# Mathematics

### Subject Overview

Mathematics is at the core of the curriculum, providing a platform upon which other subjects can develop. The topics covered at KS3 are continued and extended in greater depth at KS4 and KS5. Mathematics is a **life skill** and we want students to **function numerically** in the world. Extra-curricular activities are arranged to enhance student understanding of the **practical application of mathematics** and to engender a love of subject.

## Mrs Michelle HughesSubject Leader for Mathematics |
## Mr Thabo NkoaneStudent Achievement Manager for Mathematics |
## Mrs Hazel AllenMathematics Teacher |

## Mr Matthew DippleMathematics Teacher |
## Mr Chris DowrickMathematics Teacher |
## Mrs Sarah HassardMathematics Teacher |

## Mrs Tracey SmithMathematics Teacher |

We emphasize the importance of basic **numeracy skills **and believe that students benefit from carrying out mathematical investigations to develop their **problem-solving and** **independent enquiry** skills.

We believe that every child should be able to:

**recall and apply**their knowledge of the times-tables rapidly and accurately- extend their understanding and knowledge, for example of the number system, to include decimals, fractions, percentages, powers, roots and surds
**solve problems**by applying their mathematical knowledge to a variety of routine and non-routine problems- solve problems by breaking them down into simpler steps
- reason mathematically by making connections between number relationships and their algebraic representations
- make generalisations and develop an argument
- know it is acceptable to make mistakes, as that is how they learn
- ask questions to further their understanding

**Consolidation of learning and key skills**, as well as the opportunity to explore, are central to the delivery of mathematics as they reinforce understanding. Homework demonstrates whether students truly understand what they have been learning and is used to tailor teaching in lessons. The cycle of setting and assessing work that is established in the lower years is consolidated at KS4.

The assessment schedule has the intention of helping students with **recall and independent revision**, skills which we look to develop at each key stage, and is designed to **maximise student progress**.

We understand the power of an effective** intervention** programme since progress in Maths is often an individual, rather than a class endeavour. There are a number of supportive intervention strategies used to **maximise student confidence** and ultimately their progress. For example, we provide small group teaching by **experienced Maths teachers** for students who may have SEND needs or a specific weakness with numeracy. These run alongside the core curriculum delivery at KS3 and KS4 and allow students to consolidate their learning.

We recognise that for some students, particularly the disadvantaged students, further support enhances their mathematical **confidence and ability**. This is facilitated through the Maths Nurture Group and small group support.

At A level, we want to give students who enjoy Mathematics the chance to **explore it in more depth** and to engage with complex, challenging and exciting work. We emphasize the balance between enjoyment and hard work and explain how Maths A Level is a **facilitating** subject which supports a number of career paths.

The reformed A Level means that students have a **broader basis** on which to build. In order to bridge from GCSE to A Level, there is a **transition module**, supported by an algebra assessment which gives feedback to students and teachers. The new GCSEs have provided a better bridge to A Level.

For those students taking Further Maths, we try to give students the opportunity to **study all branches of Mathematics**, including Decision Mathematics, which complements the single A Level Mathematics course.

### Year 7 Overview

Students are taught the following topics in Year 7:

**Number**

- use the four operations (addition, division, multiplication and subtraction) applied to whole numbers and decimals up to two decimal places
- add, subtract and order negative numbers, use and understand coordinates in all four quadrants
- add and subtract simple fractions and solve problems involving fractions
- round numbers and measures to one decimal place
- use the concepts and vocabulary of factors, multiples, prime numbers, squares and their roots

**Ratio, Proportion and Rates of Change**

- change between standard units of time, convert between 12hr and 24hr clocks and read and interpret time on a calculator
- use ratio notation, including reduction, to the simplest form and divide a quantity into a given ratio

**Algebra**

- use and understand concepts and vocabulary of terms, expressions and equations
- simplify and manipulate algebraic expressions by collecting like terms
- generate terms of a sequence using term to term or position to term rules
- construct and solve linear equations with an unknown on one side only

