# Mathematics

As part of our Maths vision, we strive for all students to become fluent in the fundamentals of Mathematics, developing conceptual knowledge and an ability to recall and apply knowledge rapidly and accurately.

Our aim is to ensure that our students can reason mathematically and solve problems and to develop a `can do` attitude and perceive themselves as resilient and become great Warlingham and lifelong learners.

Our curriculum aims to ensure that all students develop Mathematics knowledge, conceptual understanding, Skills and Learner attributes through our core strands of Number, Algebra, Ratio & Proportion, Statistics and Probability. The curriculum is a progression model, through which the ‘big ideas’ are developed and built upon, as students develop their own schema for Maths, underpinned by the continual development around students' curiosity, fluency, reasoning and problem-solving skills.

Key Skills running through our curriculum maps

• Fluency
• Resilience
• Reasoning Skills
• Communication Skills
• Problem-solving

### The Core Concepts

The key strands below run through and are continually built upon through our KS3, KS4 and KS5 curriculum maps.

• Number
• Algebra
• Ratio, proportion and rates of change
• Geometry and measures
• Probability
• Statistics

## key stage 3

### Year 7

Data handling

• Representing data
• Interpreting data
• Comparing data

Number

• Calculating and estimates
• Multiples and factors

Algebra

• Simplifying and writing expressions
• Substitution into expressions and formulae

Algebraic thinking

• Sequences

Place value and proportion

• Fraction, decimal and percentage equivalence

Applications of number

• Solving problems with addition and subtraction
• Solving problems with multiplication and division
• Fractions and percentages of amounts

Fractional thinking

• Addition and subtraction of fractions

Lines and angles

• Constructing, measuring and using geometric notation
• Developing geometric reasoning

Reasoning with number

• Developing number sense
• Sets and probability
• Prime numbers and proof

#### Year 8

Number

• Calculations with directed numbers
• Powers and roots
• Multiples and factors

Area and Volume

• Area of 2D shapes
• 3D shapes characteristics
• Surface are and volume of 3D shapes
• Measures

Dealing with Data

• Representing data
• Interpreting data

Proportional Reasoning

• Ratio and scale
• Multiplicative change
• Multiplying and dividing fractions

Representations

• Working in the cartesian plane
• Tables and probability

Algebraic techniques

• Brackets, equations and inequalities

Algebraic techniques

• Brackets, equations and inequalities (continued)
• Sequences

Developing number

• Fractions and percentages

Developing geometry

• Angles in parallel lines and polygons
• Line symmetry and reflection

#### Year 9

Number

• Place Value
• HCF/LCM
• Indices
• Standard Form
• Surds

Algebra

• Expressions
• Expanding / Factorising
• Sequences
• Equations
• Formulae

Interpreting and representing data

• Scatter Graphs
• Statistical Diagrams
• Averages

Fractions, Ratio and Percentages

• Fractions
• Ratio
• Ratio and Proportion
• Percentages
• Fraction Decimal and Percentage Equivalents

Angles and Trigonometry

• Angle properties of polygons
• Pythagoras Theorem
• SOHCAHTOA

Area and Volume

• Perimeter, area and volume of 2D and 3D shapes
• Circles, arc lengths and sectors

Graphs

• Linear graphs and y = mx + c
• Real life graphs
• Quadratic, cubic and reciprocal graphs

Transformations and Constructions

• Plans and elevation
• Rotation, reflection and translation of shapes
• Enlargement about a point given a scale factor
• Constructions and bearings
• Loci

## Key Stage 4

### Year 10 & Year 11

#### Edexcel GCSE Mathematics

Students are assessed and streamed towards the end of Year 9 and will continue their journey through the GCSE progression model. Students will follow either the Higher or Foundation curriculum map and will be continually challenged thorough each unit of work.

#### Foundation

Perimeter, Area and Volume

• Rectangles, Triangles and Parallelograms
• Trapezia and changing units
• Area of compound shapes
• Surface Area of 2D shapes
• Volume of prisms

Graphs

• Coordinates
• Linear Graphs
• Y = mx + c
• Real life graphs
• Distance-time graphs

Transformations

• Translation
• Reflection
• Rotation
• Enlargement
• Describing Transformations

Ratio and Proportion

• Writing ratios
• Using ratios
• Ratios and Measures
• Comparing using ratios
• Using proportion
• Proportion and graphs
• Proportion Problems

Right-angled triangles

• Pythagoras` theorem
• Trigonometry (Sine, Cosine and Tangent Ratio)
• Finding lengths and angles using trigonometry

Probability

• Calculating probability
• Two events
• Experimental probability
• Venn diagrams
• Tree diagrams

Multiplicative Reasoning

• Percentages
• Growth and decay
• Compound measures
• Distance, Speed and Time
• Direct and inverse proportion

Constructions, loci and bearings

• 3D solids
• Plans and elevations
• Accurate drawings
• Scale drawings and maps
• Constructions
• Loci and regions

• Expanding double brackets

Perimeter, Area and Volume

• Circumference of a circle
• Area of circles
• Area of semi circles and sectors
• Composite 2D shapes and cylinders
• Pyramids and cones
• Spheres and composite solids

Fractions, indices and standard form

• Multiplying and dividing fractions
• The laws of indices
• Writing large and small numbers in standard form
• Calculating with standard form

