# Maths

The teaching of Mathematics at Westfield Academy aims to encourage students, regardless of their Key Stage to:

- Develop their understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment.
- Develop abilities to reason logically and recognise incorrect reasoning, to generalise and to construct mathematical proofs.
- Extend their range of mathematical skills and techniques and use them in unstructured problems.
- Develop an understanding of coherence and progression in mathematics and of how different areas of mathematics can be connected.
- Recognise how a situation may be represented mathematically and understand the relationship between ‘real world’ problems and standard, and other mathematical models and how these can be refined and improved.
- Use mathematics as an effective means of communication.
- Acquire the skills needed to use technology such as calculators and computers effectively, recognise when such use may be inappropriate and be aware of limitations.
- Develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general.
- Take increasing responsibility for their own learning and the evaluation of their own mathematical development.

## Key Stage 3

At KS3, pupils consolidate their existing mathematical understanding from KS2 and extend their knowledge of number, algebra, geometry and statistics as detailed below. Students are taught Mathematics in sets by ability level. There are termly tests for assessment and setting purposes, along with end-of-year tests.

## Year 7

##### Half-Term 1: Number

- Place value in integers and arithmetic of integers
- Arithmetic involving decimals
- Arithmetic with negative numbers
- Introduction to indices, powers and roots
- Rounding
- Student Research Project

##### Half-Term 2: Number

- Calculations based on estimation
- Factors, multiples and primes
- HCF and LCM
- Introduction to fractions (simplifying and equivalent)
- Arithmetic involving fractions
- Student Research Project

##### Half-Term 3: Ratio & Proportion

- Converting between fractions, decimals and percentages (non-calculator)
- Converting between fractions, decimals and percentages (calculator)
- Calculating percentages (non-calculator)
- Calculating percentages (calculator)
- Sharing ratio
- Simplifying ratios
- Pie charts
- Student Research Project

##### Half-Term 4: Algebra

- Order of operations (BIDMAS)
- Writing formula and expression
- Substitution
- Collecting like terms
- Expanding single brackets
- Factorising
- Test
- Test Review
- Student Research Project

##### Half-Term 5: Geometry & Measures

- Area of rectangles and triangles
- Area of parallelograms and trapezium
- Area of simple compound shapes
- Angle facts
- Perimeter of polygons
- Measuring and drawing angles
- Symmetry
- Student Research Project

##### Half-Term 6: Algebra

- Generating and describing sequences
- Plotting coordinates
- Solving equations
- Student Research Project

These topics are taught in the order shown; all our students cover the same material regardless of set.

## Year 8

##### Half-Term 1: Number & Proportion

- Laws of indices
- Negative indices and zero power
- Standard form
- Multiplying and dividing improper fractions
- Fraction of quantity
- Percentage of quantity
- Student Research Project

##### Half-Term 2: Algebra

- Solving equations with unknowns on both sides
- Change the subject of the formula
- Expanding brackets
- Nth term
- Drawing linear graphs
- Gradient/intercept of a straight line
- Interpret in context the gradient and intercept of a real-life graph
- Student Research Project

##### Half-Term 3: Geometry & Measures

- Area and circumference of quarter-, semi- and full- circles
- Volume and surface area of a cuboid
- Pythagoras' theorem
- Transformations
- Student Research Project

##### Half-Term 4: Algebra

- Direct proportion
- Real-life graphs
- Similar shapes
- Compound units (speed and density)
- Student Research Project

##### Half-Term 5: Geometry & Measures

- Angles in parallel lines
- Bearings
- Properties of quadrilaterals
- Constructions
- Isometric drawings
- Nets
- Plans and elevations
- Properties of 3D shapes
- Student Research Project

##### Half-Term 6: Probability & Statistics

- Calculate and interpret averages (mean, median and mode) and range
- Draw and interpret bar charts
- Draw and interpret scatter diagrams
- Introduction to probability
- Listing outcomes (sample space)
- Mutually exclusive events
- Independent events
- Activity Week
- Test
- Test Review
- Student Research Project

These topics are taught in the order shown; all our students cover the same material regardless of set.