**Geometry and Measures**

- apply formulae to calculate and solve problems involving perimeters and areas of rectangles, triangles and compound shapes
- apply properties of angles at a point, angles on a straight line and angles in a triangle
- describe, sketch and draw 2D shapes that have reflective and rotational symmetry
- calculate volume and surface area of cubes and cuboids

**Statistics**

- draw and interpret bar and pie charts
- calculate and compare averages using mean, mode, median and range

**Probability**

- use appropriate language and vocabulary associated with probability, including the probability scale from 0 to 1
- identify and list all outcomes of single events

### Year 8 Overview

Students are taught the following topics in Year 8:

**Number**

- estimations and approximations of calculations using both whole numbers and decimals
- find fractions of quantities, order and perform all four operations on fractions
- find a percentage of an amount, find percentage increase/decrease and use the equivalence between fractions, decimals and percentages
- understand and use order of operations with or without a calculator
- recognise and use multiples, factors, highest common factors, lowest common multiples, powers and their roots

**Ratio, Proportion and Rates of Change**

- use units of measurement (length, time, area, volume) to estimate and draw/interpret scale drawings
- convert within metric units and know equivalents of metric and imperial units
- use and understand links between ratio, proportion and fractions
- compare two ratios, interpret and use ratio in a range of contexts including solving word problems

**Algebra**

- simplify, manipulate and transform algebraic expressions by multiplying out both single and double brackets
- substitute values into formulae and expressions
- solve linear equations with integer coefficients (unknown on both sides) with or without brackets
- recognise and use equations and graphs of straight lines

**Geometry and Measure**

- calculate area of a trapezium, parallelogram and surface area of prisms
- use formulae for circumference and area of a circle
- solve geometrical problems using angles made by parallel lines and using side and angle properties of quadrilaterals
- use a compass and a ruler to construct triangles, quadrilaterals and bisectors
- describe and use both bearings and loci
- translate and enlarge 2D shapes and use a combination of reflection, rotation, translation and enlargement
- calculate volume of cuboids, prisms and know various 3D shapes using faces, edges and vertices

**Statistics**

- identify sources of data and appropriate sample size
- construct and use stem and leaf diagrams and scatter graphs
- compare two or more distributions and time series graphs
- justify and communicate the results of a statistical enquiry

**Probability**

- find and record all possible outcomes of two or more events using sample space, Venn diagrams and tree diagrams
- find and record all mutually exclusive outcomes
- compare experimental probability with theoretical probability

### GCSE Overview

Foundation & Higher Tier

NUMBER, RATIO & PROPORTION

• Arithmetic with integers and decimals, rounding, place value, limits of accuracy and error interval

• Factors, multiples and primes

• Indices, powers and roots

• Standard form

• Fractions and reciprocals

• Fractions, decimals and percentages conversion

• Percentages

• Ratio

• Multiplicative reasoning: direct and inverse proportion, compound measures

ALGEBRA

• Manipulating expressions, expanding and factorising

• Expressions and substitution into formulae

• Linear equations and inequalities

• Straight-line graphs

• Sequences

• Quadratic equations: expanding and factorising

• Plotting graphs: quadratic, cubic, reciprocal

• Rearranging equations and formulae

• Linear simultaneous equations

• Real-life graphs

GEOMETRY & MEASURES

• Plans, elevations, nets

• Constructions, loci, bearings and scale drawings

• Properties of shapes, parallel lines and angle facts

• Interior and exterior angles of polygons

• Perimeter, area and volume: including circles, cylinders, cones and spheres

• Transformations

• Right-angled triangles: Pythagoras and trigonometry

• Similarity and congruence in 2D

• Vectors

PROBABILITY & STATISTICS

• Drawing and interpreting graphs, tables and charts

• Representing data, including pie charts, scatter graphs

• Averages and range

• Statistics, sampling, collecting data

• Probability: including tree and Venn diagrams

Higher Tier only

NUMBER, RATIO & PROPORTION

• Calculations using upper and lower bounds

• Surds

• Repeated proportional change

ALGEBRA

• Expanding triple brackets

• Solving quadratic equations and inequalities, solving simultaneous equations algebraically, equation of a circle

