#### KS3 Maths

 Year Long Term Objective: Create a more coherent understanding of mathematics by developing fluency with number, connecting topics and creating opportunities for students to see the deeper structures. Challenge students to think and speak mathematically. Create a relevant and engaging curriculum by linking topics to real life applications and the history of the mathematics. Year Autumn 1 Autumn 2 Spring 1 Spring 2 Summer 1 Summer 2 Medium Term Objective: Develop fluency with number and begin to understand the number system as a connected whole by developing a deep and connected understanding 7 PLACE Value Multiplication and Division Powers and Roots Fractions Manipulating and simplifying expressions continued Estimation and using a calculator Addition and Subtraction Area and Perimeter of rectilinear shapes Order of Operations Manipulating and simplifying expressions Introduction to Data Negative Numbers Medium Term Objective: Develop multiplicative reasoning skills to a high level. Use axioms in mathematics to think mathematically and discover angle properties. Begin to understand the power of generalisation in solving real life problems. 8 Percentages Ratio continued Drawing, measuring and constructing Area and Circumference of circles Formulae The Cartesian Grid Ratio Proportional Reasoning Polygons and Angles Linear Equations Sequences Linear Inequalities Medium Term Objective: Develop upon the foundations of data handling, helping students to see how statistics has and continues to help us understand our world. Develop proportional reasoning into an understanding of how ratios are used in triangle geometry. Begin to understand the uses of quadratics equations in mathematical modelling. 9 Bivariate data and time series Introduction to Probability Triangles continued Standard Form Advanced manipulating and simplifying expressions Quadratics Congruence and Similarity Triangles Circles Advanced Linear graphs and Equations Advanced Data
• ### Resources

 Name Link Hegarty Maths – used for homework and independent learning, pupils will receive a login HegartyMaths Timetable Rockstars – pupils will receive their own login Times Tables Rock Stars (ttrockstars.com) KS3 Maths Revison guides can be purchase online through Amazon, CGP, Waterstones etc. BBC Bitesize KS3 Maths – BBC Bitesize Maths Made Easy KS3 Maths Resources | English and Science | Maths Revision (mathsmadeeasy.co.uk) Corbett Maths – videos, worksheets Corbettmaths – Videos, worksheets, 5-a-day and much more Mathsgenie – videos, worksheet Maths Genie – Free Online GCSE and A Level Maths Revision NRICH – rich problem solving activities Secondary Students (maths.org)
• ### Videos

Place Value

Example Key Words

## Integer

A whole number, positive or negative (including zero).

## Significant Figure

The first non-zero digits in a number.

## Place holder

A significant zero in the decimal representation of a number

## Whole number

A number with no digits after the decimal point.

Example Key Words

## Sum

The result when two things are added together.

## Difference

The result when two things are subtracted from each other.

## Commutativity

Involving the condition that a group of quantities connected by operations gived the same result whatever the order of te quantities involved e.g. 2 x 3 = 3 x 2

## Associativity

Involving the condition that a group of quantities connected by operations gives the same results whatever the grouping, i.e. in whichever order the operations are performed, as long as the order of the quantities remains the same. E.g. (2 x 3) x 4 = 2 x (3 x 4)

Multiplication/Division

Example Key Words

## Product

The result when two things are multiplied together.

## Inverse

The opposite operation.

## Integer

A whole number, positive or negative (including zero).

## Factors

A number that divides exactly into another number.

## Multiples

A value in a number’s times table.

Area/Perimeter of rectilinear shapes

Example Key Words

## Rectilinear shape

A shape that has straight sides and right angles.

A four-sided shape.

## Area

The space inside a 2D shape.

## Perimeter

The total distance around the outside of a shape.

## Compound shape

Shape made up of two or more smaller shapes.

Negative Numbers

Example Key Words

## Negative

Any number less than zero

## Positive

A number greater than zero

## Directed Numbers

Another way to describe negative numbers

## Integer

A whole number, positive or negative (including zero)

## Product

The result when two things are multiplied together.

## Sum

The result when two things are added together

Powers, Roots and Primes

Example Key Words

## Multiple

A value in a numbers times table

## Factor

A number that divides exactly into another number

## Index/indices

Another name for a power.

