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 fluency in algebra, and developing their deep understanding of all areas of the curriculum. The 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 provides opportunities for students to participate in practical work, group work, investigations and e-learning. There is a large emphasis on helping students understand the real-world applications and cultural significance of mathematics in today's society. Students develop collaboration skills and mathematical oracy through discussion, explanation and reasoning activities. 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 placed in ability sets, enabling students to master topics at the appropriate pace.

In Year 10, students continue in sets and 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 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
  • Straight line graphs and coordinates

Ratio, percentage and rates of change

  • Fractions/Decimals/Percentages
  • Percentages
  • Ratio and proportion

Geometry and measures

  • Area of 2D shapes
  • Angles in polygons

Probability and statistics

  • Probability

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
  • 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, polygons and parallel lines
  • 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

  • Scatter graphs

Keystone Year: Year 9

Number

  • Indices
  • Standard form
  • Surds

Algebra

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

Ratio, percentage and rates of change

  • Compound interest
  • Reverse percentages

Geometry and measures

  • Geometry in parallel lines and polygons
  • Pythagoras
  • Trigonometry
  • Constructions
  • 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

 

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

Algebra

  • Algebraic fractions
  • Algebraic equations
  • Substitution, expanding brackets and factorising
  • Sequences
  • Plotting graphs
  • Equations and algebra
  • Functions
  • Iteration
  • Pre-calculus
  • Numerical methods

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 and transformations
  • Advanced trigonometry

Probability and statistics

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

Year 11

Number

  • 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
  • Binomial expansion
  • Coordinate geometry in the (x,y) plane
  • Trigonometry & radians
  • Exponentials and logarithms
  • Differentiation
  • Integration
  • 2D and 3D Vectors
  • Modelling
  • Functions
  • Sequences and series

Statistics

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

Mechanics

  • Kinematics
  • Vectors in kinematics
  • Projectiles

Year 13

 

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

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

Further mechanics

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

Year 13 Further Maths

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

Decision mathematics

  • Algorithms
  • Graph theory
  • Algorithms on graphs
  • Route inspection
  • Traveling salesman problem
  • Linear programming
  • Simplex method
  • Critical path analysis