# Maths

## curriculum intent

The act of learning mathematics wires students brains for problem-solving; it is a way to develop tools, methods and tactics to solve problems that they may never see again, but it is these skills and techniques that will help them approach problems in a practical sense when they encounter them in wider life.

Students in Years 7 and 8- Foundation years cover the fundamental skills and knowledge required up to GCSE Grade 5, building upon their numeracy from Key Stage 2, ensuring a strong fluency in algebra, and developing their deep understanding of all areas of the curriculum. Use of various techniques, such as mastery and flipped learning, not only engages the students in the subject but creates independent, resilient and reflective learners who are able to apply their knowledge to real-world problem-solving scenarios.

The Year 9 Keystone curriculum aims gives opportunities for students to participate in practical work, group work, investigations and e-learning. There is a large emphasis on SMSC aspects of mathematics to enable students to understand the importance of mathematics in the world today. Furthermore, the course emphasises building on the foundations of Years 7 and 8 and prepares for the subsequent start of GCSE. To this end, students are in ability sets, enabling students to master topics at the appropriate pace.

In Year 10, students stay in sets and will commence the GCSE Higher Tier. Students are given regular exam-type questions throughout, thus increasing confidence in problem-solving skills. Students therefore become more familiar with non-routine problems eg where they will need to use multiple topic areas and skills to answer a question.

Students in Year 11 complete the GCSE course and revise content, so that they master key topic areas in preparation for the exam. Regular exam questions and practice papers ensure that they are increasingly familiar with the topics and the type of questions that appear in the GCSE. By the time the GCSE season commences, students are well drilled on what to expect. Students in set 1 study the OCR Level 3 Free Standing Mathematics Qualification in Additional Maths and students in set 2 study AQA Level 2 Certificate in Further Mathematics. Both courses enhance preparation for GCSE, ensuring that students are A-level ready, and they provide a useful head start on their course, should they wish to take it.

A-Level focuses on flipped learning, aiming to create independent, resilient mathematicians, with less dependence on a single resource; this also ensure that the students are more inquisitive and confident problem-solvers.

Students choose Further Mathematics if they have had previous success in the subject and have an irrefutable love of mathematics. Students dig deeper in common A Level topics, expanding their understanding, but also encounter new concepts. The aim is to broaden top mathematicians’ minds, explore new areas of the subject to help satisfy their inquisitive minds and provide them with a taste of mathematics for higher education.

## foundation years: Year 7 and 8

## Year 7

**Number**

- Fractions
- Negative numbers and BIDMAS
- Properties of numbers
- Rounding and estimating
- Arithmetic and decimals

**Algebra**

- Algebra introduction and brackets
- Equations
- Sequences
- Straight line graphs

**Ratio, percentage and rates of change**

- Fractions/Decimals/Percentages
- Percentages
- Ratio and proportion

**Geometry and measures**

- Area of 2D shapes and circles
- Angles
- Transformations
- Construction

**Probability and statistics**

- Probability
- Averages and range
- Constructing and interpreting charts

## Year 8

**Number**

- Rules of Indices
- Prime factors, LCM and HCF
- Fractions
- Negative numbers
- Using a Calculator
- Upper and lower bounds
- Estimating and checking answers

**Algebra**

- Using algebra
- Drawing and using graphs
- Sequences
- Expanding brackets and solving equations
- Rearranging formulae
- Factorising into single brackets and introduction to quadratic factorisation
- Introduction to linear simultaneous equations

**Ratio, percentage and rates of change**

- Percentage increase and decrease
- Percentage change
- Compound interest
- Further ratio

**Geometry and measures**

- Angles and polygons
- Area of 2D shapes, compound shapes
- Circles – area, perimeter and compound shapes
- Pythagoras’ Theorem
- Trigonometry – right-angled triangles and SOH CAH TOA
- Volume of prisms

**Probability and statistics**

- Averages, range and frequency tables
- Scatter graphs

## Keystone Year: year 9

**Number**

- Indices
- Standard form
- Binary system
- Financial maths

**Algebra**

- Expanding brackets to form linear, quadratic and cubic expressions
- Factorising linear and quadratic expressions
- Solving linear and quadratic equations
- Straight line graphs

**Ratio, percentage and rates of change**

- Compound interest
- Reverse percentages

**Geometry and measures**

- Geometry in parallel lines and polygons
- Pythagoras
- Trigonometry
- Constructions
- Circle theorems
- Compound measures

**Probability and statistics**

- Averages and spread from a set of numbers
- Averages from grouped data
- Box plots
- Sampling, bias and capture/ recapture
- Relative frequency, expected probability
- Independent events and mutually exclusive events and tree diagrams

## GCSE: years 10 and 11

**Exam Board: Pearson Edexcel**

## Year 10

**Number**

- Arithmetic with fractions and decimals
- Using a calculator
- Surds
- Indices and standard form
- LCM, HCF and factor trees
- Rounding and estimating

**Algebra**

- Algebraic fractions
- Substitution, expanding brackets and factorising
- Sequences
- Plotting graphs
- Equations and algebra
- Functions
- Iteration

**Ratio, percentage and rates of change**

- Proportion – direct and indirect

**Geometry and measures**

- Circle theorems
- Area and volume
- Right angled triangles
- Straight line geometry
- Similarity and congruence
- Advanced trigonometry

**Probability and statistics**

- Data Handling
- Statistical graphs including histograms
- Tree diagrams and Venn diagrams

## Year 11

**Number**

Numerical methods

- Bounds of accuracy
- Further surds

**Algebra**

- Algebraic fractions
- Quadratics, solving, completing the square and simultaneous equations
- Circle equations
- Inequalities
- Graph transformations
- Exponential functions
- Proof

**Ratio, percentage and rates of change**

- Gradients of real-life curves and area beneath graph

**Geometry and measures**

- Vectors and vector geometry

**Probability and statistics**

- Conditional probability.

## A Level: years 12 and 13

**Exam board: Pearson Edexcel**

## Year 12

**Pure mathematics**

- Algebra and functions
- Algebraic methods, proof and the binomial expansion
- Coordinate geometry in the (x,y) plane
- Trigonometry
- Exponentials and logarithms
- Differentiation
- Integration
- Vectors
- Modelling
- Radians
- Functions

**Statistics**

- Statistical sampling
- Data presentation and interpretation
- Probability
- Binomial distribution
- Normal distribution
- Statistical hypothesis testing
- Correlation and regression

**Mechanics**

- Quantities and units in mechanics
- Kinematics
- Forces and Newton’s Laws

## Year 13

**Pure mathematics**

- Sequences and series
- Binomial expansion
- Trigonometry
- Differentiation
- Integration
- Vectors
- Numerical methods
- Parametric equations
- Modelling

**Mechanics**

- Moments
- Forces and friction
- Projectiles
- Further kinematics

## A Level Further Maths: Years 12 and 13

## Year 12

All content from the A-Level maths course (see above)

**AND**

**Core mathematics**

- Complex numbers
- Proof
- Matrices
- Roots of polynomials
- Series
- Volume of revolution
- Vectors

## Year 13

**Core mathematics**

- Further complex numbers
- Further series
- Methods in calculus
- Polar coordinates
- Hyperbolic functions
- Differential equations

**Further pure mathematics**

- Further trigonometry – t-formulae
- Further vectors
- Conic sections
- Inequalities
- Series
- Further calculus
- Numerical methods

**Further mechanics**

- Momentum and Impulse
- Work, Energy and Power
- Elastic, Springs and Strings
- Elastic Collisions in one dimension
- Elastic Collisions in two dimensions