## Prime number

A number that has no factors except itself and 1

## Surd

The square roots of numbers that cannot be simplified into a whole number or rational number

## Power

A way of showing that a number or letter (the base) is being multiplied by itself a certain number of times. The power tells you how many of the base multiply together

Order of Operations

Example Key Words

## BIDMAS

A way of describing the order that operations should be done in a calculation

## Operation

Something you do to one or more numbers, such as add, subtract, multiply or divide

## Inverse

The opposite operation

## Function

A relation or expression involving one or more variables

## Order

The sequence in which the operations should be performed

Manipulating and simplifying expressions

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

Fractions

Example Key Words

## Numerator

The top number of a fraction

## Denominator

The bottom number of a fraction

## Equivalent fractions

Fractions that are equal in size but are written differently

## Reciprocal

You can find the reciprocal of a number by swapping the places of the numerator and denominator

## Fraction

A part of a whole, written as one number on top of another

## Simplest terms

A fraction in its simplest terms cannot be cancelled down

Estimation and Use of a Calculator

Example Key Words

## Approximation

A number that is not exact because it has been rounded or estimated

## Rounding

Replacing a number with a similar sized number which is easier t work with (e.g. rounding 2.13 to 2)

## Estimate

A rough guess found by using rounded numbers

## Significant figure

The first non-zero digits in a number

Introduction to Data

Example Key Words

## Discrete date

Date that can only take certain values, it can not be measured. There are only a limited numbers of values it can take. Discrete date can also be non-numerical

## Continuous data

Data that is measured rather than counted. Continuous data can take any value

## Average

A measure of the most typical value in a set of date. Mean, median and mode are types of average.

Percentages

Overview

Understand the concept of a percentage and calculate simple percentages of amounts

Convert between FDP

Calculate percentage increase and decrease

Write a quantity as a percentage of another

Calculate percentage change

Example Key Words

Percentage, tax, interest

Ratio

Overview

Use ratio notation to express relationships

Simplify ratios

Simplify ratio and a unit ration 1:n or n:1

Divide a quantity into a ratio

Scale drawing and maps

Problems and applications of ratio

Example Key Words

Ratio, proportion, scale, unit ratio

Ratio continued

Overview

Use ratio notation to express relationships

Simplify ratios

Simplify ratio and a unit ration 1:n or n:1

Divide a quantity into a ratio

Scale drawing and maps

Problems and applications of ratio

Example Key Words

Ratio, proportion, scale, unit ratio

Proportional Reasoning

Overview

Compare quantities (value for money, exchange rate etc)

Scaling up/down e.g. recipes, shapes

Conversion graphs

Changing between units of time, length, area and capacity

Reverse percentages and finding the original value given a percentage change

Example Key Words

Proportional, direct, inverse, unitary

Drawing, measuring and constructing

Overview

Using a ruler to measure lines and protractor to measure angles, labelling segments and angles correctly

Using a compass to draw circles and arcs

Construct triangles given SSS, SAS and ASA

Construct a perpendicular bisector, perpendicular from a point to a line and angle bisector

Drawing and reading scale drawing and loci

Example Key Words

Perpendicular, construct, congruent, locus, bisector

Polygons and Angles

Overview

Naming, labelling and recognising the features of triangles

Naming, labelling and recognising the features of quadrilaterals

Naming and recognising the features of other polygons

Identify angles on a straight line, around a point and vertically opposite

Identify angles in parallel lines

Bearing

Interior and exterior angles in polgons

Example Key Words

Regular, irregular, alternate, corresponding, co-interior

Area and Circumference of circles

Overview

Recap rectilinear area and perimeter

Recap area of triangles and quadrilaterals

Calculate circumference and area of circles

More complex area of compound shapes, problems involving area

Example Key Words

Linear Equations

Overview

Solve simple one and two step equations

Solve equations with variables on both sides

Solve complex linear equations

Applications to forming and solving equations in a geometric or real life context

