﻿ Mathematics - Subject Information - The Forest School
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Subject Lead of Maths:                                 Mr G Hawkett
Teacher of Maths / KS3 Coordinator:         Mr T McNeill                                                                                       Teacher of Maths /  KS4 Coordinator:        Mr M Massey                                                                                Teacher of Maths:                                          Mrs D Turner                                                                                  Teacher of Maths:                                          Miss N Thiagarajan                                                                      Teacher of Maths:  Mr S Taplin

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.
The department is housed in a suite of 6 classrooms, and a range of resources are used to enhance the learning of mathematics. Computer technology is used regularly by teachers and students alike, and is a standard part of the learning process.
We are very proud of our results at all Key Stages. At Key Stage 3, the vast majority of our students achieve well above expected levels. At Key Stage 4, around a third achieve at level 7-9 for GCSE and over 80% achieve at level 4-9. At A level around 75% of our students achieve at least a B grade. Our uptake for Key Stage 5 courses is very strong - we have around 40 students who study to A level each year. We also offer Further Maths to a small number of students.

#### KS3

Mathematics – Key Stage 3

 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

Please find the details for Maths at KS3

#### KS4

Mathematics – Key Stage 4

 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 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

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.

#### KS5

 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

Each year, pupils enter the UK Mathematics Trust (UKMT) Maths challenge competition at both individual and team levels at all Key Stages. We also run a monthly maths puzzle for pupils, which is well supported by all.

#### Additional information/ related activities

Each year, pupils enter the UK Mathematics Trust (UKMT) Maths challenge competition at both individual and team levels at all Key Stages. We also run a monthly maths puzzle for pupils, which is well supported by all.

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