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

Mathematics Assessment Framework – Key Stage 3

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

Deduce π by taking circumference ÷ diameter.
Use π to work out circumferences; Area of a circle
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

Year 7 Assessment Schedule

Year 8 Assessment Schedule

Year 9 Assessment Schedule

Knowledge Organisers - Year 7

Autumn 1 - Basic Number and Decimals

Autumn 1 - Factors and Multiples

Autumn 2 - Sequences

Spring 1 - 2D Shapes

Spring 1 - Angles

Spring 1 - Construction

Spring 2 - Coordinates

Spring 2 - Transformations

Summer 1 - Factors and Multiples

Summer 2 - Fractions

Summer 2 - Percentages

Summer 2 - Ratio

Knowledge Organisers - Year 8

Autumn 1 - Forming and solving equations

Autumn 1 - Inequalities

Autumn 2 - Accuracy and Estimation

Autumn 2 - Linear Graphs

Spring 1 - Proportion

Spring 1 - Ratio

Spring 1 - Real Life Graphs

Spring 2 - Bivariate data

Spring 2 - Univariate data

Summer 1 - Angles in Polygons

Summer 1 - Bearings

Summer 2 - Circles

Summer 2 - Surface Area

Summer 2 - Volume

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

Year 10 Assessment Schedule

Year 11 Assessment Schedule

Additional Support Available/Useful Links

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

2D Shapes

Accuracy and Estimation

Angles

Angles in Polygons

Basic Number and Decimals

Factors and Multiples

Forming and Solving Equations

YEARS 12 and 13

Exam Board and syllabus code:

Year 12 - AS GCE in Mathematics (8MA0)
Year 13 – Advanced GCE in Mathematics (9MA0)
Year 12/13 Further Maths – Year 12 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.

See www.mathscareers.org.uk