Mathematics
In Mathematics the art of asking questions is more valuable than solving problems. It is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. Mathematics is essential to everyday life, critical to science, technology and engineering and necessary for financial literacy and most forms of employment.
A high-quality Mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of Mathematics and a sense of enjoyment and curiosity about the subject.
The Mathematics department is a forward thinking and innovative department that strives to ensure that students of all abilities are nurtured and challenged to achieve their full Mathematical potential. Our aim is to provide lessons of the highest quality where pupils are engaged, encouraged to question, and reason, mathematically and are inspired to develop a love of learning. This will provide the pupils with the resilience and confidence to cope with Mathematics in everyday life and their chosen career.
Key Stage 3
The Key Stage 3 Mathematics spiralling curriculum model is designed to build on students’ knowledge and understanding from Key Stage 2. This ensures that students have a strong numerical and algebraic fluency to build a deep fundamental understanding of each topic. Students will be able to use the mathematical language learnt to explain their ideas and independently apply new concepts to problems in unfamiliar situations, including other subjects across the curriculum. Students are given the opportunity to test their skills by entering the Junior UKMT Maths challenge.
At Key Stage 3 students are taught in mixed ability classes. In Year 7 our curriculum covers the fundamental mathematical elements with a focus on Number and Algebra to fill any gaps from Key Stage 2 ensuring all students are on an equal footing. We are committed to ensuring students have a deep conceptual understanding of the topics covered and are not simply taught 'tricks' to get to the right answer. There is a consistent approach with the methods used to teach topics accurately from the outset and an insistence on algebraic fluency. We encourage students to not be reliant on a calculator and continue to develop their mental arithmetic and fraction skills embedded at Key Stage 2.
In Year 8 our curriculum builds upon the concepts developed in Year 7. We continue to develop the number and algebra elements while introducing new concepts and topics to further strengthen and broaden the students understanding of Mathematics and its wider role in everyday life. This developmental journey is illustrated below:
Timetable
Over a fortnightly timetable students receive:
- 6 hours of guided classroom learning
- 1 hour 20 minutes of guided independent homework in Year 7
- 2 hours of guided independent homework in Year 8
Enrichment and Extra Curricular
To Read
- Why Do Buses Come in Threes?: The Hidden Mathematics of Everyday Life Rob Eastaway, Jeremy Wyndham
- How Long Is a Piece of String?: More Hidden Mathematics of Everyday Life Rob Eastaway, Jeremy Wyndham
- How Many Socks Make a Pair?: Surprisingly Interesting Everyday Maths Rob Eastaway
- Singh, S (2002) The Code Book: The Secret History of Codes and Code-breaking
- Singh, S. (2014) The Simpsons and their Mathematical Secrets
To Watch
- The History of Mathematics in 300 Stamps - Professor Robin Wilson
- What Maths Really Does - Professor Alain Goriely
- The Sound of Symmetry and the Symmetry of Sound - Marcus du Sautoy
- Hidden Figures (Rated PG) - 2016 American biographical drama film about African American female mathematicians who worked at the National Aeronautics and Space Administration (NASA) during the Space Race
To Listen
- Mr Barton Maths Blog | Podcast http://www.mrbartonmaths.com/blog/category/podcast/ Mr Barton is a Maths Teacher, TES Maths Adviser. Listen to this podcast where he shares techniques to solve maths efficiently.
- The Numberphile Podcast https://www.numberphile.com/podcast Interviews with people who love numbers and mathematics.
- Math Mutationhttp://mathmutation.blogspot.com/ a podcast for people of all ages where we discuss fun, interesting, or just plain weird corners of mathematics that you would not have heard in school
- Mathematics Simplified https://anchor.fm/anjali.sharma Maths is often dreaded as a subject by most of the students. Here is an attempt to simplify various topics in Mathematics and help reduce Maths Phobia.
- The Powers of Math https://anchor.fm/courtney-powers1998 Tired of being confused about math? The Powers of Math podcast explains basic Algebra concepts in a straightforward way and discusses practical applications of math in business and everyday life.
To Research
- Which bank offers the best interest rates for saving money?
- If you were lost with only a map and a compass, how could you find your exact position?
- What is the probability of winning the top prize in the National Lottery?
