## Sixth Form Open Evening

# Maths

The Mathematics Department aims to equip all students with the tools to solve problems and think analytically. We want all students to leave with the skills to carry out day to day activities that involve the use of mathematics. Students will benefit from experienced, passionate teachers who enjoy their subject and have an invested interest in getting the most out of their God given talents.

## KEY STAGE 3

### YEAR 7

### Autumn 1

Carrying out long multiplication and division:3-digit by 2-digit

Using negative numbers in context and the four operations

Understanding the order of operations

Knowing prime numbers up to 100

Divisibility checks in this order for 2,5,10,3,4,6,9,11**

Finding factors of numbers and multiples

Finding HCF AND LCM between 2 and 3 different numbers.

Naming polygons (n=3-10)

Understanding the geometrical properties of triangles and quadrilaterals

Naming common 3D shapes.

Identifying faces, edges and vertices

Working with nets of shapes

Constructing and interpreting plans and elevations

Calculating with fractions in simple cases.

Calculating simple fractions of quantities

Understanding place value

Rounding to various decimal places

Ordering decimals

Rounding to 1 significant figure

Long multiplication and division, including decimals

Estimation

### Autumn 2

Outcomes

Naming, measuring and drawing angles

Using the angle sum on a straight line = 180º and Quads and Triangles

Solving problems involving parallel lines

Knowing triangle proofs (exterior angle & angle-sum)

Solving problems involving polygons, e.g. interior angles including working backwards.

Solving simple problems involving polygons. NOT ALGEBRA

Calculating simple percentages of quantities.

Finding percentages of an amount using calculator

Calculating an increase or decrease by a percentage, including VAT

Using data collection sheets

Questionnaires

Explaining sampling techniques and pros and cons

Finding mean, median, mode and range of raw data

Knowing pros and cons of each average, and which to use to compare two distributions

Working back from the mean to find sum of data and frequency

MMMR from a frequency table

Calculating moving averages

### Spring 1

Estimating lengths

Converting between metric and imperial units using known facts

Converting between units of area, e.g. m² to cm²

Using simple scale drawings

Solving problems involving similar triangles (+ve scale factor)

Deriving simple expressions

Simplifying simple algebra

Expanding brackets such as x(x+4)

Factorising, e.g. x² - 5x and 12x – 8

Expanding and simplifying brackets and expressions

Substituting negative numbers into algebraic expressions

Using simple formulae (include unit conversion) **not inverse**

IF TIME: Expand (x+2)(x-5)

IF TIME: Factorise Quadratics

Converting between fractions, decimals and percentages

Ordering fractions, decimals and percentages

Quantity of an anount as a percentage.

Calculating profit and loss

Converting fractions to a ratio, e.g. 1/3 of a whole is 1:2

Proportion questions (e.g. recipes not exchange rates)

Simplifying ratios

Dividing quantities into ratios

Solving questions that include fractions, dec % and ratio

### Spring 2

Constructing and interpreting bar charts to compare two sets of data

Constructing a stem and leaf diagram

Interpreting a stem and leaf diagram to find the median

Interpreting a time series graph

Constructing a pie chart, and comparing two sets of data

Constructing and interpreting scatter graphs and correlation

Drawing and using lines of best fit and creating predictions and knowing when predictions are valid.

Introduce two way tables

Identifying lines of symmetry

Identifying planes of symmetry

Identifying rotational symmetry

Carry out enlargements in simple cases (i.e. no point)

Carry out simple reflections and rotations

Solving simple equations, e.g. 5x = 25 and x-2=6

Solving simple equations, e.g. 3y + 2 = 8

Solving equations, including unknowns on both sides

Deriving and solving equations from worded problems

Deriving and solving equations from diagrams and polygons

Using a formula inversely, e.g. find x if y=3 where y = 2x-1

### Summer 1

Finding simple squares, cubes and roots

Calculating indices and roots, e.g. 4³, 2³ x 3²,‘the cube of 4’

Using a calculator, e.g. ‘1∙5³’ and ‘square root of 23∙78’

Include standard form intorduction.

Stating simple probability

Listing all outcomes for a single event

Using the fact that the sum of probabilities is 1

Finding missing probability from a list or table of results

Understanding and using relative frequency

Finding probabilities from a 2-way table

Estimating probability from diagrams, pie charts and tables

Finding terms in a linear sequence

Finding the nth term

Knowing whether terms are within a sequence

Recognising non-linear number sequences

Recognising complex number sequences

### Summer 2

Finding area and perimeter of rectangles and kites

Finding area of triangle, regular polygons, compound shapes

Calculating area or circumference of a circle given radius

Calculating volumes in simple cases

Completing tessellations

Using co-ordinates in four quadrants

Calculating midpoints of a point (and work backwards)

Constructing simple linear graphs

Understanding unstructured linear graphs

Using conversion graphs

Measuring simple bearings

Drawing and measuring bearings

Constructing accurate drawings and angles and bearings

## YEAR 8

PLEASE note: Although some of the topics featured in the year 8 scheme have the same topic names as year 7, they are a progression in difficulty and level.