Congruence, similarity and vectors

• Similarity and enlargement
• Using similarity
• Congruence
• Vectors

Further Algebra

• Graphs of cubic and reciprocal functions
• Non-linear graphs
• Solving simultaneous equations
• Rearranging formulae
• Proof

#### Higher

Equations and Inequalities

• Solving Linear and Quadratic Simultaneous Equations

Probability

• Combined Events
• Mutually Exclusive Events
• Experimental Probability
• Independent Events and Tree Diagrams
• Conditional Probability
• Venn Diagrams and Set Notation

Multiplicative Reasoning

• Growth and Decay
• Compound Measures
• Ratio and Proportion

Similarity and Congruence

• Congruence
• Geometric Proof
• Similarity in 2D and 3D shapes

Further Trigonometry

• Accuracy
• Graphs of Sine, Cosine and Tangent Function
• Sine Rule and Cosine Rule
• Solving Problems in 3D
• Transforming Trigonometric Graphs

Further Statistics

• Sampling
• Cumulative Frequency
• Box Plots
• Histograms
• Comparing and Describing Populations

Equations and Graphs

• Solving Simultaneous Equations graphically
• Representing Inequalities Graphically
• Graphs of cubic functions

Circle Theorems

• Tangents
• Angles in circles
• Applying circle theorems

Further Algebra

• Rearranging Formula
• Algebraic Fractions
• Surds
• Functions
• Prove a result using Algebra

Vectors and Geometric Proof

• Vectors and vector notation
• Vector arithmetic
• Parallel vectors and collinear points
• Solving geometric problems

Proportion and Graphs

• Direct Proportion
• Inverse Proportion
• Exponential Functions
• Non-Linear Graphs
• Translating Graphs of functions
• Reflecting and stretching graphs of functions

## key stage 5

### Pearson Edexcel A Level Mathematics (9MA0)

#### Year 12

##### Pure

Algebraic Expressions

• Simplifying algebraic expressions and surds

Equations and Inequalities

• Solving simultaneous equations
• Solving inequalities

Graphs and Transformations

• Analysing polynomial and reciprocal graphs
• Transforming graphs

Straight Line Graphs

• Manipulating y = mx + c

Algebraic Methods

• Factor theorem
• Dividing polynomials
• Proof

Trigonometric Ratios

• Sine & Cosine Rule
• Area of a Triangle
• Trigonometric graphs

Binomial Expansion

• Expand using binomial formula

Trigonometric Identities & Equations

• Using trigonometric identities
• Solving trigonometric equations

Circles

• Equation of a circle
• Solving geometric problems using straight lines in circles
• Solving problems using properties of a circle

Vectors

• Using vector notation
• Solving geometric problems using vectors

Differentiation

• 1st principles
• Differentiating expressions with varying powers of x.

Integration

• Integrating expressions with varying powers of x.
• Solving problems regarding the area under a curve

Exponentials and Logarithms

• Exponential graphs and modelling
• Laws of logarithms
• Solving equations using logarithms
##### Mechanics

Modelling in Mechanics

• Modelling techniques
• SI units
• Vectors

Constant Acceleration

• Displacement and velocity graphs
• SUVAT equations

Forces and Motion

• Force diagrams
• Newtons Laws
• Connected particles

Variable Acceleration

• Functions of time
• Using calculus
##### Statistics

Data Collection

• Sampling methods
• Types of data
• Large data set

• Calculating types of average
• Coding

Representations of data

• Drawing and interpreting box plots
• Drawing and interpreting cumulative frequency curves
• Drawing and interpreting histograms

Correlation

• Drawing and interpreting scatter diagrams
• Interpreting regression lines

Probability

• Using tree diagrams
• Using Venn diagrams
• Mutually exclusive and independent events

Statistical Distributions

• Binomial distribution

Hypothesis Testing

• Carrying out one and two tailed tests

#### Year 13

##### Pure

• Find arc length and area of sectors
• Solving trigonometric equations
• Small angle approximations

Trigonometric Functions

• Sec, Cosec & Cot
• Identities and inverse functions

Trigonometry and Modelling

• Double angle formulae
• Rsin(X+a)

Algebraic Methods

• Partial fractions

Functions and Graphs

• Modulus function
• Composite and inverse functions

Sequences and Series

• Arithmetic sequences and series
• Geometric sequences and series

Binomial Expansion

• Expand using fractions and negatives

Parametric Equations

• Converting parametric and cartesian equations
• Finding points of intersection

Differentiation

• Trigonometric functions, logarithms and exponentials
• Chain, product and quotient rules
• Parametric
• Implicit

Numerical Methods

• Iteration
• Newton-Raphson method

Integration

• Trigonometric functions, logarithms and exponentials
• By substitution and parts
• Partial fractions
• Trapezium rule
• Differential equations

Vectors

• 3D vectors
##### Mechanics

Moments

• Resultant moments
• Equilibrium
• Centres of mass

Forces and Friction

• Resolving forces
• Friction
• Inclined planes

Projectiles

• Horizontal motion
• Any angle projection

Application of Forces

• Statics
• Dynamics and inclined planes

Further Kinematics

• Position vectors
• Variable acceleration using calculus
##### Statistics

Regression, correlation and hypothesis testing

• Exponential models
• Calculating the pmcc
• Hypothesis testing

Conditional probability

• Set notation
• Conditional probability
• Venn diagrams and tree diagrams

The normal distribution

• Finding probabilities
• Solving inverse problems
• The standard normal distribution
• Approximating a binomial distribution
• Hypothesis testing