To Visit
- Bletchley Park
- Bank of England Museum
- LEGOLAND® Windsor Resort
Year 9 - Foundation Year
During the Foundation Year students will continue to develop knowledge and understanding from Key Stage 3 ensuring that they have a strong numerical and algebraic fluency.
Many topics are designed to develop a world view based in scientific rigour, develop moral values and demonstrate the rich history and cultural context in which it was first used or discovered. The whole purpose is to demonstrate the power of deductive logic and problem solving through use of rigorous, proven techniques. This should encourage pupils to question “why” more often, to interrogate motives and to avoid assumption when analysing any given problem.
Students are set at the beginning of Year 9 to allow for smaller classes for lower sets. This provides greater opportunity for one-to-one help from the teacher during lessons for students that find the subject more challenging. Teachers all follow the same scheme of work but there is flexibility in the pace and level of challenge in lessons based on the needs of each class. The variety of topics that are studied within the foundation year are summarised in the diagram below:
Timetable
Over a fortnightly timetable students receive:
- 7 hours of guided classroom learning
- 2 hours of guided independent homework
Enrichment and Extra Curricular
To Read
- Singh, S (2002)
The Code Book: The Secret History of Codes and Code-breaking - Singh, S (1997) Fermat’s last theorem
- Bellos, A. (2011) Alex’s Adventures in Numberland
To Watch
- The History of Mathematics in 300 Stamps - Professor Robin Wilson
- What Maths Really Does - Professor Alain Goriely
- The Sound of Symmetry and the Symmetry of Sound - Marcus du Sautoy
- A Beautiful Mind (Rated 12) - a 2001 American biographical drama film based on the life of the American mathematician John Nash, a Nobel Laureate in Economics and Abel Prize winner.
- Hidden Figures (Rated PG) - 2016 American biographical drama film about African American female mathematicians who worked at the National Aeronautics and Space Administration (NASA) during the Space Race
To Listen
- Mr Barton Maths Blog | Podcast http://www.mrbartonmaths.com/blog/category/podcast/ Mr Barton is a Maths Teacher, TES Maths Adviser. Listen to this podcast where he shares techniques to solve maths efficiently.
- The Numberphile Podcast https://www.numberphile.com/podcast Interviews with people who love numbers and mathematics.
- Math Mutation http://mathmutation.blogspot.com/ a podcast for people of all ages where we discuss fun, interesting, or just plain weird corners of mathematics that you would not have heard in school
- Mathematical Objects https://aperiodical.com/podcasts/mathematical-objects/ Katie Steckles and Peter Rowlett chat about some aspect of mathematics using a mathematical object as inspiration.
- The Art of Mathematics https://anchor.fm/the-art-of-mathematics Conversations, puzzles, book reviews, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.
To Research
- How are bounds of accuracy used in manufacturing?
- How do quadratic formulae make games such as Angry Birds possible?
- Mathematical investigations –Follow this link to discover a number of investigations to put your Maths skills to the test.
To Visit
- Bletchley Park
- Bank of England Museum
- British Museum
- LEGOLAND® Windsor Resort
Key Stage 4
The Key Stage 4 Mathematics spiralling curriculum model is designed to continue to build on the knowledge and understanding students obtained during Key Stage 3 and the Foundation Year. The intention is to ensure students have strong numerical, problem solving and algebraic fluency to build a deep fundamental understanding of each topic. An emphasis continues to be placed on the power of deductive logic and problem solving through use of rigorous, proven techniques. The Students will be able to use mathematical language to explain their ideas and independently apply new concepts to problems in unfamiliar situations, including other subjects across the curriculum. Students in sets 1 and 2 are provided with the opportunity to undertake the Level 2 certificate in Further Mathematics, alongside their regular Mathematics lessons. This allows them to further develop their base skills, but to also develop advanced skills in areas such as co-ordinate geometry and calculus that will help to prepare them to study Mathematics at A Level. Students can choose to undertake the Intermediate UKMT maths challenge, where they will require all of their logical problem-solving skills to succeed. Students in Year 10 and 11 have the opportunity to be involved a number of enrichment opportunities including STEM trips, the Mathematics club and Peer mentoring of younger students. The image below illustrates this stage of the students' journey.