### Autumn 1

Recap order of operations and Negatives.

Divisibility checks in this order for 2,5,10, 3,4,6,9,11

Knowing prime numbers up to 100

Finding factors of numbers and multiples.

Finding the prime factor decomposition of a number

Finding the highest common factor and lowest common multiple

Understanding the geometry of triangles and quadrilaterals

Solving problems involving parallel lines

Working out the exterior and interior angles as well as sum.

Solving problems involving polygons, e.g. interior angles including working backwards.

Working with nets of shapes

Constructing and interpreting plans and elevations

Performing all operations with fractions and integers, mixed numbers and fractions as well as mixed and mixed.

Finding fractions and mixed numbers of an amount

Reciprocals

Long multiplication and division, including decimals as well Multiplication and division by a number between 0 and 1

Rounding to 1 significant figure

Estimation

Estimation and division by a number of less than 1

### Autumn 2

Outcomes

Prove the area of triangles and quadrilateral

Calculating area or circumference of a circle given radius or diameter

Finding area and perimeter of triangles, regular polygons, compound shapes

Calculating volumes in simple cases

Finding volumes of 3D shapes including prisms

Finding percentages by mental methods and calculator

Calculating an increase or decrease by a percentage

Calculating percentage decrease and increase

Calculating compound interest and simple interest

Extend to reverse if time.

Using data collection sheets

Questionnaires

Explaining sampling techniques and pros and cons

Finding mean, median, mode and range of raw data. Extend to Calculating moving averages

Knowing pros and cons of each average, and which to use to compare two distributions

Working back from the mean to find sum of data and frequency

MMMR from a frequency table

### Spring 1

Finding dimensions of a formulae

Converting between metric and imperial units using known facts

Measuring simple bearings

Drawing and measuring bearings

Understanding, using and solving problems with bearings

Simplifying simple algebra

Expanding brackets such as x(x+4)

Factorising, e.g. x² - 5x and 12x – 8

Expanding brackets and simplifying the result

Expanding and simplifying brackets and expressions

Substituting negative numbers into algebraic expressions

Substitution into complex formulae

Expand (x+2)(x-5)

Factorise Quadratics

Converting between fractions, decimals and percentages

Ordering fractions, decimals and percentages

Calculating with ratios

Simplifying ratios

Solving problems involving proportion in simple cases

Calculating with ratios in recipes

Solving questions that include all the above facts.

### Spring 2

Interpreting a stem and leaf diagram to find the median

Interpreting a time series graph

Using data collection sheets

Finding probabilities from a 2-way table

Drawing box plots

Using ‘fx’ in a frequency table

Constructing a pie chart

Constructing a stem and leaf diagram

Constructing and interpreting scatter graphs

Drawing and using lines of best fit

Understanding correlation

Use of Pythagoras’ Theorem

Coordinates

Finding the length of a line given 2 points

Finding the midpoint between two points

Using coordinates in 3D problems

Solving simple equations, e.g. 3y + 2 = 8

Using a formula inversely, e.g. find x if y=3 where y = 2x-1

Solving equations, including unknowns on both sides

Deriving and solving equations from diagrams

Solving equations

Rearranging simple formulae

### Summer 1

Calculating indices and roots, e.g. 4³, 2³ x 3²,‘the cube of 4’

Using a calculator, e.g. ‘1∙5³’ and ‘square root of 23∙78’

Using a calculator in complex situations

Using the rules of indices in numeric situations

Calculating problems involving numbers in standard form

Using the fact that the sum of probabilities is 1

Understanding and using relative frequency

Finding missing probability from a list or table of results

Recognising complex number sequences

Finding the nth term for a linear sequence

Solving cubic equations by trial and improvement

Introduction to Inequalities and simple solving.

### Summer 2

Carrying out enlargements in simple cases

Identifying planes of symmetry

Carrying out simple transformations

Carry out transformations including translation with vectors

Solving problems involving similar triangles (+ve scale factor) ****IF TIME****

Constructing simple linear graphs

Using conversion graphs

Understanding unstructured linear graphs

Solving simultaneous equations by graphical methods

Using y = mx+c to find the gradient and equation of a line without drawing

Graphing quadratic functions in simple cases

Solving quadratic equations graphically

Interpreting real-life graphs, eg travel graphs

Constructing the perpendicular bisector of a given line

Constructing loci

Constructing accurate drawings and angles

Carrying out constructions, eg triangles in all situations

Completing tessellations

## KEY STAGE 4

### YEAR 9

Depending on set your students will be learning some if not all of the following.

### Autumn Term 1

Indices

Calculating with negative numbers

Decimals

Rounding and estimation

Fractions

Percentages

Writing algebraic expressions and substitution

Simplifying algebraic expressions and expanding brackets

Factorising

Solving linear equations

### Autumn Term 2

Properties of angles

Collecting data

Representing data

Probability

### Spring Term 1

Percentages 2

Ratio and Proportion

Graphs and equations

Expressions and equations

Linear sequences

### Spring Term 2

Units

·3D shapes, surface area and volume

Transformation and coordinates

Representing and processing data and averages

### Summer Term 1

Indices and standard form

Speed, Distance, Time

Inequalities

Rearranging a formula

### Summer Term 2

Trigonometry

Statistics

Probability

Construction and loci

## YEAR 10 - Edexcel

### Year 10 Higher:

### Autumn1

Properties of numbers including indices

Decimals, four operations.

