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#### KS4 Maths – Foundation

 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. 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.

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

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.