The Ridgeway, St Albans, Herts, AL4 9NX |
Mathematics
At Sandringham School, we aim to provide a Mathematics curriculum which ensures that students appreciate Mathematics as a dynamic and vibrant subject in its own right, whilst building the capacity to solve practical problems in the real world.
Our aim is that students will develop a love and appreciation of Mathematics by :
- Becoming fluent in mathematics, through varied and frequent practice, so that they are able to apply and recall knowledge rapidly.
- Being able to reason mathematically by developing an argument, justification or proof using mathematical language.
- Applying their knowledge to a variety of routine or non-routine problems with increasing sophistication.
We recognise that Mathematics is of a cumulative nature, and the repeated revisiting of topics leads to progressively deeper understanding of the underlying principles. This enables students to apply these principles across a range of subjects and contexts.
This process of regular and repeated practice of challenging topics requires perseverance and resilience.
In turn this enables students to develop their logical thinking and, through the use of systematic methods, communicate and solve a variety of problems, thus providing them with a foundation for understanding the world.
Key Stage 3
In Key Stage 3, students will continue to develop their numerical processing skills, using written and mental methods. We aim to progress students’ geometrical reasoning skills and their ability to break down complex problems into simpler parts and explain their methods in arriving at a solution. Students will also be introduced to more complex algebraic skills to prepare them for the GCSE content.
All students follow a scheme of work based upon the National Curriculum, but are set according to ability, so they are studying at a level that suits them. Set changes can occur at any time, but will usually take place following assessments. Students follow their personalised learning journeys based on prior attainment from KS2 and mapped to expected outcomes at GCSE.
At Key Stage 3 students will have 3 lessons a week.
In Year 9 we have two extension Mathematics groups, who begin the GCSE course at the start of Year 9 and in Year 10 they take the Level 3 Award in Algebra. They will then finish the GCSE course in Year 11.
Assessment
The students will be formally assessed at the end of each unit of work, which is approximately once every half term, with small, class assessments throughout the year.
One test each year is an open book assessment where students will be able to create a one page sheet for homework which they will be able to refer to during the assessment. This encourages students to adopt good revision skills.
Home Learning
Home learning is set once a week and could be a pre-lesson learning task or consolidation of content taught during the week. This may be written Home Learning or one set from an online resource website.
Key Stage 4
All students study GCSE Mathematics. We follow the Edexcel Specification, which is a linear course. The content of the specification is covered over a two-year period, and then assessed with three examinations in May and June of Year 11.
The GCSE Mathematics course is divided into two tiers – Higher and Foundation. We consider the tier of entry for individual students throughout the two-year course, with a final decision usually being made following year 11 Trial Examinations. Students can be awarded a Grade 1 through to a Grade 5 on Foundation, and a Grade 4 through to a Grade 9 on Higher tier.
We aim to enable students to:
- develop fluent knowledge, skills and understanding of mathematical methods and concepts.
- acquire, select and apply mathematical techniques to solve problems.
- reason mathematically, make deductions and inferences, and draw conclusions.
- comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.
The content of the course can be split into six main topics: Number, Algebra, Ratio, Proportion and Rates of Change, Geometry and Measures, Probability and Statistics.
Students take three examination papers, each equally weighted. The first paper is non calculator, whilst a calculator is required for the second and third papers. Each paper is out of 80 marks, and lasts 90 minutes.
Year 9 Set 1 classes
Year 9 set 1 classes begin the GCSE course in year 9, then study key algebra topics in depth during year 10. These students sit the Edexcel Level 3 Award in Algebra, in the summer of year 10. This is a single 2 hour exam, and results in either a pass or an unclassified grade. Students then complete the GCSE course in year 11, and sit their GCSE exams in summer of year 11.
Level 3
Paper code: AAL30, Externally assessed
Availability: January and June series
First assessment: June 2013
100% of Award
Overview of content
- Algebraic manipulation and solution of equations
- Inequalities and number sequences
- Linear and curved graphs, distance and time graphs, speed and time graphs
Overview of assessment
- The award is assessed through a 2 hour examination set and marked by Edexcel.
- The total number of marks for the paper is 90.
- The qualification is awarded as pass or unclassified.
