# 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

Preparation is the key to success. Our intent in KS3 Maths is to prepare students for their mathematical journey at school and beyond. Students experience a KS3 curriculum which supports them to gain a deeper understanding of topics and development of reasoning skills. The curriculum also aims to enable students to recall and apply key knowledge and apply a structured and logical approach to problem-solving effectively. Throughout our lessons, skills are broken down into key steps, and we ensure that students master each small step before moving on to the next. We then build these skills together towards the end of a topic to ensure students are able to make links between the skills and topics they have studied and so that they are able to apply them to complex problems.

## Year 7

**Topic:**

Numbers

**Prior knowledge / skills:**

- Build on KS2 knowledge of measuring objects and using rules, protractors and other measuring equipment
- Use of a ruler
- Number lines and negative numbers

**Key concepts / knowledge / skills covered this half-term:**

- Place value of integers and decimals - ordering integers and decimals
- Addition and subtraction of integers
- Multiplication and division of integers (x and / by 10, 100, 1000)
- Addition and subtraction of decimals - multiplication of decimals by integers and decimals
- Division of decimals by integers
- Division of decimals by decimals
- Negative numbers in practical contexts
- Addition and subtraction of directed numbers
- Multiplication and division of directed numbers
- Square and cube numbers and roots
- Understand index rotation for higher powers
- Rounding to the nearest whole number or multiples of 10
- Rounding to specified number of decimal places
- Rounding to specified significant figures (extend to estimation for higher set)

**Assessment:**

- Baseline test in September
- In lesson formative assessments: hinge, exit questions
- Book scrutiny: once a half-term
- Summative assessments: once a term
- Retrieval topics

**Personal development opportunities:**

KS3 Maths competition taking place every year; all students will be entered.

**Homework requirements:**

https://sites.google.com/westfield.academy/ks3maths?usp=sharing

## Year 8

**Topic:**

Numbers

**Prior knowledge / skills:**

- Indices notation
- Multiplying and dividing; understanding of power and roots
- Finding reciprocals of numbers / fractions
- Multiply by powers of 10
- Convert between improper fractions and mixed numbers

**Key concepts / knowledge / skills covered this half-term:**

- Understand and use the 'addition' law for indices; understand and use the 'subtraction' law for indices
- Understand and use the power-to-a-power law
- Understand why a number to the power zero is 1; write negative integer powers as unit fractions
- Understand the notation and conventions for standard index form
- Convert between normal form and standard form for large & small numbers
- Convert between improper fractions and mixed numbers; multiply by improper fractions and mixed numbers; understand division as multiplication by the reciprocal
- Work out the fraction of an amount; work out fractional changes by multiplying by a fraction
- Understand the use of multipliers to work out percentage changes
- Use a calculator to work out percentage changes
- Student research / problem-solving

**Assessment:**

- In lesson formative assessments: hinge, exit questions
- Book scrutiny: once a half-term
- Summative assessments: once a term; Year 8 follows the OCR foundation curriculum
- Retrieval topics

**Personal development opportunities:**

KS3 Maths competition taking place every year; all students will be entered.

**Homework requirements:**

https://sites.google.com/westfield.academy/ks3maths?usp=sharing

## Year 9

**Topic:**

Numbers

**Prior knowledge / skills:**

- Understanding factorise is the inverse of multiplying out brackets; HCF
- Collecting like terms; understanding brackets means to multiply
- Factor pairs; directed numbers

**Key concepts / knowledge / skills covered this half-term:**

- Recognise 2-digit prime numbers; find factors and multiples of numbers; find common factors and common multiples of two numbers; find HCF and LCM of two numbers by listing
- Find square roots and cube roots; recognise the powers of 2, 3, 4, and 5; understand surd notation on a calculator
- Know and use the laws of Indices; addition, subtraction, power-to-a-power
- Understand zero and negative indices
- Add and subtract fractions; use fractions to solve problems
- Multiply and divide fractions; use fractions to solve problems
- Convert between proper and improper fractions; calculate with improper fractions
- Add and subtract directed numbers
- Multiply and divide with directed numbers
- Substitute fractions into simple algebraic expressions
- Substitute and simplify expressions involving directed numbers

**Assessment:**

- In lesson formative assessments: hinge, exit questions
- Book scrutiny: once a half-term
- Summative assessments: one a term; Year 9 follows the OCR Foundation curriculum
- Retrieval topics

**Personal development opportunities:**

KS3 Maths competition taking place every year; all students will be entered.

**Homework requirements:**

https://sites.google.com/westfield.academy/ks3maths?usp=sharing

## 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 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.