Example Key Words

Expression, equation, variable, inverse, linear

Formulae

Overview

Write formulas in words and letters

Substitute values into formulae using inputs and outputs

Rearrange linear formulae

Rearrange non linear formulae

Rearrange formulae with factorisation

Example Key Words

Formulae, input, output, non-linear, factorisation

Congruence and Similarity

Overview

Draw a scatter graph

Interpret relationships from scatter graphs, recognise correlation

Draw and predict from a line of best fit

Interpret and construct tables and line graphs for time series data

Example Key Words

Bivariate, correlation, causation, interpolate, extrapolate

Sequences

Overview

Generate terms of a sequence from term to term and position to term rules

Find the nth term of an arithmetic sequence

Recognise simple geometric sequences, quadratic sequences, common sequences

Example Key Words

Sequence, arithmetic, geometric, generate, nth term

The Cartesian Grid

Overview

Plot 2D coordinates in four quadrants

Express number relationships algebraically

Represent number relationships on a Cartesian grid

Sketch graphs of straight lines and quadratics by finding a table of values

Read/estimate values of variables from a graph

Sketch the graph given the gradient and y intercept

Identify graphs of real life situations

Find speed from distance time graphs, acceleration and distance from velocity time graphs

Example Key Words

Linear Inequalities

Overview

Solve linear inequalities in one variable

Represent the solutions on a number line

Represent linear inequalities in two variables on a Cartesian grid

Identify integer solutions to inequalities

Example Key Words

Inequality, linear, variable, integer solutions

Bivariate data and time series

Overview

Draw a scatter graph

Interpret relationships from scatter graphs, recognise correlation

Draw and predict from a line of best fit

Interpret and construct tables and line graphs for time series data

Example Key Words

Bivariate, correlation, causation, interpolate, extrapolate

Introduction to Probability

Overview

Record, describe and analyse the frequency of outcomes of simple probability experiments

Calculate theoretical probability

Generate theoretical sample spaces and use these to calculate probabilities

Record outcome and possibilities using frequency trees, two way tables and simple Venn diagrams. Use these to calculate probabilities

Sets and logic, including more advanced work on Venn Diagrams

Example Key Words

Probability, theoretical, experimental, mutually exclusive, exhaustive

Triangles

Overview

Use Pythagoras’ Theorem to calculate missing sides of a right angled triangle

Use Trigonometry to calculate missing sides and angles of a right angled triangle

Exact values of sine, cos and tan for 0, 30, 45, 60 and 90 degrees

Problems involving Pythagoras and trigonometry including bearings

Example Key Words

Pythagoras’ Theorem, Trigonometry (sine, cosine, tangent), hypotenuse, adjacent, opposite

Triangles continued

Overview

Use Pythagoras’ Theorem to calculate missing sides of a right angled triangle

Use Trigonometry to calculate missing sides and angles of a right angled triangle

Exact values of sine, cos and tan for 0, 30, 45, 60 and 90 degrees

Problems involving Pythagoras and trigonometry including bearings

Example Key Words

Pythagoras’ Theorem, Trigonometry (sine, cosine, tangent), hypotenuse, adjacent, opposite

Circles

Overview

Identify parts of circles

Calculate the circumference and area of a circle

Problems with circumference and area of circles

Calculate the arc length and sector area

Identify and use Circle Theorems

Prove Circle Theorems

Example Key Words

Subtended, equidistant, Alternate Segment Theorem, cyclic quadrilateral

Standard Form

Overview

Write large numbers in standard form

Write small numbers in standard form

Compare numbers that are in standard form

Add and subtract numbers in standard form

Multiply and divide numbers in standard form

Problems and applications to standard form

Example Key Words

Standard form, index form, ordinary form

Overview

Construct two linear simultaneous equations from a context and represent the solution graphically

Find the solution to two simultaneous linear equations algebraically and check solutions

Identify equations of parallel and perpendicular lines

Advance y = mx + c questions – finding the equations given two points or a point and the gradient

Example Key Words

Overview

Expand more than two brackets

Factorise the difference of two squares

Simplify algebraic fractions, including numerical factor, single letter factors and bracket factors

Example Key Words

Overview

Introduce the f(x) = notation as a substitution for y =

Solving quadratic equations by factorising, the quadratic formula, completing the square or graphically

Select the best method for solving quadratic equations

Example Key Words

Variable, coefficient, roots, function of x, turning points (minimum/ maximum points), completing the square, Quadratic formula

Overview

Averages of grouped data

Graphical representations of continuous and grouped data – cumulative frequency, box plots and frequency polygons

Measures of spread – interquartile range

Compare data sets

Example Key Words

Cumulative frequency, quartile, spread, class interval, box plot