- Calculators are not allowed
The Edexcel Level 3 Awards in Algebra require students to demonstrate application and understanding of the following:
- Roles of symbols
- Algebraic manipulation
- Formulae
- Simultaneous equations
- Quadratic equations
- Roots of a quadratic equation
- Inequalities
- Arithmetic series
- Coordinate geometry
- Graphs of functions
- Graphs of simple loci
- Distance-time and speed-time graphs
- Direct and inverse proportion
- Transformations of functions
- Area under a curve
- Surds
Key Stage 5
At Key Stage 5 we aim to foster students’ love of mathematics. This is done by ensuring that the students understand mathematical processes in a way that promotes confidence, encourages curiosity and provides a strong foundation for further study. By extending their range of mathematical skills and techniques, we hope to enable the students to apply the techniques they have learnt to other areas of study and understand the relevance of mathematics in the world of work.
We currently follow the Edexcel specification. It is a linear course with all students studying Pure Mathematics, Mechanics and Statistics. Students are introduced to logarithms, calculus and more complex trigonometry in addition to further developing their algebraic and geometric skills. Many of these new techniques are then used to solve problems in both mechanics and statistics.
In addition to mathematics, students can also study further mathematics. It covers areas that are not covered in the single qualification, such as complex numbers and matrices as well taking a deeper and broader look at calculus amongst other topics. Half of the further mathematics course is pure mathematics and currently we offer further mechanics and decision mathematics modules to complement them. This gives students the opportunity to study something that to many of them is completely new. Further mathematics is taken as a 4 A level so for this course only we offer students the chance to take an AS level at the end of year 12.
Further Mathematics is very useful if you want to study mathematics at university although it is not a requirement at most institutions. We have had many students who have gone onto study mathematics, the sciences, engineering, computer science or Economics at degree level.
Assessment
We set all prospective students some work to do over the summer break between the end of year 11 and the start of year 12. The idea of this is to bridge the gap between the two qualifications and to get students to start thinking mathematically again. We assess this by means of a baseline test in the first week back in September.
Further tests covering both the pure and applied elements of the course in each half term period. Students are informed of assessments, including the topics to be covered, in good time to aid their preparation and revision.
This is followed by half termly tests including the year 12-threshold exams in June of each year.
Mathematical studies
For Year 12 students, Mathematical Studies is another course that we offer. Mathematical Studies (Level 3) is a relatively new qualification that runs for 1 year. In terms of UCAS points, it is equivalent to an AS course. Any student who has gained a grade 5 or higher in GCSE Mathematics is welcome to join. The course helps to develop students’ mathematical skills and thinking and supports courses such as A-level Psychology, Sciences and Geography as well as technical and vocational qualifications.
Useful Links
In addition to Mathswatch outlined above there are many more websites which will help support independent study in Mathematics.
www.bbc.co.uk/education/mathsfile
Suggested Reading
Earlier Years – KS3
Penrose the Mathematical Cat
The Number Devil – Hans Magnus Enzenberger
The Murderous Maths series (by the creators of Horrible Histories)
YouTube – The Numberphile
To Further Develop Interest
The Simpsons and their Mathematical Secrets – Simon Singh
Euclid in the Rainforest by Joseph Mazur
Beating the Odds and How long is a piece of string by Rob Eastaway & John Haigh
Alex in Numberland by Alex Bellos
Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott (Also an animated movie released in 2007)
17 Equations that Changed the World by Ian Stewart
Hidden Figures by Margot Less Shetterly – read the book AND watch the film
From 0 to Infinity in 26 Centures – The Extraordinary Story of Maths – by Chris Waring
The Number Mysteries – Marcus Du Sautoy
The Calculus Wars – Jason Bardi
Short Film – The Love of Calculus based on Goldbach’s Conjecture available on YouTube.
The Poincare Conjecture – Donal O’Shea
Longitude – Dara Sobel
In addition, for those interested in taking their mathematical studies further (or just furthering their interest), we include (with some duplication as to be expected):
Recommended By Cambridge University
Makers of Mathematics by S. Hollingdale (Penguin, 1989)
There are not many books on the history of mathematics which are pitched at a suitable level. Hollingdale gives a biographical approach which is both readable and mathematical. You might also try E.T. Bell Men of Mathematics (Touchstone Books, Simon and Schuster, 1986). Historians of mathematics have a lot to say about this (very little of it complimentary) but it is full of good stories which have inspired generations of mathematicians.
