Mathematics
Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.
William Paul Thurston
Contact
Head of Maths: Mr S. Cookson  cooksons@harpergreen.net
Subject overview
Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A highquality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
Students are encouraged to make plenty of contributions in lessons, to listen carefully to the ideas of others, and to critically reflect upon contributions. We explicitly teach learners the appropriate ways to talk like mathematicians, and to listen to one anothers' ideas and reasoning.
Key Stage 3 Mathematics overview
We follow the National Curriculum for Mathematics at Key Stage 3.
Students build on their KS2 study, and are taught to:
 Develop fluency
 Reason mathematically
 Solve problems
We teach the following topics:
 Number
 Statistics
 Probability
 Geometry and measures
 Ratio, proportion and rates of change
 Algebra
Year 7
Half Term 1

Half Term 2

Half Term 3

 Place Value,
 Axioms and Arrays,
 Factors and Multiples,
 Order of Operations

 Positive and Negative numbers,
 Expressions,
 Equations and Inequalities.

 Angles,
 Classifying 2D shapes,
 Constructing Triangles and Quadrilaterals.

Knowledge:
 Understand the place value columns in base 10 Name nine and ten digit numbers in base 10
 Understand range of notations for quantities of time
 Develop calculation strategies
 Define prime numbers, square and cube numbers, factors
 Understand order of operation
Skills:
 Using the multiplicative relationships between different columns in base 10
 Develop sense of flexible number composition by solving problems involving time of day and quantities of time
 Understand commutative, associative and distributive properties
 Compare and contrast scaling, area, repeat addition and grouping models
 Interpret the order of operations

Knowledge:
 Negative numbers in variety of contexts
 Understand the meaning of absolute value
 Define algebraic notations
 Understand inequality notations
Skills:
 Compare and order positive and negative numbers
 Calculate with negative numbers using all four operations
 Use negative numbers for scaling
 Collect like terms, substitute numerical values, identify equivalent expressions

Knowledge:
 Define acute and obtuse angles
 Know angle facts, define parallel and perpendicular lines corresponding, alternate and cointerior angles
 Classify polygons, triangles and quadrilaterals
 Generalise results for properties of special types of triangles and quadrilaterals
 Recognise congruency
Skills:
 Draw and estimate angles
 Use angle facts to find missing angles, form and solve equations from contexts arising from properties of triangles and quadrilaterals
 Construct triangles and quadrilaterals using ruler, compass and protractor

Assessment
 Weekly quiz
 Two homework quizzes (one prelearning and one postlearning quiz)
 Cumulative learning checkpoint towards end of HT.

Assessment
 Weekly quiz
 Two homework quizzes (one prelearning and one postlearning quiz)
 Cumulative learning checkpoint towards end of HT.
 Autumn Assessment

Assessment
 Weekly quiz
 Two homework quizzes (one prelearning and one postlearning quiz)
 Cumulative learning checkpoint towards end of HT.

Half Term 4 
Half Term 5 
Half Term 6 
 Coordinates,
 Area of 2D shapes,
 Transforming 2D figures.

 Prime factor decomposition,
 Conceptualising and comparing fractions,
 Manipulating and calculating with fractions

 Manipulating and calculating with fractions,
 Ratio,
 Percentage.

Knowledge:
 Reading coordinates from all three quadrants Recognise and plot horizontal and vertical lines Recognise and describe reflections, rotations, translations and simple enlargements
 Define similar shapes
Skills:
 Solve geometric problems involving missing coordinates
 Finding midpoint of a line Reflect, rotate and translate the object, combine the different transformations, enlarge shapes by a simple scale factor
 Recognise which transformations produce congruent shapes
 Explore the ratios within and between similar shapes

Knowledge:
 Define factors, multiples, square and cube numbers, prime numbers and triangular numbers, HCF, LCM, square and cube roots
 Recognise and name equivalent fractions
Skills:
 Write a number as a product of primes, use indices to record repeated multiplication
 Represent fractions in multiple ways, convert between fractions and decimals, write fractions in their simplest form, compare and order numbers, express one quantity as a fraction of another

