# Mathematics

**‘Without maths, there’s nothing you can do. Everything around you is mathematics.**

**Everything around you is numbers.’ Shakuntala Devi, Mathematician**

Mathematics is an incredibly important skill to learn. It is all around us in all aspects of our lives. Not only are the actual skills learnt in mathematics important it also teaches us soft skills such as critical thinking, problem solving, writing, reasoning and resilience among others which are hugely desirable in almost all careers. Mathematics also opens the doors to a huge range of careers – in the fields of science, technology and engineering amongst others.

At Garth our aim is to create resilient, enthusiastic and confident learners who believe they can succeed. Mathematics provides students with uniquely powerful ways to describe, analyse and understand the world. Students who are functional in mathematics are able to think independently in applied and abstract ways, and can reason and solve problems. Mathematics is a hugely creative subject. The language of mathematics is universal.

Subject Leader – **Mr N Sleeman**

**YEARS 7 and 8**

Mathematics at Garth Hill College follows a mastery approach - where learning how to solve mathematical problems is at the core of mathematics lessons. All pupils will study essentially the same topics at the same time, with those in higher sets exploring topics in greater depth. The content studied each term builds on previously studied material and the links between all areas of study are made clear.

**KS3 Objectives**

Mathematics Assessment Framework – Key Stage 3

**Content - Year 7**

**Autumn**

- Place value
- Factors, multiples and primes
- Positive and negative numbers
- Expressions, equations and sequences

**Spring**

- Angles
- 2D Shapes
- Constructing triangles
- Coordinates
- Area of Triangles and Rectangles
- Transforming 2D figures

**Summer**

- LCM and HCF
- Fractions
- Ratio
- Percentages

**Content - Year 8**

**Autumn**

- Forming and solving equations
- Forming and solving inequalities
- Linear Graphs
- Accuracy and estimation

**Spring**

- Ratio and real life graphs
- Direct and inverse proportion
- Univariate data
- Bivariate data

**Summer**

- Parallel lines
- Angles in polygons
- Bearings
- Circles and composite shapes
- Volume of prisms
- Surface area of prisms

**Assessment**

- Students will be given a 3 assessed pieces every half term which covers half-termly topics.
- Students will also be given an ‘end of year’ exam.
- Excellent, Good, Developing, and Emerging criteria can be found here in the Year 7 and 8 Assessment Framework.

**Assessment Schedule**

**Knowledge Organisers - Year 7**

Autumn 1 - Basic Number and Decimals

Autumn 1 - Factors and Multiples

Summer 1 - Factors and Multiples

**Knowledge Organisers - Year 8**

Autumn 1 - Forming and solving equations

Autumn 2 - Accuracy and Estimation

**YEARS 9, 10 and 11**

**Exam Board and syllabus code**

AQA - Mathematics (8300)

**Content**

We aim to inspire young people to enjoy maths, to develop their thinking skills, to exceed their expectations in public examinations and to be functionally numerate in the workplace. For the current GCSE course pupils are assessed on their skills, knowledge and understanding in relation to number, algebra, geometry and measures and statistics. The aims of the course are to enable pupils to:

- develop knowledge, skills and understanding of mathematical methods and concepts • acquire and use problem-solving strategies
- select and apply mathematical techniques and methods in mathematical, everyday and real world situations
- reason mathematically, make deductions and inferences and draw conclusions
- interpret and communicate mathematical information in a variety of forms appropriate to the information and context.

At both foundation and higher tier, we are following the scheme of work which is in line with Mathematics Mastery, our partnership organisation, and follow their 5 year GCSE mastery plan. Learners also have access to an online personal text book.

**Assessment**

Throughout the course, pupils are assessed during each unit and at the end of each stage.

At the end of the course, pupils sit three papers – each worth 80 marks – at either foundation or higher tier. The first of these papers is undertaken without a calculator, whereas a (scientific) calculator is required for the second and third paper.

Pupils passing the foundation tier examinations will be awarded a grade between 5 and 1. Pupils passing the higher tier examinations will be awarded a grade between 9 and 3.

**Home Learning**

Home learning is set each week for all learners with the aim of consolidating, broadening or extending understanding. This will include a variety of written practice, past papers, online tasks, research and revision.

