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Slides and handouts from previous years

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Increasing participation in Core Maths, AS/A level Mathematics and Further Mathematics

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Full archive of all the posts from Month of Math.

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Registration starts on March 18, 2024. The competition will take place on April 19, 2024.

Competition Sites

The competition in the UK will take place in Cambridge, Glasgow, Edinburgh and Oxfordshire.

Schedule

9:30-10:00 Arrival and Registration
10:15-10:30 Rules and instructions for competition
10:30-12:30 Competition
12:45-13:15 Announcement of Results

Involved Countries

Austria, Czechia, Estonia, Germany, Hungary, Iran, Poland, Romania, Slovakia, Switzerland, UK.

Prizes

The best teams will receive certificates and prizes according to their placement.

Organizers

All times are in timezone Europe/London unless stated otherwise.
Data protection policy
© Naboj IT Team 2024 (v2024.17)

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Registration starts on March 18, 2024. The competition will take place on April 19, 2024. Competition Sites The competition in the UK will take place in Cambridge, Glasgow, Edinburgh and Oxfordshire. Schedule 9:30-10:00 Arrival and Registration 10:15-10:30 Rules and instructions for competition 10:30-12:30 Competition 12:45-13:15 Announcement of Results Involved Countries Austria, Czechia, Estonia, Germany, Hungary, Iran, Poland, Romania, Slovakia, Switzerland, UK.

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IB Maths Resources from Intermathematics

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IB Maths Exploration Guides
Guides
Exploration Essentials Guide (63 pages)

Give yourself a comprehensive understanding of all the essential information required to get an excellent mark on your coursework.

Understand the marking criteria - and exactly what is required in each strand to get top scores, learn very common student mistakes, get guidance as to how to choose a good topic to maximise your chances of getting good grades, and get an introduction to some excellent graphical packages

Download here.

Statistics for Explorations Guide (55 pages)

There are many modelling techniques for fitting curves to data - but students often rely on technology without demonstrating clear understanding. Learn the various methods for fitting curves complete with how to lay this out in a coursework exploration to show a good knowledge of what mathematics you are using.

Download here

Modelling for Explorations Guide (50 pages)

There are many modelling techniques for fitting curves to data - but students often rely on technology without demonstrating clear understanding. Learn the various methods for fitting curves complete with how to lay this out in a coursework exploration to show a good knowledge of what mathematics you are using.

Download here

Andrew

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IB Exploration Guides - Getting a 7 on IB maths coursework (ii)

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IB Maths Exploration Guides Below you can download some comprehensive exploration guides that I've written to help students get excellent marks on their IB maths coursework. These guides are suitable for both Analysis and also Applications students. Over the past several years I've written over 200 posts with exploration ideas and marked hundreds of IAs...

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GCSE Maths Rocket | Free Revision Worksheets, Exam Papers & Video Tutorials!

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Welcome to GCSE Maths Rocket! Your hub for free revision resources, including video tutorials, worksheets, past papers, and exam-style questions.

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Up to Y13

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Do you like solving mind-bending mathematical brainteasers?

Can you and your friends untangle some fiendish puzzles?

Would you like the chance to use your mathematical skills to win some great prizes?

Then the MathsBombe is for you!

MathsBombe is aimed at students up to Year 13 (England and Wales), S6 (Scotland), Year 14 (Northern Ireland). You don't need to be a computer whizz or a mathematical genius - you just need to keep your wits about you and be good at solving puzzles!

What do I have to do and how can I take part?

The competition will start on Wednesday 27th January 2021.

Every two weeks a new pair of puzzles will be released, on Wednesday afternoons at 4pm (UK time). Each puzzle set contains two mathematical puzzles for you and your team to solve. The puzzles span the whole spectrum of mathematics: from fiendish logic puzzles in pure mathematics to applications of mathematics in real-world settings. You'll need to keep your wits about you and `think-outside-the-box': complicated techniques from A-level or computer coding probably won't help you!

The organisation of the competition in 2021 will be different from previous years. While we are still releasing puzzles, the competition is open to the public with no registration. Unfortunately there won't be a forum this year.

