# 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
- Misleading 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*= m*x*+ 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
- Gradients
- 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

**Quadratic equations and graphs **

- Expanding double brackets
- Plotting quadratic graphs
- Using quadratic graphs
- Factorising quadratic expressions
- Solving quadratic equations

**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 Quadratics
- 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 Quadratic Functions
- Solving quadratic graphs graphically
- Graphs of cubic functions

**Circle Theorems **

- Radii and Chords
- 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

**Quadratics**

- Solving quadratic equations
- Identifying quadratic graph properties

**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**

- 1
^{st}principles - Differentiating expressions with varying powers of x.
- Solve problems regarding gradients

**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

**Measures of location and spread**

- Calculating types of average
- Calculating types of spread
- 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

**Radians**

- 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**

- Addition formulae
- Double angle formulae
- Rsin(X+a)

**Algebraic Methods**

- Proof by contradiction
- 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
- Link with partial fractions

**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