## Key Stage 4

KS4 is a three-year course. The Higher Tier follows the Edexcel Exam Board whilst the Foundation Tier follow the OCR Exams Board.

In May/June, Year 11 take three exam papers. For the Higher Tier - Paper 1 (non-calculator) and Papers 2 & 3 (calculator). For the Foundation Tier - Paper 1 (calculator), Paper 2 (non-calculator), and Paper 3 (calculator). Since 2017, there has been an emphasis on problem-solving as well as showing mathematical methods for both Higher and Foundation Tiers.

Students are taught Mathematics in sets by ability level. The top 2 sets follow an accelerated course to include an additional AQA Further Mathematics (Level 2) course. Students sit two exams; calculator and non-calculator based.

## Year 9

##### Half-Term 1

**Foundation**

- Review of factors, multiples, prime numbers
- Review of powers and roots
- Index laws
- Zero and negative indices
- Fractions
- Directed numbers
- Solve linear equations
- Student Research Project

**Higher**

- LCM and HCF
- Review of fractions
- Review of directed numbers
- Evaluating expressions involving fractions & negative numbers
- Review fraction, decimal and percentage
- Convert recurring decimals to fractions
- Standard form
- Estimation
- Rounding, upper and lower bounds
- Review of basic algebra: collect & simplify like terms
- Expand brackets
- Student Research Project

##### Half-Term 2

**Foundation**

- Solve linear equations
- Inequalities
- Changing the subject
- Expanding brackets
- Factorise expressions
- Expanding brackets
- Factorise quadratic expressions
- Student Research Project

**Higher**

- Factorise expressions
- Factorise quadratics
- Solver linear and inequalities equations
- Forming and solving equations
- Changing the subject of a formula
- Linear sequences
- Non-linear sequences (geometric, quadratic, Fibonacci)
- Nth term of a quadratic sequence
- Student Research Project

##### Half-Term 3

**Foundation**

- Rotations, Reflections, Translations and Enlargement
- Describe transformations
- Perimeter of a polygon
- Area of rectangles, triangles, parallelograms and trapeziums
- Area and circumstance of a circle
- Area and perimeter of simple sectors of a circle
- Area and perimeter of compound shapes
- Solve a range of problems involving area and perimeter
- Volume and surface area of cubes and cuboids
- Student Research Project

**Higher**

- Review of angle facts
- Angles in polygons
- Constructions and loci
- Pythagoras' theorem in 2D and 3D
- Trigonometry in right-angled triangles
- Student Research Project

##### Half-Term 4

**Foundation**

- Sequences
- Generate a geometric sequence from a term-to-term rule
- Using the nth term of other types of sequence
- Straight line graphs
- Gradient and y-intercept
- Interpret graphs drawn from real-life contexts
- Pythagoras Theorem
- Student Research Project

**Higher**

- Line segment - midpoint, length and gradient
- Review of plotting linear graphs
- Use and understand y = mx + c
- Simultaneous equations: graphical solutions
- Simultaneous equations: algebraic solutions
- Plot quadratic, cubic and reciprocal graphs
- Sketching graphs
- Student Research Project

##### Half-Term 5

**Foundation**

- Direct proportion
- Share a quantity in a given ratio
- Fractions, decimals and percentages
- Student Research Project

**Higher**

- Ratios
- Direct proportion
- Inverse proportion
- Reverse percentages
- Compound interest and depreciation
- Compound measures
- Student Research Project

##### Half-Term 6

**Foundation**

- Pie charts
- Stem and leaf diagram
- Frequency polygon
- Frequency table
- Scatter graphs
- Data collection and sampling
- Student Research Project

**Higher**

- Review of areas of plane shapes, including reverse probs
- Arcs, sectors and segments
- Area and perimeter of compound shapes
- Volume and surface area of cubes and cuboids and prisms
- Volume and surface area of prisms, cylinders, spheres and cones
- Student Research Project

