Mathematics

"The essence of mathematics is not to make simple things complicated, but to make complicated things simple." — Stan Gudder

 

Subject Overview
At The Forest School, we aim to make learning mathematics an enjoyable and rewarding experience for all students. They follow the National Curriculum for the subject, and this is enhanced by a number of extra-curricular activities, trips and visits. Students are set on entry to the school, sometimes in two half year groups, and we have a well-established pattern of tests, assessments and homework. Set changes are made at regular intervals, following each of these assessments.

Our uptake for Key Stage 5 courses is very strong - we have around 30 students who study to A level each year. We also offer Further Maths to a small number of students. 

We feel that our curriculum is designed to create opportunities for intellectual development, improvement of practical skills, emotional/social development and a solid platform for diverse career pathways.

Curriculum Intent
Our mathematics curriculum is designed to empower all students with the knowledge, skills, and mindset needed to navigate the world with confidence, think critically, and pursue further academic and career opportunities. We aim to foster curiosity, resilience, and problem-solving abilities that are essential for lifelong learning.

In every lesson, students are encouraged to embody the school motto of ASPIRE, where every individual is valued not only for what they can already do, but also for their willingness to tackle challenges and persevere when facing difficulties—an essential part of mathematical growth.

Above all, we strive to ensure that every student achieves more in mathematics than they first believed possible. This ambition applies to the short term, within each lesson; the medium term, across each academic year; and the long term, throughout each key stage.

Curriculum Implementation
Our Mathematics department is dedicated to delivering a robust, engaging, and inclusive curriculum that prepares students with the essential skills and knowledge to thrive in an increasingly mathematical and technological world. Our curriculum is carefully aligned with, and often goes beyond, the National Curriculum expectations. This is true for all Key Stages, ensuring a seamless progression of mathematical understanding. We place a strong emphasis on student-centered approaches, where students actively explore concepts through high level questioning, problem-solving tasks, and real-life applications. Technology is integrated throughout our teaching to promote independent learning in a supportive, risk-free, safe learning environment.

Our team of highly qualified and passionate Mathematics teachers are committed to continuous professional development, ensuring they stay at the forefront of modern teaching methods and digital innovations. Assessment for learning is embedded into every stage of our curriculum, with a balanced approach that includes homework tasks, summative/formative assessments and end-of-term examinations. Assessment data is used carefully to tailor teaching and provide targeted support where needed. To further aid learning, we provide access to a wide range of course texts, mathematical software, and e-learning platforms. We also foster a strong culture of support and inclusivity, offering extra support sessions, Maths intervention sessions as well as giving opportunities for students to stretch their thinking via competitions and problem solving clubs. 

No matter their starting point, all students are encouraged to develop a positive attitude toward Mathematics, fostering both confidence and curiosity.

Curriculum Impact
The impact of our Mathematics curriculum is evident through strong academic outcomes, with students consistently achieving or exceeding national expectations. Our spiral curriculum ensures a clear progression of knowledge, allowing students to build on prior learning while reinforcing key concepts and deepening their understanding over time. This approach fosters confidence and resilience, as students are regularly challenged and supported to take ownership of their learning and view mistakes as valuable learning opportunities.

Students engage enthusiastically with the subject, actively participating in lessons, enrichment activities, and independent study. As a result, they leave each Key Stage well-prepared for the next phase of their education—whether that be GCSEs, A-levels, apprenticeships, or employment. Regular assessment, both formative and summative, enables teachers to quickly identify gaps in understanding and tailor their teaching accordingly. Targeted, constructive feedback supports continuous progress for all learners.

Ultimately, we strive to ensure that every student recognises the value of mathematics in everyday life, understands its relevance across a range of disciplines, and leaves school as a confident, numerate, and analytical thinker—well-equipped to succeed in a modern, data-driven world.

Key Stage 3 (Years 7–8):
Outline the topics covered, skills developed, and assessment methods used in Key Stage 3.