**How Parents and Carers Can Support**

- Make sure that your child has all the equipment they need including a scientific calculator, ruler, protractor and a good quality pair of compasses.
- Keep rehearsing mental calculations, such as times tables, with them.
- Point out where you use mathematics whether in personal finance, at work or recreationally.
- Encourage your child to complete their home learning and to show how they have found their answers.
- Talk with your child about what they are doing and how they have reached their conclusions.
- Be positive in your approach to mathematics. Your child will pick up on and may adopt your attitude towards the subject.
- Use the booster packs on www.mymaths.co.uk

Year 11 Assessment Schedule - Half Term 1

**Additional Support Available/Useful Links**

- https://www.kerboodle.com/users/login
- www.mymaths.co.uk
- http://www.bbc.co.uk/education/subjects/z6pfb9q
- https://www.cgpbooks.co.uk/School/books_ocr_maths_range
- http://www.mathscareers.org.uk/14-16/
- www.mrbartonmaths.com/freeresources.htm
- https://hegartymaths.com/

**Reading List**

For pupils:

- Revision Guides and Workbooks for QAQ GCSE Maths – CGP
- 17 Equations that Changed the World – Ian Stewart
- 1089 and All That – David Acheson
- How to Cut a Cake – Ian Stewart

For parents:

- More Maths for Mums and Dads – Rob Eastaway and Mike Askew

**Knowledge Organisers**

**YEARS 12 and 13**

**Exam Board and syllabus code:**

- Year 12 Starting September 2017 / Year 13 Starting September 2018 MEI
- Level 3 Advanced Subsidiary GCE in Mathematics (B)
- Level 3 Advanced Subsidiary GCE in Further Mathematics (B)
- Level 3 Advanced GCE in Mathematics (B)
- Level 3 Advanced GCE in Further Mathematics (B)

**Legacy – Current Year 13 only Edexcel **

- Level 3 Advanced Subsidiary GCE in Mathematics (8371)
- Level 3 Advanced Subsidiary GCE in Further Mathematics (8372)
- Level 3 Advanced GCE in Mathematics (9371)
- Level 3 Advanced GCE in Further Mathematics (9372)

**Year 12 and Year 13 AQA**

- Level 3 Certificate Mathematical Studies (1350)

**Content AS/A Level from September 2017**

**AS/A Level Mathematics**

**Pure Mathematics **

- AS & A level: Pure mathematics includes proof, algebra, graphs, sequences, trigonometry, logarithms, calculus and vectors.
- A level only: Learners study these topics in more depth and also study functions, numerical methods and differential equations.

**Statistics **

- AS & A level: Statistics includes working with data from a sample to make inferences about a population, probability calculations, using a binomial distribution as a model, and statistical hypothesis testing.
- A level only: Learners study these topics in more depth and also study the Normal distribution.
- There is a pre-release data set for both AS and A level. The purpose of the large data set is that learners experience working with real data in the classroom and explore this data using appropriate technology.

**Mechanics **

- AS & A level: Mechanics includes kinematics, working with forces and Newton’s laws.
- A level only: Learners study these topics in more depth and also study motion under gravity, friction and simple moments.

**AS/A Level Further Mathematics**

**Core Pure Mathematics **

- AS and A level: Some pure topics from AS level Mathematics are studied in greater depth, while some new topics are introduced. Algebraic work with series is extended. The powerful technique of proof by induction is used in various contexts. Complex numbers are introduced, including their geometrical representation. Matrices are used to solve systems of equations and to explore transformations. Scalar products of vectors are applied to problems involving planes.
- A level only: In addition to studying these topics in more depth, learners also applied vector methods to problems involving lines and planes and calculus techniques are extended, including the use of hyperbolic functions and polar coordinates, and culminate in the solution of differential equations.

**Statistics a **

- In this option, situations are modelled by discrete random variables; the suitability of models is tested using chi-squared tests. Bivariate data are investigated, with tests for correlation and association and modelling using regression.

**Mechanics a **

- In this option, basic principles of forces and their moments, work and energy, impulse and momentum and centres of mass are used to model various situations. These include rigid bodies in equilibrium; particles moving under gravity, on a surface, in a circle, attached to springs; bodies colliding with direct or oblique impact.

