#### KS4 Curriculum

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Home > Curriculum > KS4 Maths – Foundation

#### 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. |
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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. |
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10 |
Number | Fractions and Percentages | Angles | Graphs | Ratio and Proportion | Multiplicative Reasoning |

11 |
Algebra | Equations, Inequalities and sequences | Averages and Range | Transformations | Right Angled Triangles |

Number

Overview

– 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

## Product

The result when two or more numbers are mutiplied together

## Inverse

The opposite operation

## Integer

A whole number, positive, negative or zero

## Significant figure

The first non zero digits of a number

## Factors

A number that divides exactly into another number

## Multiple

A value in the number’s time table

Fractions and Percentages

Overview

– Working with fractions

– Calculating with fractions

– Fractions, decimals and percentages

– Calculating percentages 1

Example Key Words

## Numerator

The top number of a fraction

## Denominator

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

## Percent

Out of one hundred

## Percentages and fractions

Percentages are fractions with a denominator of 100

Angles

Overview

– 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.

## Parallel

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

## Polygon

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.

## Quadrilateral

A four sided shape.

Graphs

Overview

– Coordinates

– Linear graphs

– Gradient and y = mx + c

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

– Distance-time graphs

Example Key Words

## Coordinate

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

## Gradient

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

Overview

– Writing and using ratios

– Ratios and measures

– Comparing ratios

– Using proportion

– Proportion and graphs

– Proportion problems

Example Key Words

## Ratio

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

## Proportion

Describes a relationship between two variables.

Multiplicative Reasoning

Overview

– 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

## Depreciation

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.

Algebra

Overview

– Algebraic expressions

– Simplifying expressions

– Substitution

– Formulae

– Expanding brackets

– Factorising

Example Key Words

## Expression

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

## Variable

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

## Expand

Multiply out brackets to remove them from an expression

## Factorise

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

## Simplify

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

Equations, Inequalities and sequences

Overview

– Solving equations 1

– Introducing inequalities

– Formulae

– Generating sequences

– Using the nth term of a sequence

Example Key Words

## Variable

A symbol that stands for an unknown quantity

## Equation

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

## Inequality

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

## Formula

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

## Term

A number in a sequence

## Sequences

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

Averages and Range

Overview

– Mean and range

– Mode and median

– Estimating the mean

– Sampling

Example Key Words

## Mean

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

## Median

Place all values in order and find the middle value.

## Mode

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

## Range

The difference between the largest and smallest value.

## Frequency

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

## Sample

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

Transformations

Overview

– Translation (To include computer generated imagery and vectors)

– Reflection

– Rotation

– Enlargement

– Combining transformations

Example Key Words

## Transformation

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

## Translation

This changes the position of a shape

## Reflection

This flips the shape over – it is the mirror image

## Rotation

Turning a shape around a fixed point.

## Enlargement

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

Overview

– Pythagoras’ theorem

– Trigonometry: the sine ratio

– Trigonometry: the cosine ratio

– Trigonometry: the tangent ratio

Example Key Words

## Hypotenuse

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.