A Russian Childhood by S. Kovalevskaya (trans. B. Stillman) (Springer, 1978, now out of print)
Sonya Kovalevskaya was the first woman in modern times to hold a lectureship at a European university: in 1889, in spite of the fact that she was a woman (with an unconventional private life), a foreigner, a socialist (or worse) and a practitioner of the new Weierstrassian theory of analysis, she was appointed a professor at the University of Stockholm. Her memories of childhood are non-mathematical but fascinating.
She discovered in her nursery the theory of infinitesimals: times being hard, the walls had been papered with pages of mathematical notes.
Alan Turing, the Enigma by A. Hodges (Vintage, 1992)
A great biography of Alan Turing, a pioneer of modern computing. The title has a double meaning: the man was an enigma, committing suicide in 1954 by eating a poisoned apple, and the German code that he was instrumental in cracking was generated by the Enigma machine. The book is largely nonmathematical, but there are no holds barred when it comes to describing his major achievement, now called a Turing machine, with which he demonstrated that a famous conjecture by Hilbert is false.
The Man Who Knew Infinity by R. Kanigel (Abacus, 1992)
READ THE BOOK AND THEN WATCH THE FILM
The life of Ramanujan, the self-taught mathematical prodigy from a village near Madras. He sent Hardy samples of his work from India, which included rediscoveries of theorems already well known in the West and other results which completely baffled Hardy. Some of his estimates for the number of ways a large integer can be expressed as the sum of integers are extraordinarily accurate, but seem to have been plucked out of thin air.
A Mathematician’s Apology by G.H. Hardy (CUP, 1992)
Hardy was one of the best mathematicians of the first part of this century. Always an achiever (his New Year resolutions one year included proving the Riemann hypothesis, making 211 not out in the fourth test at the Oval, finding an argument for the non-existence of God which would convince the general public, and murdering Mussolini), he led the renaissance in mathematical analysis in England. Graham Greene knew of no writing (except perhaps Henry James’s Introductory Essays) which conveys so clearly and with such an absence of fuss the excitement of the creative artist. There is an introduction by C.P.Snow.
Littlewood’s Miscellany (edited by B. Bollobas) (CUP, 1986)
This collection, first published in 1953, contains some wonderful insights into the development and lifestyle of a great mathematician as well as numerous anecdotes, mathematical (Lion and Man is excellent) and not-so-mathematical. The latest edition contains several worthwhile additions, including a splendid lecture entitled ‘The Mathematician’s Art of Work’, (as well as various items of interest mainly to those who believe that Trinity Great Court is the centre of the Universe). Thoroughly recommended.
The man who loved only numbers by Paul Hoffman (Fourth Estate, 1999)
An excellent biography of Paul Erdos, one of the most prolific mathematicians of all time. Erdos wrote over 1500 papers (about 10 times the normal number for a mathematician) and collaborated with 485 other mathematicians. He had no home; he just descended on colleagues with whom he wanted to work, bringing with him all his belongings in a suitcase. Apart from details of Erdos’s life, there is plenty of discussion of the kind of problems (mainly number theory) that he worked on.
Surely You’re Joking, Mr Feynman by R.P. Feynman (Arrow Books, 1992)
Autobiographical anecdotes from one of the greatest theoretical physicists of the last century. It became an immediate best-seller. You learn about physics, about life and (most puzzling of all) about Feynman. Very amusing and entertaining.
Simon Singh. Fermat’s Last Theorem (Fourth Estate)
You must read this story of Andrew Wiles’s proof of Fermat’s Last Theorem, including all sorts of mathematical ideas and anecdotes; there is no better introduction to the world of research mathematics.
Singh’s later The Code Book (Fourth Estate) is not so interesting mathematically, but is still a very good read.