Exam board/Qualification: Edexcel GCSE
- 3 papers x 90 minutes at the end of Year 11
- 1 Non-calculator and 2 calculator papers
Timetable
Over a fortnightly timetable student receive:
- 7 hours of guided classroom learning
- 2 hours 40 minutes of guided independent homework
Enrichment and Extra Curricular
To Read
- Singh, S (1997) Fermat’s last theorem
- Bellos, A. (2011) Alex’s Adventures in Numberland
- Barrow, J D (2000) The Book of Nothing
- Bellos, A. (2015) Alex through the Looking Glass
- Stewart, I. (2010) Professor Stewart’s Hoard of Mathematical Treasures
To Watch
- What Maths Really Does - Professor Alain Goriely
- Forbidden Crystal Symmetry - Sir Roger Penrose
- Big Data's Big Deal - Professor Viktor Mayer-Schonberger
- Love and Math - Professor Edward Frenkel
- Closing the Gap: the quest to understand prime numbers - Vicky Neale
To Listen
- Mr Barton Maths Blog | Podcast http://www.mrbartonmaths.com/blog/category/podcast/ Mr Barton is a Maths Teacher, TES Maths Adviser. Listen to this podcast where he shares techniques to solve maths efficiently.
- The Numberphile Podcast https://www.numberphile.com/podcast Interviews with people who love numbers and mathematics.
- Math Mutation http://mathmutation.blogspot.com/ a podcast for people of all ages where we discuss fun, interesting, or just plain weird corners of mathematics that you would not have heard in school
- Mathematical Objects https://aperiodical.com/podcasts/mathematical-objects/ Katie Steckles and Peter Rowlett chat about some aspect of mathematics using a mathematical object as inspiration.
- The Art of Mathematics https://anchor.fm/the-art-of-mathematics Conversations, puzzles, book reviews, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.
- Tetrahedra https://anchor.fm/Tetrahedra A math and science podcast providing a brief yet comprehensive presentation into a wide variety of STEM topics and DIY project ideas and challenges.
- Relatively Prime Stories from the Mathematical Domain https://relprime.com/ A mathematics podcast from ACMEScience featuring the best math stories from the world of maths.
To Research
- How can quadratic inequalities assist engineers when designing new equipment?
- How can you model the flight of a ball and predict where it will land?
- Mathematical investigations – Follow this link to discover a number of investigations to put your Maths skills to the test.
To Visit
- Bletchley Park
- Bank of England Museum
- British Museum
- LEGOLAND® Windsor Resort
Key Stage 5
Students who undertake the challenge of A Level Mathematics will have a love of the subject; they are individuals that enjoy learning and will seek help from their teachers both inside and outside of lessons. Students studying A Level Mathematics have the ambition to take Mathematics deeper and further in their careers, at university or further education and are motivated to impart knowledge on future generations.
To ensure that students are prepared for the increased challenge presented by the move from GCSE to A Level, we have a transition program in place which students complete over the summer. This allows for all students to improve their algebraic skills before they join us which is essential to their success on this course.
Students will be able to develop their use of mathematical language to explain their ideas and independently apply new concepts to problems in unfamiliar situations, including other subjects across the curriculum. Many topics are designed to develop a world view based in scientific rigour, develop moral values and demonstrate the rich history and cultural context in which it was first used or discovered. The whole purpose is to demonstrate the power of deductive logic and problem solving through use of rigorous, proven techniques. This should encourage pupils to question “why” more often, to interrogate motives and to avoid assumption when analysing any given problem. Students are encouraged to lead mathematical discussions explaining key principles they have discovered and to use mathematical language while developing their ability to verbalize Mathematics.