Rounding and estimation

Fractions, four operations

Percentages

Substitutions and formulae

Simplifying algebraic expressions

Expanding single and double brackets

Factorising

### Autumn 2

Solving equations including fractional

Angles

Angles in polygons

Bearing

Ratio and proportion / speed distance time graphs

Similar shapes

### Spring 1

Presenting and processing data

Averages from tables

Area of rectilinear s

Volume of prisms

### Spring 2

Pythagoras including 3D

Trigonometry and trigonometric ratios

Using the sine and the cosine rules

Circle theorems

### Summer 1

Equation of a straight line

Transformation

Algebra: Changing the subject of a formula

Quadratic equations

Standard forms and surds

### Summer 2

Construction and loci

Probability

Upper and lower bounds

Simplifying algebraic fractions

Solving equations containing fractions

Vectors

GCSE MATHS Exam board

EDEXCEL

Year 10 Higher:

Autumn1 - Properties of numbers including indices Decimals, four operations. Rounding and estimation Fractions, four operations Percentages Substitutions and formulae Simplifying algebraic expressions Expanding single and double brackets Factorising

Autumn 2 - Solving equations including fractional Angles in polygons Bearing Ratio and proportion / speed distance time graphs Similar shapes

Spring 1 - Presenting and processing data Averages from tables Area of rectilinear s Volume of prisms

Spring 2 - Pythagoras including 3D Trigonometry and trigonometric ratios Using the sine and the cosine rules Circle theorems

Summer 1 - Equation of a straight line Transformation Algebra: Changing the subject of a formula Quadratic equations Standard forms and surds

Summer 2 - Construction and loci Probability Upper and lower bounds Simplifying algebraic fractions Solving equations containing fractions Vectors

Year 10 Foundation:

Autumn1 - Numbers properties including simple indices Decimals Rounding and estimation Fractions Percentages Ratio and proportion

Autumn 2 - Forming algebraic expressions Substitution Simplifying and expanding Forming and solving equations Inequalities Linear sequences

Spring 1 - Perimeter and area of rectilinear Area and circumference of a circle Surface area and volume of prisms

Spring 2 - Angles in quadrilaterals Angles in polygons Bearing Construction

Summer 1 - Pythagoras Collecting and processing data Scatter graphs Averages from tables Estimated mean

Summer 2 - Probability Representing linear functions graphically Representing and solving inequalities Transformation

### Year 11

Exam Board:

Edexcel

Programme of Study:

Year 11 - Higher

Autumn 1 Inequalities and formula Graphs and equations Simultaneous equations Quadratics

Autumn 2 Quadratics Area and volume Line and scatter graphs Indices Standard form

Spring 1 Surds Similar shapes Direct and inverse proportion probability

Spring 2 Probability Pythagoras and trigs Trigonometry (non right angle_ Vectors Transformation Algebraic fractions

Summer 1 Proof Circle geometry

Year 11 - Foundation

Autumn 1 Numbers properties including simple indices Decimals Rounding and estimation Fractions Percentages Ratio and proportion

Autumn 2 Forming algebraic expressions Substitution Linear graphing Simplifying and expanding Forming and solving equations Inequalities Linear sequences

Spring 1 Perimeter and area of rectilinear Area and circumference of a circle Surface area and volume of prisms Angles

Spring 2 Angles in

## SIXTH FORM

### YEAR 12 – edexcel (AS level)

### Autumn Term 1

Algebra and Quadratics

Equations AND Inequalities

Sketching Curves

Mathematical Modelling

Representing Data- Location

Representing Data-Dispersion

Representing Data

### Autumn Term 2

Coordinate Geometry

Sequences and Series

Differentiation

Integration

Probability

Correlation

### Spring Term 1

Algebra

Sine and cosine

Exponentials

Coordinate Geometry

Binomial Expansion

Regression

Discrete Random Variables

Normal Distribution

### Spring Term 2

Radians and Sectors

Geometric Sequence

Trig Graphs and Trig Identities

Differentiation

Integration

### Summer Term 1

Revision

### Summer Term 2

Beginning A2 topics (Trigonometry)

YEAR 13– edexcel (a level)

### Autumn Term 1

Algebraic Fractions

Functions

Exponential Functions

Mathematical Modelling

Kinematics

### Autumn Term 2

Numerical Methods

Transformations of Graphs

Trigonometry 1 & 2

Differentiation

Dynamics

### Spring Term 1

Partial Fractions

Coordinate Geometry

Binomial Expansion

Differentiation

Statics

Moments

### Spring Term 2

Vectors in Calculus

Vectors in Mechanics

Integration

### Summer Term 1

Revision