Knowledge:
 Define and identify improper fractions and mixed numbers Understand and use the language and notation of ratio, define equivalent rations
 Define and understand percentages as a ratio of two quantities
 Create links between fractions and percentages
 Understand that percentage is a quantity out of 100
Skills:
 Use fractions of an amount
 Calculate with fractions and decimals using all four operations
 Convert between improper fractions and mixed numbers
 Connect ratio and fractions
 Construct equivalent rations
 Construct tables of values using graphs
 Compare ratios
 Express a quantity as a percentage of another
 Find percentages of amounts
 Increase or decrease quantity by a percentage

Assessment
 Weekly quiz
 Two homework quizzes (one prelearning and one postlearning quiz)•
 Cumulative learning checkpoint towards end of HT.
 Spring Assessment

Assessment
 Weekly quiz
 Two homework quizzes (one prelearning and one postlearning quiz)
 Cumulative learning checkpoint towards end of HT.

Assessment
 Weekly quiz
 Two homework quizzes (one prelearning and one postlearning quiz)
 Cumulative learning checkpoint towards end of HT
 End of Year Assessment

Year 8
Half Term 1 
Half Term 2 
Half Term 3 
 Venn Diagrams
 Types of Number
 Arithmetic with Mixed Numbers

 Negative Numbers
 Form and Solve Algebraic Equations
 Sequences

 Constructions
 Angle Facts and Parallel Lines
 Metric Conversions

Knowledge:
 Properties of numbers (factors, multiples, primes, indices)
 Set notation for Venn diagrams
 Parts of fractions and mixed numbers
Skills:
 Construct and interpret Venn Diagrams
 Identify and sort numbers by property
 Perform 4 operations with fractions
 Perform 4 operations with mixed numbers

Knowledge:
 Algebraic conventions
 Laws of directed number
 Number theory (natural numbers)
Skills:
 Apply 4 operations to directed number,
 Form algebraic expressions from written and geometric context
 Solve a range of equations
 Generate and describe sequences of numbers.

Knowledge:
 Types of angle
 Basic angle facts
 Angle facts in parallel lines
 Conversion facts.
Skills:
 Construct angles, triangles, bisectors
 Use known angle facts to find missing angles including in parallel lines.
 Convert between a range of metric measures, including areas and volumes

Assessment
 Fortnightly retrieval quiz
 Learning checkpoint towards the end of HT.

Assessment
 Fortnightly retrieval quiz
 Learning checkpoint towards the end of HT.

Assessment
 Fortnightly retrieval quiz
 Learning checkpoint towards the end of HT.
 Formal assessment.

Half Term 4 
Half Term 5 
Half Term 6 
 FDP Conversions Percentage Change Proportion
 Ratio
 Speed

 Rounding
 Area and Circumference of a Circle
 Properties of 3D Shapes Volume

 Charts and Graphs Averages

Knowledge:
 Basic FDP equivalences
 Proportional relationships
 Formulae for compound measures.
Skills:
 Convert between fractions, decimals and percentages
 Increase and decrease by a percentage
 Find percentage changes
 Use unitary method for proportion problems
 Share in ratio
 Simplify ratio
 Convert ratio to fractions,
 Calculate with speed/distance/time.

Knowledge:
 Place value
 Parts of circles
 Circle formula
 Properties of 3D shapes
 Formulae for volume and surface area
Skills:
 Round to varying degrees of accuracy (inc. dp and sf,)
 Find areas of circles
 Circumference of circles
 Identify and count faces, edges and vertices
 Draw plans and elevations
 Find volumes and surface area of 3D shapes

Knowledge:
 Meaning of averages and range
 Uses of, and meaning imparted by, charts and graphs
Skills:
 Draw and interpret bar charts, pie charts, scatter graphs, frequency polygons
 Find averages and range and use these to compare sets of data.

Assessment
 Fortnightly retrieval quiz
 Learning checkpoint towards the end of HT.

Assessment
 Fortnightly retrieval quiz
 Learning checkpoint towards the end of HT.

Assessment
 Fortnightly retrieval quiz
 Learning checkpoint towards the end of HT
 Formal assessment.