Although you can't register a team for the competition this year, you are welcome to team up with your friends and attempt the puzzles together. You will be able to check if your solution is right, and we'll let you know if you are the first person to find the solution for that puzzle!

If you would like to be notified about this and future Mathsbombe competitions, please sign up for an email reminder.

About the organisers.

MathsBombe is organised by the Department of Mathematics at The University of Manchester. It is the sister competition to the Alan Turing Cryptography Competition.

The competition is supported by the Dame Kathleen Ollerenshaw Trust.

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Do you like solving mind-bending mathematical brainteasers? Can you and your friends untangle some fiendish puzzles? Would you like the chance to use your mathematical skills to win some great prizes? Then the MathsBombe is for you! MathsBombe is aimed at students up to Year 13 (England and Wales), S6 (Scotland), Year 14 (Northern Ireland).

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ATM experts are sharing ideas through Maths Snacks videos, to support children and parents whilst children are away from school for whatever reason or for use in the classroom. The videos are a mix of tasks, puzzles, challenges and games; selected to support and enrich mathematics taught at school.

Many videos can be accessed by very young children, with a little bit of adult support, and all are relevant to pupils across the school age range. There's hardly ever a single right answer and there are many ways of working on tasks. The videos are designed to entice and to focus on working in the ways mathematicians do; such as exploring situations, looking for patterns and rules, asking questions and seeking answers, and trying out and testing ideas.

If you find these videos useful and want to support our work you can become a member, or make a donation via our Paypal link

Accessible for all

Accessible for those who have a little mathematical experience

Parents can work with their children. All family members can join in. This isn't cheating! Encourage children to have a go; ask them what they are noticing and what they have found out, ask them if there are more ways of completing the task. Why not make another similar task using different shapes or numbers? Make their maths snacking enjoyable!

Maths Snacks can supplement the work being sent home from school or, for those unable to access the work from school, these Maths Snacks provide a healthy alternative. Children will need a pencil and paper; and they might need a pair of scissors, dice, counters or buttons and a calculator.

By keeping mathematically fit, children on their return to school will be in good mental shape to reconnect and progress with their school mathematics courses. Who knows? They may continue maths snacking!

Thank you for choosing to use these materials in your organisation. These videos are Copyright 2020 by the Association of Teachers of Mathematics, and they are free to use and redistribute under the terms of the CC-BY-3.0 licence (see https://creativecommons.org/licenses/by/3.0/ for full details). In particular, you must ascribe the source of these materials; you can do this by quoting the italicised text below.

A small group of people, Geoff Faux, Pip Huyton, Peter Lacey, Mike Ollerton, Colin Taylor and Helen Williams, all of whom are members of the Association of Teachers of Mathematics, voluntarily created a collection of 2-minute videos, which the ATM have freely circulated; they were initially for use during COVID-19 Lockdown. However, because of the positive responses the ATM have received, we believe the videos might also be used as resources in mathematics classrooms. If you like these then why not join with us in the ATM community at www.atm.org.uk/Membership-Types Any feedback about how children work on these snacks would be greatly appreciated.

Thank you to the following for their contribution to Maths Snacks.

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ATM experts are sharing ideas through Maths Snacks videos, to support children and parents whilst children are away from school for whatever reason or for use in the classroom. The videos are a mix of tasks, puzzles, challenges and games; selected to support and enrich mathematics taught at school.

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Amazing bank of activities! Search function ont great. Either filter through the collections or use google to search: topic + "amplify activity".

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The 'activities' within units are often really good

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SCHOOL CURRICULUM MATERIALS
Click on the underlined links to access the detailed material for each part of the MEP course

Year R to Year 6 Course Material
The primary material includes a full Mathematics scheme of work for pupils in Reception through to year 6 (ages 5-11). For each year there are practice books, detailed lesson plans, and copy masters to be used in lessons, as well as general information about the Primary MEP project.

Adapted version of Year 1 for use in South Africa Course Material
The MEP Year 1 pupil material translated into two South African languages, Sesotho and Setswana, which is being used in schools in North West Province.

Spanish Language version of Year 1 to Year 4 Course Material
The MEP primary material translated into Spanish and has implemented successfully in a school in Chile.

