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# Mathematics

## Curriculum Intent:

“Mathematics provides a deep conceptual understanding of the world, enabling students who apply concepts accurately to approach and solve unfamiliar problems with confidence.”

The Mathematics Curriculum Area vision

• For all pupils to really enjoy and have a positive attitude towards Mathematics so that they can appreciate the power and beauty of the subject.
• For all pupils to develop a deep and secure knowledge to enable them to become inquiring thinkers and achieve their maximum potential.
• For all pupils to develop mathematical fluency and the ability to reason mathematically.
• For all pupils to have confidence in approaching a variety of problems.
• For all pupils to become keen to take risks and make mistakes; they then learn from these mistakes in order to progress.
• For all staff to promote excellence in teaching and learning throughout the school.
• For all staff to work together within the curriculum area and share our good practice amongst ourselves and with other curriculum areas.

Maths is offered as:

• Core subject Years 7, 8, 9, 10 &11
• IB Application and Interpretations Year 12 & 13 (Standard and Higher)
• IB Analysis and Approaches Year 12 & 13 (Standard and Higher)

## Key Stage 3 Mathematics

Curriculum Overview

Students at Key Stage 3 have 7 hours per fortnight following the White Rose Maths scheme of learning, allowing for the transition from primary school to GCSE.

 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Year 7 Algebraic Thinking: · Sequences · Understand and use algebraic notation · Equality and equivalence Place value and proportion · Place value and ordering integers and decimals · Fraction, decimal and percentage equivalence Applications of Number · Solve problems with addition and subtraction · Solve problems with multiplication and division · Fractions and percentages of amounts Directed number · Four operations with directed number 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 Proportional reasoning · Ratio and scale · Multiplicative change · Multiplying and dividing fractions Representations · Working in the Cartesian plane · Representing data · Tables and probability Algebraic techniques · Brackets, equations and inequalities · Sequences · Indices Developing Number · Fractions and percentages · Standard index form · Number sense Developing Geometry · Angles in parallel lines and polygons · Area of trapezia and circles · Line symmetry and reflection Reasoning with Data · The data handling cycle · Measures of location Year 9 Reasoning with Algebra: · Straight-line graphs · Forming and solving equations · Testing conjectures Constructing in 2 and 3 dimensions · Three dimensional shapes · Constructions and Congruency Reasoning with Number: · Numbers · Using percentages · Maths and money Reasoning with Geometry · Deduction · Rotation and translation · Pythagoras’ Theorem Reasoning with Proportion · Enlargement and similarity · Solving ratio and proportion problems · Rates Representations · Solve problems using graphs, tables and algebra

Year 7

Year 7 pupils have 7 lessons a fortnight and are taught in house groups. Pupils will begin to build on the mathematical skills from Key Stage 2 and extend their understanding of number, algebra, geometry and statistics whilst developing fluency in number They will begin to develop mathematical reasoning through problem solving activities throughout their lessons and mathematical enrichment lessons. These lessons take place once per term and focus on allowing pupils to explore areas of mathematics and be able to communicate and explain ideas in written work and investigations. Pupils interested in solving extra problems outside of lessons are invited to Parallel Maths to extend their learning in an engaging way. Pupils with a strong track record in the department will also be invited to participate in the Junior Maths challenge.

Year 8

Year 8 pupils have 7 lessons a fortnight and are taught in ability groups. Pupils will begin to build on the mathematical skills from Year 7 and extend their understanding of number, algebra, geometry and statistics whilst developing fluency in number and algebra. They will become more familiar with reasoning through problem solving activities in lessons and mathematical enrichment lessons. These lessons take place once per term and focus on allowing pupils to explore areas of mathematics and be able to communicate and explain ideas in written work and investigations. Pupils interested in solving extra problems outside of lessons are invited to Parallel Maths to extend their learning in an engaging way. Pupils with a strong track record in the department will also be invited to participate in the Junior Maths challenge.

Year 9

Year 9 pupils have 7 lessons a fortnight and are taught in ability groups. Pupils will continue to extend their understanding of number, algebra, geometry and statistics and continue developing fluency but there will be a much stronger emphasis on mathematical reasoning through problem solving activities throughout their lessons and mathematical enrichment lessons. These lessons take place once per term and focus on allowing pupils to explore areas of mathematics and be able to communicate and explain ideas in written work and investigations. Pupils interested in solving extra problems outside of lessons are invited to Parallel Maths to extend their learning in an engaging way. Pupils with a strong track record in the department will also be invited to participate in the Intermediate Maths challenge.

The skills learned during Key Stage 3 allow pupils to use and apply the standard techniques of mathematics, to reason, interpret and communicate mathematically and to solve problems within mathematics and other contexts. Students are provided with a solid foundation to enable them to be successful in Mathematics later.