## Year 10

##### Half-Term 1

**Foundation**

- Calculations and approximations
- HCF and LCM
- Standard forms
- Bounds
- Review of percentage changes, with and without a calculator
- Use of multipliers for percentage changes
- Student Research Project

**Higher**

- The six index laws (including roots)
- Solving equations involving indices
- Surds: implying, brackets
- Surds: expressions involving fractions
- Calculating with rounded numbers
- More complex proportional relationships
- Student Research Project

##### Half-Term 2

**Foundation**

- Ratio and proportion
- Compound percentage changes
- Reverse percentages
- Compound measures
- Inverse proportion
- Vectors
- Student Research Project

**Higher**

- Review of Pythagoras' and trigonometry
- Reflection, rotation and translation
- Enlargements by fractional and negative scale factors
- Combining transformations
- Vector algebra
- Bearings
- Student Research Project

##### Half-Term 3

**Foundation**

- Angles
- Angles in parallel lines
- Bearings
- Angles in polygons
- Construction and loci
- Student Research Project

**Higher**

- Two-way tables
- Probability
- Venn diagrams
- Relevative frequency
- Mutually exclusive events and combined events
- Conditional probability

- Student Research Project

##### Half-Term 4

**Foundation**

- Review of straight line graphs
- Review of quadratic graphs
- Plot cubic
- Recognise graphs functions
- Solve simultaneous equations graphically
- Student Research Project

**Higher**

- Factorise and solve quadratic equations
- Solve quadratic equations by completing the square
- Solve quadratic equations using the formula
- Solve quadratic equations graphically
- Solve quadratic inequalities
- Simplify harder algebraic expressions
- Student Research Project

##### Half-Term 5

**Foundation**

- Prisms
- Cylinders
- Cone, pyramids and spheres
- Pythagoras' theorem
- Trigonometry
- Student Research Project

**Higher**

- Sine and cosine rule
- 'Solve' triangles using the sine and cosine rules
- Trigonometry in three dimensions
- Angles inside circles - Circle Theorem
- Similar shapes
- Area / volume of similar shapes
- Student Research Project

##### Half-Term 6

**Foundation**

- Venn diagram
- Two-way tables
- Relative frequency
- Theoretical probability
- "And" & "Or" rule
- Tree diagrams
- Student Research Project

**Higher**

- Statistical diagrams
- Averages from grouped and ungrouped frequency tables
- Scatter diagrams
- Cumulative frequency curve
- Boxplots
- Histograms
- Student Research Project

## Year 11

##### Foundation

**Half-Term 1**

- Number calculations
- Estimate answers
- LCM and HCF
- Standard index form
- Bounds
- Percentages
- Student Research Project

**Half-Term 2**

- Compound percentage changes
- Reverse percentage problems
- Compound measure
- Inverse proportion
- Graphs of quantities in inverse proportion
- Vectors

**Half-Term 3**

- Inequalities
- Solving equations
- Changing the subject
- Expanding and simplify expression
- Factorise expressions
- Factorise quadratic expressions

**Half-Term 4**

- Rotations and reflections
- Enlargement
- Describe transformations
- Perimeter of a polygon
- Area of rectangles, triangles, parallelograms and trapeziums
- Circles
- Area and permitter of compound shapes
- Cubes and cuboids
- Vectors

**Higher (AQA Further Maths Level 2)**

- Identities (expanding and factorising)
- Pascal's triangle
- Factor theorem
- Graphs of functions with up to three parts to their domains
- Domain and range of a function
- Arithmetic for algebraic fractions with denominators being numeric, linear or quadratic
- Factor theorem
- Algebraic long division
- Drawing and sketching of functions
- Algebraic solution of linear equations in three unknowns
- Limiting value of a sequence
- Equation of a circle where the centre is not on the origin
- Differentiation (tangents and normals)
- Differentiation (gradients and stationary points)
- Matrices
- Multiplying matrices
- Transformations of the unit square
- Trigonometric identities
- Solving trigonometric equations

## Key Stage 5

The department offers the following A-Level Mathematics course: Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0).