Exam board/Qualification: Edexcel A Level
- 3 x 120 minutes papers at the end of Year 13
- 100% exam
Topics Covered
Year 12
- Proof
- Algebra and functions
- Coordinate geometry in the (x, y) plane
- Sequences and series
- Trigonometry
- Exponentials and logarithms
- Differentiation
- Integration
- Vectors
- Statistical sampling
- Data presentation and interpretation
- Probability
- Statistical distributions
- Statistical hypothesis testing
- Quantities and units in mechanics
- Kinematics
- Forces and Newton’s laws
Year 13
- Proof
- Functions and modelling
- Series and sequences
- The Binomial theorem
- Trigonometry
- Parametric equations
- Differentiation
- Numerical methods
- Integration
- Vectors (3D)
- Regression and correlation
- Probability
- The normal distribution
- Application of kinematics
- Moments
- Forces at any angle
- Applications of forces
- Further kinematics
Timetable
Over a fortnightly timetable students receive:
- 10 hours of guided classroom learning
- 10 hours of guided independent homework
Enrichment and Extra Curricular
To Read
- How to Think like a Mathematician Kevin Houston (CUP, 2009)
- Mathematics: a very short introduction, Timothy Gowers (CUP, 2002)
- The Penguin Dictionary of Curious and Interesting Numbers D. Wells (Penguin,1997)
- The MαTHβOOK Clifford A Pickover (Sterling, 2009)
- A Concise Introduction to Pure Mathematics Martin Liebeck (Chapman& Hall/CRCMathematics)
- What is Mathematics? R. Courant & H. Robbins (OUP, 1996)
- The Pleasures of Counting T.W. K ̈orner (CUP, 1996)
- A First Course in Mechanics Mary Lunn (OUP, 1991)
- Probability and Statistics M.R. Spiegel (Schaum’s outline series; McGraw-Hill, 1982)
- Beyond Numeracy J. A. Paulos (Penguin, 1991)
- The Mathematical Experience P.J. Davis & R. Hersh (Penguin, 1990)
- Yet Another Introduction to Analysis V. Bryant (CUP, 1990)
To What/To Listen
Gresham College’s Free public lectures:
https://www.gresham.ac.uk/watch/?subject=mathematics&subcat=everyday-mathematics
https://www.gresham.ac.uk/watch/?subject=mathematics&subcat=history-of-mathematics
The Universe Speaks in Numbers - Graham Farmelo
The Gömböc, the Turtle and the Evolution of Shape - Professor Gábor Domokos
Birth of an Idea: A Mathematical Adventure - Professor Cédric Villani
The History of Mathematics in 300 Stamps - Professor Robin Wilson
What Maths Really Does - Professor Alain Goriely
Forbidden Crystal Symmetry - Sir Roger Penrose
Big Data's Big Deal - Professor Viktor Mayer-Schonberger
Love and Math - Professor Edward Frenkel
Andrew Wiles London Public Lecture
The Seduction of Curves: The Lines of Beauty that Connect Mathematics, Art and the Nude - Allan McRobie
Maths v Disease - Julia Gog
Closing the Gap: the quest to understand prime numbers - Vicky Neale
The Law of the Few - Sanjeev Goyal
The Sound of Symmetry and the Symmetry of Sound - Marcus du Sautoy
Numberphille YouTube channel - Collection of fascinating videos about numbers.: https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A
Plus magazine – Internet magazine a wealth of articles about the beauty and application of maths, puzzles, podcasts, videos and book reviews: https://plus.maths.org/content/
To Research
Statistics Topics
- Premier League Finances
- The Mathematics of Bluffing
- Does Sacking a Manager Affect Results
- Maths in Court
- Digit Ratios and Maths Ability
- The Birthday Problem
Games and Codes
- Tic Tac Toe
- Game Theory and Evolution
- Knight’s Tour
- Maths and Music
- Benford’s Law to catch fraudsters
- The Game of Life
- RSA code and the internet,
- NASA and codes to the stars
To Visit
- Bletchley Park
- Bank of England Museum
- The Royal Observatory
- LEGOLAND® Windsor Resort
- The Winton Gallery
Further Mathematics
Students who take on the challenge of A Level Further Mathematics need to have a passion and proclivity for mathematics. Further Mathematics both broadens and deepens the Mathematics covered in A Level Mathematics. It is to be taken alongside A Level Mathematics and cannot be taken on its own. Students need to have experience of working with mathematical information, as well as the ability to; think logically and independently, consider accuracy, model situations mathematically, analyse results and reflect on findings.
Students will be able to develop fluency in the key Mathematics topics for science and engineering, organising and presenting a structured and logical argument, confidence in mastering challenging ideas and overcoming difficulties, thinking in an abstract and symbolic way. The curriculum involves completing Core Pure 1 and Core Pure 2 which look at very important topic such as complex numbers, hyperbolics, differential equations and methods of calculus. The optional modules we offer are Decision 1 and Further Mechanics 1 which focus on topics such as: algorithms, graphs and networks, linear programming, elastic collisions in one and two dimensions, momentum and impulse, work, energy and power. These topics link very closely with Physics and Computer Science A Level.