At Key Stage 3, we have developed a curriculum that continually reflects on and builds upon prior learning. In line with the requirements of the National Curriculum, students study a unit of work from each of the key strands: Algebra, Geometry, Statistics & Probability, and Number & Ratio. This cycle is then repeated, with each round building on the knowledge and skills previously acquired.

Students are formally assessed at the end of each unit, providing an opportunity to identify both strengths and areas for development. In Years 7 and 8, there are three formal assessment points, typically scheduled in the middle of each term.

In addition, online tasks are used throughout the two-year Key Stage to assess prior learning and highlight areas that may require further attention from teachers.

	Year 7	Year 8	Year 9
Half Term 1	Integers and decimals Sequences and functions Measures	Integers and decimals Measures Probability	Sequences and graphs Proportional Reasoning
Half Term 2	Fractions, decimals and percentages Processing data Expressions and formulae	Fractions, decimals and percentages Expressions and formulae Angles and shapes	Geometrical reasoning and construction Equations Statistics
Half Term 3	Calculation and measure Probability 2-D shapes and construction	Equations and graphs Calculations Transformations	Measures Calculations
Half Term 4	Integers, functions and graphs Percentages, ratio and proportion Expressions and equations	Sequences and roots Collecting and representing data	Graphs Probability Transformations and scale
Half Term 5	Transformations and symmetry Surveys and data Calculations	Ratio and proportion Algebra	Expressions and formulae Interpreting statistics
Half Term 6	Sequences and graphs 3-D shapes and construction Summer activities	Construction and 3-D shapes Analysing data Summer activities	3-D Shapes Calculation plus Summer activities

Key Stage 4 (Years 9 - 11):
At KS4 we follow the AQA syllabus 8300. There are 3 equally weighted papers lasting 1 hour 30 minutes each; 1 non calculator and 2 calculator. Entry is at either Foundation level where grades 1-5 can be attained or at Higher level where grades 4-9 can be attained. Examinations are taken in June of year 11 and there is no assessed coursework requirement.

In Year 9 we first ensure that the underlying skills are taught before applying, revisiting and learning to apply these skills in Years 10 & 11. Cumulative assessments are given on a monthly basis, each reassessing previous content, whilst adding new topics as they are taught

In Year 10 & 11, more emphasis is placed on the application of learning to problem solving based questions. Assessments take place every half term and gauge the understanding and progress of recent learning. Cumulative assessments take place in June of Year 10 and November/February of Year 11. 

Online tasks, throughout the three year GCSE are used to assess previous learning, identifying potential areas that teachers need to revisit.

	Year 9
Half Term 1	Sequences and graphs, Proportional Reasoning
Half Term 2	Geometrical reasoning and construction, Equations, Statistics
Half Term 3	Measures, Calculations
Half Term 4	Graphs, Probability, Transformations and scale
Half Term 5	Expressions and formulae, Interpreting statistics
Half Term 6	3-D Shapes, Calculation plus, Summer activities