This two-year course builds directly on the foundation of the GCSE Higher Level syllabus. It pre-supposes skills in basic algebraic manipulation and the ability to work logically through multistage problems to further develop mathematical understanding. Students are encouraged to think, act and communicate mathematically, providing them with the skills to analyse situations in mathematics and elsewhere. The mathematical knowledge gained will be broad and widely applicable, preparing students for a range of destinations in Higher Education and employment.

The A-Level specification has 3 components:

**Year 1: Pure Mathematics 1 (Weighting: 33 1/3%)**

- Indices and surds, polynomials, coordinate geometry, trigonometry, sequences and series, algebra and functions, differentiation and integration, numerical methods, exponentials and logarithms, proof, vectors

**Year 2: Pure Mathematics 2 (Weighting: 33 1/3%)**

- All Pure Maths content as above

**Years 1 & 2: Applied Maths - Statistics & Mechanics (Weighting: 33 1/3%)**

- Sampling, interpretation in context, standard deviation, binomial and normal distributions, hypothesis testing, use of large data sets, conditional probability (50% of paper)
- Newton's laws of motion, kinematics of motion in a straight line and under gravity, equilibrium of a particle, force as a vector and resolving forces, projectile motion, moments (50% of paper)

Regular assessment takes place, usually half-termly, to ensure students remain on top of their studies, with mock exams taking place in the Spring term. Final assessment is by three external written examinations of duration two hours each at the end of the two-year course, with no coursework.

##### Key Stage 5 Further Mathematics

The study of further mathematics adds breadth and depth to the topics covered in A-Level Mathematics. It introduces new topics, for example matrices and complex numbers. Such topics form an important part of maths-rich degrees in areas such as the sciences, engineering, statistics, economics and computing, in addition to mathematics itself. Some prestigious universities now require a Further Mathematics qualification.

The department currently offers Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0). The specification has 4 components:

**1: Mandatory Core Pure Mathematics 1 (Weighting: 25%)**

- Proof, complex numbers, matrices, further algebra and functions, further calculus, further vectors, polar co-ordinates, hyperbolic functions, differential equations, trigonometry

**2: Mandatory Core Pure Mathematics 2 (Weighting: 25%)**

- Any of the pure mathematics above

**3: Option 1 (Weighting: 25%)**

**4: Option 2 (Weighting: 25%)**

Regular assessment takes place, usually half termly, to ensure students remain on top of their studies, with mock exams taking place in the Spring term. Final assessment is by four external written examinations of duration 1.5 hours each at the end of the Upper Sixth, with no coursework.

## Exams & Assessment

##### GCSE

- Edexcel Exam Board, Higher Linear 1MA1

##### AS Level

- AQA Level 3 Certificate in Mathematical Studies

##### A-Level

- A-Level Mathematics course: Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)
- A-Level Further Mathematics course: Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0)

##### Exams

Year 7 baseline test is conducted on the second week of Term 1.1. This provides data for groupings. In general, Term 3.2 of the previous year's testing provides a baseline for the current year, Term 1.2 and 2.2 tests provide mid-year data to identify whole cohort progress and students who need further support and intervention. End of year (Summer) tests gives the final judgement for the year.

**Exam Timeline:**

- Term 1.2
- Term 2.2
- Term 3.2

## Enrichment & Extracurricular

The Maths department regularly take part in country and national level competitions and challenges with recent accomplishments including winning the Maths Challenge Hertfordshire Maths Challenge in 2021 with Year 8.

- Many students participate in the Junior, Intermediate and Senior Maths Challenge from the UK Mathematics Trust and many achieve medals, with a significant number qualifying for the subsequent rounds.
- Hans Woyda Prep Club for Years 8-13 takes place each Monday lunchtime. Hans Woyda is a prestigious maths competition which takes place each year and students from the Academy have been very successful over the years.
- 'Maths in Motion' lunchtime club for all year groups takes place on Tuesday lunchtime.
- Weekly Maths quizzes.