Marcus du Sautoy. The Music of the Primes (Harper-Collins, 2003)
This is a wide-ranging historical survey of a large chunk of mathematics with the Riemann Hypothesis acting as a thread tying everything together. The Riemann Hypothesis is one of the big unsolved problems in mathematics – in fact, it is one of the Clay Institute million dollar problems – though unlike Fermat’s last theorem it is unlikely ever to be the subject of pub conversation. Du Sautoy’s book is bang up to date, and attractively written. Some of the maths is tough but the history and storytelling paint a convincing (and appealing) picture of the world of professional mathematics.
Marcus Du Sautoy Finding Moonshine: a mathematician’s journey through symmetry
(Fourth Estate, 2008)
This book has had exceptionally good reviews (even better than Du Sautoy’s Music of the Primes listed above). The title is self-explanatory. The book starts with a romp through the history and winds up with some very modern ideas. You even have the opportunity to discover a group for yourself and have it named after you.
1. McLeish Number (Bloomsbury, 1991)
The development of the theory of numbers, from Babylon to Babbage, written with humour and erudition. Hugely enjoyable.
Recommended By Oxford University:
Popular Mathematics
- Acheson, David 1089 and All That (2002), The Calculus Story (2017)
- Bellos, Alex Alex’s Adventures in Numberland (2010)
- Clegg, Brian A Brief History of Infinity (2003)
- Courant, Robbins and Stewart What is Mathematics? (1996)
- Devlin, Keith Mathematics: The New Golden Age (1998), The Millennium Problems (2004), The Unfinished Game (2008)
- Dudley, Underwood Is Mathematics Inevitable? A Miscellany (2008)
- Elwes, Richard MATHS 1001 (2010), Maths in 100 Key Breakthroughs (2013)
- Gardiner, Martin The Colossal Book of Mathematics (2001)
- Gowers, Tim Mathematics: A Very Short Introduction (2002)
- Hofstadter, Douglas Gödel, Escher, Bach: an Eternal Golden Braid (1979)
- Körner, T. W. The Pleasures of Counting (1996)
- Neale, Vicky Closing the Gap: the quest to understand prime numbers (2017)
- Odifreddi, Piergiorgio The Mathematical Century: The 30 Greatest Problems of the Last 100 Years (2004)
- Piper, Fred & Murphy, Sean Cryptography: A Very Short Introduction (2002)
- Polya, George How to Solve It (1945)
- Sewell, Michael (ed.) Mathematics Masterclasses: Stretching the Imagination (1997)
- Singh, Simon The Code Book (2000), Fermat’s Last Theorem (1998)
- Stewart, Ian Letters to a Young Mathematician (2006), 17 Equations That Changed The World (2012)
Key Stage 3 Curriculum Maps
MATHEMATICS Curriculum Map – Year 7
MATHEMATICS Curriculum Map – Year 8
MATHEMATICS Curriculum Map – Year 9
Key Stage 4 Curriculum Maps
MATHEMATICS Curriculum Map KS4 – Year 10
MATHEMATICS Curriculum Map KS4 – Year 11
Key Stage 5 Curriculum Maps
MATHEMATICAL STUDIES Curriculum Map – Year 12
MATHEMATICS Curriculum Map – Year 12
FURTHER MATHEMATICS Curriculum Map – Year 12
MATHEMATICS Curriculum Map – Year 13
FURTHER MATHEMATICS Curriculum Map – Year 13
Super Curriculum
To access the Super Curriculum for this subject please visit the Super Curriculum page HERE
How parents / carers can support learning
Organisation: Please help support your child to be organised. Class notes – it is important that they can find their books. The use of Zippy wallets is great for helping them get organised.
Formulae Tests: there are many mathematical formulae which students need to learn. Each student is provided with a list of these. Frequent tests will be given. Please help your child by testing them at home.
Assessments: In year’s 7 to 10 students have an assessment approximately every 8 weeks. (Please see information in each Key Stage guidance). Supporting your child with revision is appreciated. Encourage them to go back through their notes and practise the examples again. Further videos, explanations and practice questions can be found on a variety of websites.
The school has purchased a link to Mathswatch this is accessed via the students sandstorm account. This consists of maths tutorial clips which explain all topics.
Login: your ‘mysandstorm’ username with @sandringham added on the end
Password: mathswatch (unless a student has already chosen to change it)