	Higher	Foundation
Year 10 - Half Term 1	Basic Calculations Place value and rounding Adding, subtracting, multiplying and dividing Algebraic Expressions Simplifying expressions Indices Expanding and factorising single brackets Algebraic fractions Angles and Polygons Angles and Lines Triangles and quadrilaterals Congruence and similarity Angles in polygons	Basic Calculations Place value Rounding Adding and subtracting Multiplying and dividing Algebraic Expressions Terms and expressions Simplifying expressions Indices Expanding and factorising single brackets Angles and Polygons Angles and Lines Triangles and quadrilaterals Congruence and similarity Angles in polygons
Year 10 - Half Term 2	Basic Data Handling Representing data Averages and spread Frequency diagrams and Histograms Fractions, Decimals and Percentages Fractions and percentages Calculating with fractions Fractions, decimals and percentages	Basic Data Handling Organising data Representing data Averages and spread Fractions, Decimals and Percentages Decimals and fractions Fractions and percentages Calculating with fractions Fractions, decimals and percentages
Year 10 - Half Term 3	Formulae and Functions Formulae Function notation Equivalences and identities Expanding and factorising double brackets Working in 2D Measuring lengths and angles Area of 2D shapes Transformations Enlargements	Formulae and Functions Substituting into formulae Using standard formulae Equations, identities and functions Expanding and factorising double brackets Working in 2D Measuring lengths and angles Area of 2D shapes Transformations Enlargements
Year 10 - Half Term 4	Probability experiments Theoretical probability Mutually exclusive events  Measures Estimation and approximation Calculator methods Measures and accuracy	Probability Probability experiments Expected outcomes Theoretical probability Mutually exclusive events Measures Estimation and approximation Calculator methods Measures and accuracy
Year 10 - Half Term 5	Equations and Inequalities Solving linear equations Solving quadratic equations Simultaneous equations Approximate solutions Inequalities Circles and Constructions Circle formulae Arcs and Sectors Circle theorems Constructions and loci	Equations and Inequalities Solving linear equations Solving quadratic equations by factorising Simultaneous equations Inequalities Circles and Constructions Circle formulae Arcs and Sectors Circle theorems Constructions Loci
Year 10 - Half Term 6	Ratio and proportion Proportion Ratio and scale Percentage change Factors, Powers and roots Factors and multiples Powers and roots Surds	Ratio and proportion Proportion Ratio Percentage change Factors, Powers and roots Factors and multiples Prime factor decomposition Powers and roots
Year 11 - Half Term 1	Basic Graphs Equation of a straight line Linear and quadratic functions Properties of quadratic functions Kinematic graphs Working in 3D 3D shapes Volume of a prism Volume and surface area	Basic Graphs Drawing straight line graphs Equation of a straight line Distance-time graphs Working in 3D 3D shapes Volume of a prism Volume and surface area
Year 11 - Half Term 2	Advanced Data Handling Averages from tables and Interquartile range Box plots and cumulative frequency graphs Scatter graphs and correlation Time series Advanced Calculations Calculating with roots and indices Exact calculations Standard form Advanced Graphs Cubic and reciprocal functions Exponential and trigonometric functions Real-life graphs Gradients and areas under graphs Equation of a circle	Advanced Data Handling Frequency diagrams Averages from tables Scatter graphs and correlation Time series Advanced Calculations Calculating with roots and indices Exact calculations Standard form Advanced Graphs Properties of quadratic functions Sketching graphs Real-life graphs
Year 11 - Half Term 3	Pythagoras, Trigonometry and Vectors Pythagoras’ theorem Trigonometric ratios Sine, Cosine and area of a triangle rules Trigonometry and Pythagoras problems Vectors Probability of Combined Events Set theory and notation Possibility spaces Tree diagrams Conditional probability	Pythagoras, Trigonometry and Vectors Pythagoras’ theorem Trigonometric ratios Trigonometry and Pythagoras problems Vectors Probability of Combined Events Set theory and notation Possibility spaces Tree diagrams
Year 11 - Half Term 4	Sequences Linear sequences Quadratic sequences Special sequences Units and Proportionality Compound units Converting between units Direct and inverse proportion Rates of change Growth and decay	Sequences Sequence rules Finding the nth term Recognising special sequences Units and Proportionality Compound units Direct proportion Inverse proportion Growth and decay
Year 11 - Half Term 5	Revision and Exam Preparation	Revision and Exam Preparation

Key Stage 5 (Years 12–13):
At Key Stage 5, we follow the AQA A-level Mathematics syllabus (7357). The qualification is assessed through three equally weighted papers, each lasting two hours. The assessments cover the following strands of Mathematics: Pure Mathematics (two-thirds of the content), Mechanics (one-sixth), and Statistics (one-sixth). All examinations are taken in June of Year 13, and there is no coursework requirement.