Exam board/Qualification: Edexcel A Level Further Mathematics
- 4 papers x 90 minutes at the end of Year 13.
- 100 % exam
Topics Covered
- Algorithms
- Graphs and Networks
- Algorithms on Graphs
- Route Inspection
- The Travelling Salesman Problem
- Linear Programming
- The Simplex Algorithm
- Critical Path Analysis
- Proof
- Complex numbers
- Matrices
- Further algebra and functions
- Further calculus
- Further Vectors
- Polar coordinates
- Hyperbolic functions
- Differential equations
- Further Calculus
- Further differential equations
- Coordinate systems
- Further vectors
- Further numerical methods
- Momentum and Impulse
- Work, Energy and Power
- Elastic, Springs and Strings
- Elastic Collisions in one dimension
- Elastic Collisions in two dimensions
Timetable
Over a fortnightly timetable students receive:
- 10 hours of guided classroom learning
- 10 hours of guided independent homework
Enrichment and Extra Curricular
To Read
- Solving Mathematical Problems Terence Tao (OUP, 2006)
- Calculus for the Ambitious T.W. K ̈orner (CUP, 2014)
- From Here to Infinity Ian Stewart (OUP, 1996)
- Archimedes’ Revenge P. Hoffman (Penguin, 1991)
- New Applications of Mathematics C. Bondi (ed.) (Penguin, 1991)
- Reaching for Infinity S. Gibilisco (Tab/McGraw-Hill, 1990)
- The New Scientist Guide to Chaos N. Hall (ed.) (Penguin, 1991)
- Chaos J. Gleick (Minerva/Random House, 1997)
- Fractals. Images of Chaos H. Lauwerier (Penguin, 1991)
- Advanced Problems in Mathematics S.T.C. Siklos (1996 and 2003)
- Mathematical Methods for Science Students G. Stephenson (Longman, 1973)
- Mathematical Methods for Physics and Engineering K F Riley, M P Hobson &S J Bence (Cambridge University Press 1998)
- Groups: A Path to Geometry R.P. Burn (CUP, 1987)
- Algorithmics — The Spirit of Computing D. Harel (Addison-Wesley, 1992)
To Watch/To Listen
- Gresham College’s free public lectures:
- The Creativity Code: How AI is learning to write, paint and think - Marcus du Sautoy
- I is a Strange Loop - Marcus du Sautoy and Victoria Gould
- From one extreme to another: the statistics of extreme events - Jon Keating
- Spacetime Singularities - Roger Penrose, Dennis Lehmkuhl & Melvyn Bragg
- Ideas for a Complex World - Anna Seigal
- How Learning Ten Equations Can Improve Your Life - David Sumpter
- Smartphones v COVID-19 - Renaud Lambiotte
- How do Mathematicians Model Infectious Disease Outbreaks - Robin Thompson
- The Butterfly Effect - What Does It Really Signify - Tim Palmer
- Andrew Wiles London Public Lecture
- The Seduction of Curves: The Lines of Beauty that Connect Mathematics, Art and the Nude - Allan McRobie
- Maths v Disease - Julia Gog
- Closing the Gap: the quest to understand prime numbers - Vicky Neale
- The Law of the Few - Sanjeev Goyal
- The Sound of Symmetry and the Symmetry of Sound - Marcus du Sautoy
- MacTutor History of Mathematics Archive - Extensive and searchable archive of the history of maths: https://mathshistory.st-andrews.ac.uk/
To Research
Pure Maths and Calculus Geometry Topics
- Fermat’s Theorem on Squares,
- Euler and e,
- Divisibility Tests,
- Chinese Remainder Theorem,
- Proof and Paradox,
- War Maths,
- The Goldbach Conjecture,
- The Riemann Hypothesis,
- Twin Primes,
- Time Travel
- Circular inversion,
- Graphically Understanding Complex Roots,
- Visualising Algebra,
- The Riemann Sphere,
- Imagining the 4th Dimension
To Visit
- National Museum of Mathematics
- The Tech Interactive
- Stonehenge
- La Sagrada Familia
- Silverstone
Careers
We have a wealth of information on our Careers page - Please click here to visit.