Assessment

Assessment in Mathematics consists of written examinations with both a non calculator and calculator element  There is one formal assessments per term which will be followed by a whole class feedback lesson.  Pupils are set home learning weekly via our online platform and teachers will feedback using this method, as well as providing verbal feedback in the class room during lessons.

• Alex’s Adventures in Numberland by Alex Bellos
• Cabinet of Mathematical Curiosities by Ian Stewart
• The Num8er My5teries by Marcus du Sautoy
• How Many Socks Make a Pair?: Surprisingly Interesting Maths by Rob Eastway
• The Curious Incident of the Dog in the Night-time by Mark Haddon
• The Penguin Dictionary of Curious & Interesting Numbers by David Wells
• The Calculus Wars by Jason Socrates Bardi
• The Code Book by Simon Singh
• The Simpsons and Their Mathematical Secrets by Simon Singh
• Humble Pi: A Comedy of Maths Errors by Matt Parker
• 50 Mathematical Ideas You Really Need to Know by Tony Crilly
• The Indisputable Existence of Santa Claus by Dr Hannah Fry

## Key Stage 4 Mathematics

Curriculum Overview

Students at Key Stage 4 have 7 hours per fortnight studying the Edexcel GCSE Mathematics qualification. Those who perform well in year 10 have the opportunity to study the AQA Level 2 Certificate in Further Mathematics as an additional qualification.

 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Year 9 Number Applications Percentages and Ratio Expressions, Identities & Equations Geometry and Transformations Constructions and Loci Compound Measures Data Probability Area and Volume Pythagoras Trigonometry Year 10 Sequences Further Data Presentation Linear Graphs and Inequalities Quadratic Equations Simultaneous Equations Measures Congruency Further Graphs Vectors Sketching curves Proportion Circle Theorems Further Trigonometry Year 11 Algebraic Fractions Proof Functions Graph Transformations FM Number & Algebra I FM Algebra II FM Algebra III FM Matrices FM Co-Ordinate Geometry FM Geometry I FM Geometry II FM Algebra IV FM Calculus Revision

Year 10

Year 10 pupils have 7 lessons a fortnight and are taught in ability groups. Pupils will have a solid foundation from Key Stage 3 and will now extend their understanding of number, algebra, geometry and statistics and continue developing fluency but there will be a strong emphasis on mathematical reasoning through problem solving activities throughout their lessons and mathematical enrichment lessons. Pupils will begin developing links between topics. These lessons take place once per term and focus on allowing pupils to explore areas of mathematics and be able to communicate and explain ideas in written work and investigations. Pupils with a strong track record in the department will also be invited to participate in the Intermediate Maths challenge.

Year 11

Year 11 pupils have 8 lessons a fortnight and are taught in ability groups. Pupils will have developed fluency in key skills and will now be focussing much more on the application to problem solving and using mathematical knowledge from a range of topics to solve more complex problems. Year 11 will focus on finishing the content of the GCSE and revision of the course. Pupils in set 1 will also study the AQA Level 2 Certificate in Further Mathematics. Pupils with a strong track record in the department will also be invited to participate in the Intermediate Maths challenge.

Throughout Key Stage 4 pupils are provided with a solid foundation for further academic and vocational study. All units of work taught provide the opportunity for pupils to hone and enhance mathematical skills, knowledge and understanding in order to help them progress to a full range of courses in further and higher education including Level 3 mathematics courses as well as undergraduate and Level 3 courses in other disciplines such as biology, geography and psychology, where the understanding and application of mathematics is crucial. The skills learned during these two years allow pupils to use and apply the standard techniques of mathematics, to reason, interpret and communicate mathematically and to solve problems within mathematics and other contexts.

Assessment at GCSE

• Paper 1 – Written examination paper with a range of question types.
• No calculator is allowed
• 1 hour and 30 minutes
• 80 marks available
• Paper 2 – Written examination paper with a range of question types.
• Calculators are allowed
• 1 hour and 30 minutes
• 80 marks available
• Paper 3 – Written examination paper with a range of question types.
• Calculators are allowed
• 1 hour and 30 minutes
• 80 marks available

All papers are equally weighted and contribute to 33.3% of the total mark awarded

• Alex’s Adventures in Numberland by Alex Bellos
• Cabinet of Mathematical Curiosities by Ian Stewart
• The Num8er My5teries by Marcus du Sautoy
• How Many Socks Make a Pair?: Surprisingly Interesting Maths by Rob Eastway
• The Curious Incident of the Dog in the Night-time by Mark Haddon
• The Penguin Dictionary of Curious & Interesting Numbers by David Wells
• The Calculus Wars by Jason Socrates Bardi
• The Code Book by Simon Singh
• The Simpsons and Their Mathematical Secrets by Simon Singh
• Humble Pi: A Comedy of Maths Errors by Matt Parker
• 50 Mathematical Ideas You Really Need to Know by Tony Crilly
• The Indisputable Existence of Santa Claus by Dr Hannah Fry

Film List

In addition to reading, there are some fantastic films inspired by mathematics and most are available on Amazon Prime or Netflix:

• The Man Who Knew Infinity (2015)
• Pi (1998)
• X + Y (2015)
• Good Will Hunting (1997)
• The Imitation Game (2014)
• A Beautiful Mind (2001)
• The Oxford Murders (2008)

## Key Stage 5 Mathematics

Curriculum Overview

Students at Key Stage 5 follow either the Mathematics: Applications and Interpretations or the Mathematics: Analysis course as part of the IB Diploma.