Year 9
Term 1

Half Term 2

Half Term 3

 Coordinates
 Linear Graphs
 Proportion
 Standard Form

 Sequences
 Algebraic Manipulation
 Substitution

 Constructions
 Loci
 Angles in Polygons
 Similar Shapes

Knowledge:
Skills:
 Plot and read coordinates
 Plot linear graphs
 Find midpoints
 Find gradient,
 Interpret linear graphs, plot and interpret real life graphs
 Convert numbers between ordinary and standard form
 Calculate with standard form

Knowledge:

Natural numbers

Algebraic notation.
Skills:
 Generate and describe sequences, including quadratic and geometric sequences
 Expand and factorise a range of expressions, including quadratic and cubic
 Substitute into expressions and formulae, including with indices and negatives.

Knowledge:
Skills:

Construct triangles and bisectors

Use a range of constructions to solve locus problems

Find sums of interior and exterior angles, single angles and solve problems

Identify similar shapes, find missing side lengths, extend to 3D shapes, finding missing areas and volumes.

Assessment
 Fortnightly retrieval quiz
 Learning checkpoint towards the end of HT

Assessment

Assessment

Half Term 4 
Half Term 5 
Half Term 6 
 Solving Equations
 Inequalities
 Further Graphs

 Transformations
 Pythagoras Theorem

 Averages
 Probability
 Scatter Graphs

Knowledge:
 Algebraic notation
 Inequality notation
 Cartesian coordinate system
Skills:

Solve equations with fractions

Variables on both sides

Brackets

Describe and represent inequalities

Solve inequalities

List integers which satisfy an inequality

Draw and interpret inequality graphs.

Knowledge:
 Equations of straight lines
 Basic angles
 Vector notation
 Cartesian coordinate system
 Square numbers
 Pythagorean Theorem.
Skills:

Translate, rotate, reflect and enlarge shapes on coordinate axes

Describe these transformations

Use Pythagoras to find the hypotenuse,

Use Pythagoras to find short sides

Solve problems with Pythagoras

Use Pythagoras to find missing lengths in 3D shapes.

Knowledge:

Mean

Median

Mode range

Frequency tables

Inequality notation

Grouped frequency

Trends of correlation.
Skills:

Find averages and range from a list of data

Find averages and range from frequency tables, including grouped frequency

Find probability of single events

Find probabilities of combined events using tree diagrams

Sample space diagrams, two way tables, frequency trees

Calculate and use relative frequency

Draw and interpret scatter graphs.

Assessment

Assessment

Assessment

Key Stage 4 Mathematics overview
We follow the Edexcel specification for Mathematics. All students are entered for either the Foundation tier or the Higher tier GCSE at the end of Year 11.
The Edexcel GCSE encourages learners to develop confidence in, and a positive attitude towards, mathematics, and to recognise the importance of mathematics in their own lives and to society. It also provides a strong mathematical foundation for learners who go on to study mathematics at a higher level post16. This specification enables learners to:
 develop fluent knowledge, skills and understanding of mathematical methods and concepts
 acquire, select and apply mathematical techniques to solve problems
 reason mathematically, make deductions and inferences and draw conclusions
 comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.
Please look at the Edexcel specification for more information about the course content.
Year 10
Year 10 GCSE Foundation tier

Half Term 1

Half Term 2

Half Term 3

 Fractions
 Rules of Indices
 Standard Form
 Percentages

 Transformations
 Enlargements
 Similar Shapes
 Bearings
 Trigonometry

 Loci
 Angle Facts
 Coordinate problems
 Vectors
 Estimation
 Accuracy

Knowledge:

Parts of fractions

Index laws

Place value.
Skills:

Find fractions of amounts

Perform 4 operations with fractions

Convert numbers to and from standard form

Perform 4 operations with standard form

Find percentages of amounts

Find percentage increase and decrease

Find percentage changes

Find one amount as a percentage of another

Reverse percentages

Compound percentages

Knowledge:
Skills:

Translate, rotate, reflect and enlarge shapes on coordinate axes

Describe these transformations, enlarge shapes by fractional and negative scale factors

Identify similar shapes

Find missing side lengths

Extend to 3D shapes

Finding missing areas and volumes

Draw bearings

Solve problems with bearings

Use scale for bearings problems

Use trigonometry to find missing side lengths and angles

Knowledge:

Loci rules

Basic angle facts

Angle facts in parallel lines

Interior and exterior angles in polygons

Cartesian coordinate system

Vector notation

Place value
Skills:

Use a range of constructions to solve locus problems

Find missing angles using a range of angle facts

Describe movements using vectors

Vector arithmetic

Make estimates of complex calculations

Define bounds of accuracy

Assessment

Assessment

Assessment

Year 10 GCSE Foundation tier 
Half Term 4 
Half Term 5 
Half Term 6 
 Coordinates,
 Area of 2D shapes,
 Transforming 2D figures

 Prime factor decomposition,
 Conceptualising and comparing fractions,
 Manipulating and calculating with fractions

 Manipulating and calculating with fractions,
 Ratio,
 Percentage

Knowledge:
 Parts of circles
 Formulae for circle measure
 Formulae for volume and surface area
 Formulae for compound measure.
Skills:
 Find the lengths of arcs
 Find areas of sectors
 Find volume and surface area of 3D shapes
 Calculate with speed/ distance/time and density/mass/volume.

Knowledge:
Skills:

Calculate sample sizes using a range of sampling methods,

Critique sampling methods

Construct a Venn diagram

Identify items from a Venn diagram using set notation

Calculate probabilities using set notation

Construct tree diagrams

Use tree diagrams to calculate probabilities.

Knowledge:
Skills:
 Expand a range of brackets including double, triple and multiple single brackets
 Factorise into a range of brackets
 Solve quadratic expressions by factorising
 Solve linear simultaneous equations by elimination and graphically.

Assessment

Assessment

Assessment

Year 10 GCSE Higher tier

Half Term 1

Half Term 2

Half Term 3

 Rules of Indices
 Standard Form
 Percentage Change (Compound)
 Surds

 Enlargements
 Bearings
 Trigonometry and Pythagoras (3D)
 Non right angled –Trigonometry

 Angle Proofs
 Circle Theorems
 Equations of Lines
 Vectors
 Bounds

Knowledge:

Laws of indices

Place value

Common integer powers

Decimal multipliers
Skills:

Use common laws of indices to simplify expressions and evaluate when using number

Calculate using standard form

Find compound percentage changes

Simplify surds

Perform 4 operations with surds

Expand brackets with surds

Rationalise the denominator.

Knowledge:
Skills:

Enlarge shapes using negative and fractional scale factors

Solve problems with bearings

Find missing lengths and angles in 3D shapes using Pythagoras and Trigonometry

Find missing side lengths and angles in nonright angled triangles using the sine rule and cosine rule

Find areas of triangles using the sine rule

Knowledge:
Skills:

Prove angle facts

Prove circle theorems

Use circle theorems to find missing angles

Solve problems with equations of lines

Describe movement using vector notation

Construct vector proofs

Find bounds of accuracy

Calculate to reasonable degrees of accuracy.

Assessment

Assessment

Assessment

Year 10 GCSE Higher tier 
Half Term 4 
Half Term 5 
Half Term 6 
 Equations of Circles
 Functions
 Transformation of Functions
 Iteration
 Tangents and Areas


Sampling Methods

Conditional Probability

Histograms

Cumulative Frequency

 Simultaneous Equations
 Solving Quadratic Equations
 Quadratic Inequalities
 Algebraic Fractions

Knowledge:
 Formula of a circle
 Function notation
 Common transformations of functions.
Skills:

Draw and interpret circles using the formula for a circle

Evaluate functions

Solve functions

Composite functions

Inverse functions

Approximate solutions by iteration

Construct iterative equations

Prove solutions by substituting into a function

Find the equation of a tangent

Find area using the equation of a tangent

Knowledge:

Sampling method

Probability rules.
Skills:

Calculate sample sizes using a range of sampling methods

Critique sampling methods

Construct and use tree diagrams for conditional probability

Draw and interpret histograms

Draw and interpret cumulative frequency graphs

Knowledge:

Quadratic graphs

Shapes of common graphs

Quadratic formula.
Skills:

Solve linear simultaneous equations

Solve nonlinear simultaneous equations

Solve quadratics by factorising

Completing the square

The quadratic formula

Solve quadratic inequalities

Find turning points and roots by completing the square

4 operations with algebraic fractions

Solve equations with algebraic fractions.

Assessment

Assessment

Assessment

Year 11
Year 11 – higher tier and foundation tier

Half Term 1

Half Term 2

Half Term 3

Half Term 4

Half Term 5

Half Term 6

Year 11 is given entirely to revision of previously taught content. This creates opportunities for teachers to tailor delivery to the individual needs of their learners.