The final option for A level Further Mathematics will be chosen from Mechanics b, Statistics b, Modelling with Algorithms, Numerical Methods, Extra Pure, Further Pure with Technology.

**Legacy Content A2 – Current Year 13 only**

The A2 Mathematics course consists of units Core 3, Core 4 and Mechanics 1. Building on AS Mathematics, these units include work on:

**C3** Algebra and functions; trigonometry; exponentials and logarithms; differentiation; numerical methods.

**C4** Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; differentiation; integration; vectors.

**M1** Mathematical models in mechanics; vectors in mechanics; kinematics of a particle moving in a straight line; dynamics of a particle moving in a straight line or plane; statics of a particle; moments.

A2 Further Mathematics consists of units Further Pure 2, Statistics 2 and Mechanics 2. Building on AS Further Mathematics and AS and A2 Mathematics, these units include work on:

**FP2** Inequalities; series, first order differential equations; second order differential equations; further complex numbers, Maclaurin and Taylor series.

**S2** The Binomial and Poisson distributions; continuous random variables; continuous distributions; samples; hypothesis tests.

**M2** Kinematics of a particle moving in a straight line or plane; centres of mass; work and energy; collisions; statics of rigid bodies.

**Assessment A Level (year 12 from September 2017; year 13 from September 2018)**

- Students submit at least one written task each week and receive constructive feedback on their work.
- Students are assessed at the end of each of the topics given above. If they do not reach the required standard, they will attend extra lessons before attempting the assessment again.
- In addition to this, students sit two rounds of pre-public examinations. The outcomes of these examinations are analysed by teaching staff alongside each student.

**For A Level Mathematics – examinations (covering Yr 12 and Yr 13 work)**

Paper 1 – Pure and Mechanics, 2 hours, worth 36.5%

Paper 2 – Pure and Statistics, 2 hours, worth 36.5%

Paper 3 – Pure Mathematics and Comprehension, 2 hours, worth 27%

**For A Level Further Mathematics – examinations (covering Yr 12 and Yr 13 work)**

Core Pure, 2 hours 40 minutes, worth 50%

Mechanics a, 1 hour 15 minutes, worth 16.6%

Statistics a, 1 hour 15 minutes, worth 16.6%

Option, 1 hour 15 minutes, worth 16.6%

**Legacy Assessment A2 (current Year 13 only)**

- Students submit at least one written task each week and receive constructive feedback on their work.
- Students are assessed at the end of each of the topics given above. If they do not reach the required standard, they will attend extra lessons before attempting the assessment again.
- In addition to this, students sit two rounds of pre-public examinations. The outcomes of these examinations are analysed by teaching staff alongside each student.
- At the end of the course, students sit a 90 minute external examination in each of the three units. These are equally weighted and the aggregate score results in an AS grade being awarded by the exam board.

**Skills/Aptitudes needed to succeed**

Students wishing to start AS Mathematics will need a minimum of a grade 6 at GCSE, although a 7 is preferred. Further level 2 qualifications in Statistics and Additional Maths are welcomed and encouraged. Learners starting the Mathematical Studies MS will need at least a grade 4 at GSCE. In particular, students will need to be competent in dealing with the algebraic content of the higher tier of GCSE mathematics. The ability to work in organised fashion, think logically and to visualise mathematical concepts will be most beneficial.

Students wishing to start AS Further Mathematics will need a minimum of a grade 7 in GCSE Mathematics, although an 8 and/or a good pass in Additional Maths are preferred.

**Benefits and Uses**

Mathematics is used in many contexts to explain the world in which we live and to support endeavours in other disciplines. Mathematical knowledge and understanding is sought after by both employers and universities.

A level mathematics is a highly regarded qualification in the fields of business, technology, science and engineering. As well as preparing students to study Mathematics at undergraduate level, is also an essential qualification for entry to courses such as Accounting, Actuarial Studies, Aeronautics, Biomedical Sciences, Chemical Engineering, Computer Science, Economics, Electronic Engineering, Mechanical Engineering and Physics. It is often required or preferred for other courses from Management to Optometry, Dentistry to Computer Science, and from Architecture to Meteorology.