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# 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, 8 and 9

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

Content - Year 7

Autumn

• Place values inc decimals; < > notation
• Addition and subtraction - traditional approaches and other methods
• Addition and subtraction - many word problems; many methods
• Multiplication - different methods + word problems
• Division - different methods + word problems
• Negative numbers - adding and subtracting negatives + word problems. NOT MULTIPLY DIVIDE!
• BODMAS (without indices)
• Intro to upper and lower bounds
• Squares and cubes, Square roots and cube roots
• Factors and LCM from lists including word problems
• Prime numbers
• More problem solving with multiples, factors, primes, etc
• Common denominators; order fractions
• Mixed numbers and improper fractions; add and subtract mixed numbers
• Multiply whole numbers by fractions.
• Place values down to thousandths; convert fractions to decimals and percentages.
• Comparing fractions of amounts; percentages of amounts
• Ratio

Spring

• Converting seconds, minutes, hours; Calculations with time
• Reading timetables
• Metric unit conversions
• More simplifying expressions; solving one-step equations.
• Solving two-step equations
• Substitute numbers for letters in formulae.
• Sequences with shapes [term by term]
• Plot coordinates in all four quadrants
• Measuring and drawing angles
• Rotational symmetry
• Recap angles on a line; around a point; vertically opposite angles; missing angles in triangles and quadrilaterals - including special triangles
• Construct Accurately draw triangles using ASA/AAS or SAS rules.
• Area by counting squares; area of rectangles, squares, triangles, and compound shapes.
• Names of 3D shapes (pyramids vs prisms); Faces + Verticies - Edges = 2
• Volume by counting cubes; actual cubes and cuboids

Summer

• Probability of events happening using words
• Basic probability using fractions; probability of something NOT happening (probabilities add to 1)
• Reading information from tables and charts; Draw bar charts
• Dual bar charts and Pictograms
• Pie charts - constructing
• Mean, Median, Mode and range
• Problem solving with MMMR

Content - Year 8

Autumn

• Multiply and divide by 0.1, 0.01, 0.001
• Multiply decimals by decimals
• Divide decimals by decimals
• Multiply and divide positive and negative numbers
• Higher powers and roots
• More powers and roots; powers of 10
• BODMAS
• Prime factor trees
• Estimating answers by rounding; problem solving using approximations
• Multiply fractions including mixed numbers
• Divide fractions including mixed numbers
• FDP conversions; especially include numbers greater than 1.
• Percentages of amounts
• Increase / decrease by a percentage.
• Simplify ratios; ratios in 1:n and n:1
• Ratio word problems
• Dividing in a ratio
• Direct proportion questions

Spring

• Speed, distance & time
• Converting imperial units
• Metric / Imperial conversions
• Scale and Scale Drawings
• Expanding brackets (single bracket) including multiplying a variable over the bracket.
• Factorising over a single bracket
• Solving equations with brackets - two methods
• Solving equations with fractions
• Solving equations with x on both sides
• Writing formulae in words
• More writing formulae with words
• Sequences - recap y7; nth term of a linear sequence
• Equations of verical and horizontal lines
• Draw lines using tables of values; Identify gradients and y-intercepts of lines
• Real-Life Graphs
• Recap y7 triangles and quadrilterals (lines of symmetry, etc)
• Properties of quadrilaterals - particularly diagonals.
• Angle questions
• Finish parallel lines; start bearings
• Bearings & Problem Solving with bearings
• Area of triangles, parallelograms and trapeziums. Include compound shapes

Summer

• Volume of prisms
• Recap y7 probability; introduce sample space diagrams
• Use of notation such as universal set, ⋂, ⋃, ⦰; Put elements into the correct location; work out probabilities
• Dual bar charts; harder pie charts
• Plot scatter diagrams; types of correlation; interpret what that correlation means;
• Draw a rough line of best fit; use that line to answer and solve problems
• MMMR from tables; identify outliers; compare distributions

Content - Year 9

Autumn

• Number Problems
• Approximations
• Power Laws
• Standard Form
• Prime Factors
• Fraction Problems
• Percentage Change
• Ratios
• Direct and Inverse Proportion
• Compound Measures
• Metric and Imperial Conversions
• Maps and Map Scales

Spring

• Algebraic Expressions
• Solving Equations
• Inequalities
• Formulae
• Sequences
• Finding the Equation of a Straight Line
• Quadratic Graphs
• Solving Equations using Graphs
• Real-Life Graphs
• Polygons
• Loci and Constructions
• Transformations
• 3D Shapes
• Pythagoras' Theorem
• Trigonometry
• Similarity and Congruence
• Geometric Relationships

Summer

• Probability from Experiments
• Theoretical Probability
• Displaying Data
• Scatter Graphs
• Averages and Range from Tables

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

Knowledge Organisers - Year 8

#### YEARS 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.

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

Additional Support Available/Useful Links

Reading List

For pupils:

• Revision Guides and Workbooks for AQA 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 - Students follow the AS syllabus (Edexcel 8MA0) but do not sit the external exam. Instead they take an internal exam at the end of the year to monitor progress.
• Year 13 – Advanced GCE in Mathematics (Edexcel 9MA0).

Year 12 & 13 Further Maths – Year 13 Advanced GCE in Mathematics (9MA0), Year 13 Advanced GCE in Further Mathematics (9FM0, option H0)

Content AS/A Level

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.
• Year 13 – Further Mechanics: studies include Momentum and Impulse, Work, Energy and Power, Strings and springs.
• Year 13 – Decision Maths: Algorithms and graph theory, critical path analysis, linear programming.

Assessment A Level 9MA0

Students sit external exams at the end of Year 13 (an internal PPE in Year 12). The external exam consists of:

• Paper 1: 9MA0/01, 2 hour exam 33% of the qualification, 100 marks, based on any of the Pure maths topics.
• Paper 2: 9MA0/02, 2 hour exam 33% of the qualification, 100 marks, based on any of the Pure maths topics.
• Paper 3: 9MA0/03, 2 hour exam 33% of the qualification, 100 marks, based on any of the Statistics and Mechanics maths topics.

Assessment A Level Further Maths 9FM0

Students sit external exams at the end of Year 13. The external exam consists of:

For A2 maths:

• Paper 1: 9MA0/01, 2 hour exam, 33% of the qualification, 100 marks, based on any of the Pure maths topics.
• Paper 2: 9MA0/02, 2 hour exam, 33% of the qualification, 100 marks, based on any of the Pure maths topics.
• Paper 3: 9MA0/03, 2 hour exam, 33% of the qualification, 100 marks, based on any of the Statistics and Mechanics maths topics.

For Further maths:

• Paper 1: 9FM0/01, 90 minute exam, 25% of the qualification, 75 marks, based on any of the Pure maths topics.
• Paper 2: 9FM0/02, 90 minute exam, 25% of the qualification, 75 marks, based on any of the Pure maths topics.
• Paper 3: 9FM0/3C, 90 minute exam, 25% of the qualification, 75 marks, based on any Further Mechanics topics.
• Paper 4: 9FM0/4D, 90 minute exam, 25% of the qualification, 75 marks, based on any Decision Maths topics.

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.