words


Add all the values together and divide by how many ther are.


Place all values in order and find the middle value.


The most popular value or item. (if in a table, it is the item with the highest frequency).


The difference between the largest and smallest value.


The number of times an event happens or the numbers of scores in a range


A small part or quantity intended to show what the whole is like



– Translation (To include computer generated imagery and vectors)

– Reflection

– Rotation

– Enlargement

– Combining transformations

Example Key Words


A change in the position, size or shape of a figure


This changes the position of a shape


This flips the shape over – it is the mirror image


Turning a shape around a fixed point.


This changes the size of the shape – it can make it smaller.

Scale factor

This defines how many times bigger or smaller an enlagement makes a shape.

Right Angled Triangles


– Pythagoras’ theorem

– Trigonometry: the sine ratio
– Trigonometry: the cosine ratio

– Trigonometry: the tangent ratio

Example Key Words


The longest side of a triangle. It is also the side opposite the right angle.

Pythagoras' Theorem

A theorem stating that in a right triangle the area of the square on the hypotenuse is equal to the sum of the areas of the squares drawn on the other two sides.

Opposite and adjacent side Side

The side opposite (opposite) and next to (adjacent) the angle you are dealing with in a triangle (not the right angle)

The Sine ratio

The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to that of the hypotenuse.

The Cosine ratio

The cosine of an angle in a right triangle is defined as the ratio of the length of the side adjacent to the angle to that of the hypotenuse.

The Tangent ratio

The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to that of the adjacent side.