Teaching is typically shared between two teachers to make full use of subject specialisms. We also ensure that all students have access to support outside of their timetabled lessons. Many students choose to use their study periods in the Mathematics department, taking advantage of the additional help available to them.

In addition to formal examinations, students complete progress assessments once every half term to monitor their understanding of recently taught material. Cumulative progress is assessed through formal mock examinations in June of Year 12, and in November and February of Year 13.

	Year 12	Year 13
Half Term 1	Indices and surds Using the laws of indices Working with surds Quadratic functions Solving quadratic equations Graphs of quadratic functions Completing the square Quadratic inequalities The discriminant Disguised quadratics Polynomials Working with polynomials Polynomial division The factor theorem Sketching polynomial functions Binomial expansion The binomial theorem Binomial coefficients Applications of the binomial theorem	Proof and mathematical communication A reminder of methods of proof Proof by contradiction Criticising proofs Functions Mappings and functions Domain and range Composite functions Inverse functions Further transformations of graphs Combined transformations The modulus function Modulus equations and inequalities Conditional probability Set notation and Venn diagrams Two-way tables Tree diagrams The normal distribution Introduction to normal probabilities Inverse normal distribution Modelling with the normal distribution
Half Term 2	Using graphs Intersections of graphs The discriminant and graphs Transforming graphs Graphs of a/x and a/x² Direct and inverse proportion Sketching inequalities in two variables Coordinate geometry Distance between two points and midpoint The equation of a straight line Parallel and perpendicular lines Equation of a circle Solving problems with lines and circles Working with data Statistical diagrams Standard deviation Calculations from frequency tables Scatter diagrams and correlation Outliers and cleaning data Probability Combining probabilities Probability distributions The binomial distribution	Sequences and series General sequences General series and sigma notation Arithmetic sequences Arithmetic series Geometric sequences Geometric series Infinite geometric series Mixed arithmetic and geometric questions Rational functions and partial fractions An extension of the factor theorem Simplifying rational expressions Partial fractions with distinct factors Partial fractions with a repeated factor General binomial expansion The general binomial theorem Binomial expansions of compound expressions Calculus of exponential and trigonometric functions Differentiation Integration Further hypothesis testing Distribution of the sample mean Hypothesis tests for a mean Hypothesis test for correlation coeffcients
Half Term 3	Trigonometric functions and equations Definitions and graphs of sine and cosine Definition and graph of tangent Trigonometric identities Introducing trigonometric equations Transformations of trigonometric graphs Harder trigonometric equations Triangle geometry The sine rule The cosine rule Area of a triangle Differentiation Sketching derivatives Differentiation from first principles Rules of differentiation Simplifying into terms of the form axn Interpreting derivatives and second derivatives Applications of differentiation Tangents and normals Stationary points Optimisation Statistical hypothesis testing Populations and samples Introduction to hypothesis testing Critical region for a hypothesis test	Radian measure Introducing radian measure Inverse trigonometric functions and solving trigonometric Modelling with trigonometric functions Arcs and sectors Triangles and circles Small angle approximations Further trigonometry Compound angle identities Double angle identities Functions of the form  Reciprocal trigonometric functions Further differentiation The chain rule The product rule Quotient rule Implicit differentiation Differentiating inverse functions   Further integration techniques Reversing standard derivatives Integration by substitution Integration by parts Using trigonometric identities in integration Integrating rational functions
Half Term 4	Integration Rules for integration Simplifying into terms if the form axn Finding the equation of a curve Definite integration Geometrical significance of definite integration   Vectors Describing vectors Operations with vectors Position and displacement vectors Using vectors to solve geometrical problems   Introduction to kinematics Mathematical models in mechanics Displacement, velocity and acceleration Kinematics and calculus Using travel graphs Solving problems in kinematics   Proof and mathematical communication Mathematical structures and arguments Inequality notation Disproof by counter example Proof by deduction Proof by exhaustion   Motion with constant acceleration Deriving the constant acceleration formulae Using the constant acceleration formulae Vertical motion under gravity Multi stage problems	Further application of calculus Properties of curves Parametric equations Connected rates of change More complicated areas   Differentiated equations Introduction to differential equations Separable differential equations Modelling with differential equations   Numerical solution of equations Locating roots of a function The Newton-Raphson method Limitations of the Newton-Raphson method Fixed-point iteration Limitations of fixed-point iteration and alternative rearrangement   Numerical integrations Integration as the limit of a sum The trapezium rule   Applications of vectors Describing motion in two dimensions Constant acceleration equations Calculus with vectors Vectors in three dimensions Solving geometrical problems   Projectiles Modelling projectile motion The trajectory of a projectile   Forces in context Resolving forces Coefficient of friction Motion on a slope
Half Term 5	Logarithms Introducing logarithms Laws of logarithms Solving exponential equations   Exponential models Graphs of exponential functions Graphs of logarithms Exponential functions and mathematical modelling Fitting models to data   Forces and motion Newton’s laws of motion Combining forces Types of force Gravity and weight Forces in equilibrium   Objects in contact Newton’s third law Normal reaction force Further equilibrium problems Connected particles Pulleys	Moments The turning effect of a force Equilibrium   Revision and Exam preparation
Half Term 6	Catch up on areas in need of further development from half terms 1-5 Preparation for mock exams Mock exams Review of mock exams