Applications and Interpretation Standard Level

 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Year 12 Exponentials and Logarithms Functions Geometry Trigonometry Sequences and Series Statistics Probability Probability Distributions Differentiation Further Statistics Internal Assessment work Year 13 Differentiation Modelling Real Life Phenomena Integration Revision

Analysis Standard Level

 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Year 12 Algebra and Functions Trigonometry Exponentials and Logarithms Geometry Sequences and Series Differentiation Summarising Data Probability Differentiation Correlation and Regression Internal Assessment work Year 13 Discrete Probability Distributions Further Differentiation Integration Revision

Applications and Interpretation Higher Level

 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Year 12 Exponentials Functions Geometry and Trigonometry Matrix Algebra Sequences and Series Complex Numbers Differentiation Statistics Vectors Probability Modelling Real Life Phenomena Probability Distributions Graph Theory Internal Assessment work Year 13 Integration Further Statistics Revision

Analysis Higher Level

 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Year 12 Algebra and Functions Binomial Expansion Counting Principles Complex Numbers Trigonometry Vectors Probability Proofs and Limits Differentiation Internal Assessment work Year 13 Integration Probability Distributions Revision

Year 12

Sixth form students follow the IB Diploma and choose to study either the Mathematics: Applications and Interpretations or the Mathematics: Analysis and Approaches course. Both pathways offer standard level and higher level and students are encouraged to study the course that will suit their future needs.

Applications and Interpretations is based around the principles studied in mathematics and allows for a development of the understanding of key mathematical concepts with an emphasis in statistical testing and techniques and decision mathematics. Analysis and Approaches is based firmly within the discipline of pure mathematics and students are provided the opportunity to employ and refine their powers of abstraction and generalisation.

All courses require the use of a Graphical Display Calculator.

At the end of Year 12, pupils will begin their Internal Assessment and will complete this over the summer holidays.

Year 13

In Year 13 pupils will begin the year by finalising their Internal Assessment based on teacher feedback. They will then focus on completing the course and revising up until the final examinations.

Assessment at IB

Applications and Interpretation:

 Type of assessment Format of assessment Time (hours) Weighting of final grade (%) External SL HL SL HL Paper 1 Compulsory short-response questions based on the syllabus 1.5 2 40 30 Paper 2 Compulsory extended-response questions based on the syllabus 1.5 2 40 30 Paper 3 Two compulsory extended-response problem-solving questions 1 20 Internal Exploration Project based on students own research 15 15 20 20

Analysis:

 Type of assessment Format of assessment Time (hours) Weighting of final grade (%) External SL HL SL HL Paper 1 Non Calculator 1.5 2 40 30 Paper 2 Calculator 1.5 2 40 30 Paper 3 Two compulsory extended-response problem-solving questions 1 20 Internal Exploration Project based on students own research 15 15 20 20

If you have an iPad or iPhone, go to iTunesU or download the iTunesU app. Now you have access to millions of courses but check out the following powerful courses to prepare you for IB maths:

The Open University offers:

• Introducing Geometry: Angles and Shapes
• Exploring Mathematics: a Powerful Tool
• Exploring Mathematics: Maths in Nature and Art

The University of Nottingham:

• Pre-University Mathematics

Oxford University:

• The Secrets of Mathematics

University of Warwick:

• Why Beauty is Truth-A Short History of Symmetry

The University of Sheffield:

• Mathematical Skills-  Exponentials and Logarithms
• Mathematical Skills – Straight Lines and Simultaneous Equations

## British Values:

British Values in Mathematics

· Respect civil and criminal law in Mathematics: students are taught to think morally and to distinguish between right and wrong in the classroom in the Mathematics lessons with regards to behaviour. The department follow the school behaviour policy using rewards and sanctions when appropriate. The staff give a clear reason why they are being issued.

· Acceptance and engagement with fundamental British values of democracy: we actively promote the fundamental British values of democracy through enrichment lessons and Internal Assessment work at IB. Pupils are free to choose their own subject for the exploration at IB, but many students at RGS who are interested in politics and carry out advanced statistical techniques on mock elections.

· Contribute positively to life in Modern Britain, students actively contribute positively: RGS enters national competitions such as the UKMT Maths challenges. Pupils also become more aware of the financial world and the world of work by studying taxation, pay day loan companies and best buys in supermarkets.