• Algebraic fractions: solving equations, simplifying and changing the subject of formulae

• Algebraic direct and indirect proportion: using statements of proportionality

• Simple algebraic proof

• Nth term quadratic sequences

• Sketching graphs of circles, cubes and quadratics

• Exponential graphs, rates of change in graphs, area under a curve

• Functions and transformations of graphs

GEOMETRY & MEASURES

• Transformations: enlargement using negative scale factors

• Circle theorems and circle geometry

• Similarity and congruence in 3D and geometric proof

• Sine and cosine rules, 1/2 ab sin C, trigonometry and Pythagoras’ Theorem in 3D, trigonometric graphs

• Vectors and geometric proof

PROBABILITY & STATISTICS

• Cumulative frequency, box plots and histograms

• Conditional probability

### A-Level Overview

Students are taught the following topics in Years 12 and 13:

**A LEVEL MATHEMATICS**

PURE:

- Algebra and functions
- Coordinate geometry in the (
*x*,*y*) plane - Trigonometry
- Exponentials and logarithms
- Proof
- Algebraic and partial fractions
- Functions and modelling
- Series and sequences
- The binomial theorem
- Trigonometry
- Parametric equations
- Differentiation
- Numerical methods
- Integration
- Vectors (2D & 3D)

APPLIED:

**Statistics**

- Statistical sampling
- Data presentation and interpretation
- Probability
- Statistical distributions – Discrete, Binomial, Normal
- Statistical hypothesis testing
- Regression and correlation

**Mechanics**

- Quantities and units in mechanics
- Kinematics 1 (constant acceleration)
- Forces and Newton’s laws
- Kinematics 2 (variable acceleration)
- Moments
- Forces at any angle
- Projectiles
- Applications of kinematics
- Applications of forces

**FURTHER MATHEMATICS**

CORE PURE:

- Complex numbers
- Series
- Matrices
- Roots of polynomials
- Linear transformations
- Calculus, including volumes of revolution
- Proof
- Vectors
- Polar coordinates
- Hyperbolic functions
- Differential equations

FURTHER MECHANICS 1:

- Momentum and impulse
- Work, energy and power
- Elastic collisions

DECISION 1:

- Algorithms and graph theory
- Algorithms on graphs
- Linear programming
- Critical path analysis
- Simplex Algorithm

We run several enrichment activities each year for students to apply functional mathematical skills in a real-life context and to develop problem-solving, decision-making and teamwork skills including:

- Years 7 and 8 take part in the Maths Fun Roadshow which enables them to engage in
**rich tasks and functional skills**They solve problems and explore ideas. - Maths in Action at Warwick racecourse for Year 9.
- BP Trading Roadshow for Year 10, during which students gain an insight into how companies make business decisions and understand how a commodity such as crude oil is traded and what factors affect market price.
- The Maths Nurture Group runs weekly and supports the Pupil Premium students with their maths skills and homework. This is organised by a teacher in the Mathematics department who is aided by A level mathematicians.

- Our students take part in the UK Mathematical Challenges run by Leeds University at KS 3, 4 and 5. The aim of the questions is to
**enrich**their mathematical thinking. - In Year 8, our Gifted and Talented students work with Year 6 students to complete the Maths Trail, where students solve mathematical problems and also familiarise themselves with the school. This has helped to establish links with our feeder primary schools
- Our More Able KS4 and 5 students attend Maths Inspiration interactive lecture shows, where the UK’s most inspiring maths speakers present mathematics live in the context of exciting, real-world applications.