Enrichment Opportunities
Our Mathematics curriculum is full of exciting enrichment opportunities. Some examples include:

• Entries for in the UK Mathematics Trust (UKMT) Maths challenge competition. This includes both individual and team entries. Each year we usually have over 300 entries!
• An off site visit to Bletchley Park, where students can learn of the Mathematics that helped contribute to the end of WW2, students also get a chance to have a go at using their own code breaking skills.
• Various STEM events throughout the year, some in school virtually, others off site
• Workshop and visits to our local partners, including Wellington College
• Mathematics Problem solving club, a separate club for KS3 and KS4
• Chess club is housed in the Mathematics department
• Numeracy buddies to help support our KS3 students

Curious about the curriculum
If you want to take what you have learnt in class and go beyond the curriculum, try these links to enhance your understanding and application of Mathematics

KS3

• Brief history or Mathematics Podcast
• Numberphile, fun videos linked to everyday maths
• Fun problem solving challenges

KS4

• Maths on the Move podcast
• The Story of Maths Episode 2 - The Genius of the East
• The Story of Maths Episode 3 - The Frontiers of Space
• The Story of Maths Episode 4 - To Infinity and Beyond
• Mathematical puzzles to solve
• Mathematical ‘real life’ problems
• Maths Challenge questions

KS5

• Maths on the Move podcast
• Mathematics TED talks
• Behind the Stats Podcast
• Mathematics in society short Podcasts
• Black Heroes of Mathematics conference talk

Looking for something to read:
If you want to further develop your passion for Mathematics whilst also improving your reading, try some of these books and articles.

