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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 inter-connected 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 high-quality 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 co-interior 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 pre-learning and one post-learning quiz)
  • Cumulative learning checkpoint towards end of HT.

Assessment

  • Weekly quiz
  • Two homework quizzes (one pre-learning and one post-learning quiz)
  • Cumulative learning checkpoint towards end of HT.
  • Autumn Assessment

Assessment

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

Assessment

  • Weekly quiz
  • Two homework quizzes (one pre-learning and one post-learning quiz)
  • Cumulative learning checkpoint towards end of HT.

 

 

Assessment

  • Weekly quiz
  • Two homework quizzes (one pre-learning and one post-learning 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:

  • Cartesian coordinate system

  • y=mx+c,

  • Proportional relationships

  • Place value

  • Index notation.

 

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:

  • Loci rules

  • Formulae for interior and exterior angles

  • Similarity. 

 

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

  • 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
  •  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

  • 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.

 

 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 post-16. 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:

  •  Equations of straight lines

  • Basic angles

  • Vector notation

  • Cartesian coordinate system

  • Similarity

  • Rules for bearings

  • Trigonometric ratios

 

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

  • Fortnightly retrieval quiz

  • Learning checkpoint towards the end of HT

Assessment

  • Fortnightly retrieval quiz

  • Learning checkpoint towards the end of HT

  • Formal assessment

Assessment

  • Fortnightly retrieval quiz

  • Learning checkpoint towards the end of HT

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:

  • Sampling methods

  • Set notation

  • Probability (and/or) rules

 

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:

  • Algebraic notation

 

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

  • Fortnightly retrieval quiz

  • Learning checkpoint towards the end of HT. 

Assessment

  • Fortnightly retrieval quiz

  • Learning checkpoint towards the end of HT

  • Formal assessment.

Assessment

  • Fortnightly retrieval quiz

  • Learning checkpoint towards the end of HT. 

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:

  • Cartesian coordinate system

  • Bearings rules

  • Trigonometric ratios

  • Pythagorean formula

  • Sine rule

  • Cosine rule

  • Sine rule for area. 

 

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 non-right angled triangles using the sine rule and cosine rule

  • Find areas of triangles using the sine rule

Knowledge:

  • Proofs of angle facts

  • Proofs of circle theorems

  • Circle theorems y=mx+c

  • Vector notation

  • Place value.

 

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

  • Fortnightly retrieval quiz

  • Learning checkpoint towards the end of HT

Assessment

  • Fortnightly retrieval quiz

  • Learning checkpoint towards the end of HT

  • Formal assessment

Assessment

  • Fortnightly retrieval quiz

  • Learning checkpoint towards the end of HT

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 non-linear 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

  • 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

 

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.