KS3

• Murderous Maths, The Phantom X - Kjartan Poskitt
• Murderous Maths, The Perfect Sausage - Kjartan Poskitt
• Murderous Maths, Savage Shapes - Kjartan Poskitt
• Murderous Maths, Guaranteed to Mash Your Mind - Kjartan Poskitt
• Murderous Maths, Guaranteed to  Bend Your Brain - Kjartan Poskitt
• Murderous Maths, Easy Questions - Evil Answers - Kjartan Poskitt
• Murderous Maths, Do You Feel Lucky - Kjartan Poskitt
• Murderous Maths, Desperate Measures - Kjartan Poskitt
• Murderous Maths, Awesome Arithmetricks - Kjartan Poskitt
• Murderous Maths, The Key to the Universe - Kjartan Poskitt
• Murderous Maths, The Key to the Universe - Kjartan Poskitt
• The Number Devil, A Mathematical Adventure -  Hans Magnus Enzensberger
• The Magic of Math - Arthur Benjamin
• Professor Stewart’s Hoard of Mathematical Treasures - Ian Stewart
• Professor Stewart’s Cabinet of Mathematical Curiosities - Ian Stewart
• Professor Stewart’s Casebook of Mathematical Mysteries - Ian Stewart
• What If? Serious Scientific Answers to Absurd Hypothetical Questions - Randall Munroe
• The Neptune File - Tom Standage
• Alex’s Adventures in Numberland - Alex Bellos
• The Code Book, The Secret History of Codes and Code Breaking - Simon Singh
• Introducing Mathematics, A Graphic Guide - Ziauddin Sardar and Jerry Ravetz.
• Wonders Beyond Numbers, A Brief History of all Things Mathematical -  Johnny Ball
• Maths on the Back of an Envelope - Rob Eastaway
• Isaac Newton - James Gleick
• The Math Book - Clifford A. Pickover
• How To, Absurd Scientific Advice for Common Real World Problems - Randall Munroe
• Measuring the Universe - Kitty Ferguson
• Difficult Riddles for Smart Kids - M Prefontaine
• The Nothing That Is - The history of the digit zero - Robert Kapla
• Mathematical articles targeted for KS3
• Articles for young mathematicians

KS4

• Why do Buses Come in Threes - Rob Eastaway
• How long is  Piece of String - Rob Eastaway
• Humble Pi. What makes a bridge wobble when it’s not meant to? Billions of dollars mysteriously vanish into thin air? - Matt Parker
• The Maths Book - Big Ideas Simply Explained - Matt Parker
• Does God Play Dice - Ian Stewart
• Game, Set and Math - Ian Stewart
• Chaos, The amazing Sciences of the unpredictable - James Gleick
• Einstein’s Universe - An exploration into the key ideas regarding relativity and their implications - Nigel Calder
• The Unexpected Hanging - Martin Gardner
• Fractal Music - Martin Gardner
• Mathematical Carnival - Martin Gardner
• The Cracking Code Book - Simon Singh
• Alex Through The Looking Glass - Alex Bellos
• Proofs Without Words - Roger Nelson
• The Mathematical Universe: An alphabetical journey through the great proofs, problem and personalities - William Dunham
• Nrich articles for KS4 students
• What did Ada Lovelace’s program actually do?
• How Gauss taught us the best way to hold a pizza

KS5

• Things to make and do in the fourth dimension - Matt Parker
• Fermat’s last Theorem - Simon Singh
• The Music of the Primes - A look at Riemann's hypothesis and the relevance of a formula to generate primes - Marcus Du Sautoy
• Finding Moonshine - A book full of insight into the nature of symmetry and the people who study it - Marcus Du Sautoy
• Dr Riemann's Zeros - The search for the $1,000,000 solution to the greatest problem in Mathematics - Karl Sabbagh 
• How Big is Infinity - An exploration into the most perplexing, stimulating and surprising questions in Mathematics - Tony Crilly
• A Brief History of Time - From the Big Bang to Black Holes - Stephen Hawking
• An Imaginary Tale: The Story of the square root of -1 - Paul Nahin
• e The Story of a Number - What is e, it's origins and applications - E Maor
• Six Easy Pieces - The fundamentals of Physics explained - Richard Feynman.
• Short Mathematical articles
• Nrich Mathematical articles

Resources and Facilities:
The department is housed upstairs in the refurbished “Core” block. Our department is made up of 7 classrooms, and a range of resources are used to enhance the learning of mathematics. 

Computer technology and use of online programs are used regularly by teachers and students alike, and is a standard part of the learning process.

Contact information
If you'd like to find out more please contact Mr M Massey, Subject Leader on mmassey@forest.academy