These pages contain interactive mateial relating to sections of the Year 3, Year 4 and Year 5 schemes of work. The Year 3 resources are interactive versions of the Practice Book pages and of every fifth page of the 3a practice book, which are intended for reviewing the material covered in the earlier pages. The Year 4 resources are interactive versions of the Practice Book pages. The Year 5 resources are probability simulations relating to specific activities in the Y5 lesson plans. These materials are still being developed.

The key stage 3 material includes a full Mathematics scheme of work for pupils in years 7 to 9 (ages 11-14). The core materials for each year group are the pupil texts, lesson plans, teaching notes, overhead slides, diagnostic tests and revision tests.

Also included are extra exercises and activities, mental tests and practice book answers. The Y7 and Y8 materials also include more detailed lesson plans. Some general information about how MEP and the Numeracy Strategy work together including tables to generate National Curriculum levels from MEP tests are available.

These pages contain interactive tutorials for sections in the Year 7, Year 8 and Year 9 schemes of work. These are designed for pupils who have missed a lesson or done badly in a test, and need to get an introduction to (or reminder of) a particular topic. They are intended for situations where a Maths specialist is not immediately available to help the pupil. They have also been used with some success in homeschooling situations and with interactive whiteboards in schools. The material covered in a particular interactive tutorial closely matches with the corresponding text book section. These materials are still being developed.

GCSE Course Material
The MEP GCSE course consists of 19 core units and an optional 20th unit on Statistics. The pupil books are available in printed form and online. There are detailed schemes of work for four different levels of ability. There is teacher support material for each unit (only available online). There is also a GCSE Revision Pack, a Handling Data pack (including coursework guidance), and an optional additional unit on proof (all only available online).

WJEC Entry Level Certificate Course Material (formerly CoEA)
This material was developed as part of the MEP Demonstration Project to support the Welsh Exam Board's Certificate of Educational Achievement in Mathematics. This certificate is now known as the Entry Level Certificate in Mathematics (see the WJEC site for more information). The Certificate course is for candidates in Y10 and Y11 who are unlikely to achieve a grade in GCSE Mathematics. As such, it is designed so that candidates can achieve some success. The material includes two practice books and teacher support material, including teaching notes, overhead slides, mental tests and revision tests.

Step-Up to A-Level - Interactive Transition Material
This material is for students who have completed their GSCE Maths course and are about to start A-Level Maths. It is intended to help prepare students for the "step up" to A-Level Maths by ensuring they have a good grasp of the knowledge and skills they have already developed at Higher GCSE level.

A-Level Course Material
The A-Level course is still under development but will eventually consist of resources that can be used in conjunction with the syllabuses of the main examination boards. The branches of mathematics covered by the course are Pure/Core Mathematics, Mechanics, Statistics and Decision Mathematics.

NEW Core Maths Subject Support
We provide here resources for the main topic areas covered in each of the exisiting Level 3 Mathematics qualifications known collectively as Core Maths. For each unit there are text exercises with answers plus interactive exercises for use by both teachers and students. We also have a full online assessment package for self certification in Core Maths Subject Knowledge.

MEP NEWS
This section contains information about recent MEP developments

Interactive online versions of all the Year 3 Practice Book pages are now available. The Year 4 resources are now being developed and, at present, the first 80 pages have been made interactive, with more to follow. Interactive Year 3 Pages Complete and Year 4 Started (16th January 2009)

The Year 3 pages can be accessed at https://www.cimt.org.uk/projects/mepres/primary/y3int/
The Year 4 pages can be accessed at https://www.cimt.org.uk/projects/mepres/primary/y4int/

Interactive online versions of the Year 3 Practice Book pages are now available. These resources are still being developed and, at present, the first 80 pages have been made interactive, with more to follow. Interactive Year 3 Practice Book Pages (24th January 2007)

The new pages can be accessed at https://www.cimt.org.uk/projects/mepres/primary/y3int/

Since the announcement of the new two-tier Mathematics GCSE commencing in September, we have had many inquiries from teachers as to whether we would be making amendments to our GCSE schemes of work and resources. We have now studied the specifications from the main exam boards for the new two-tier course and have decided NOT to change the current GCSE schemes of work or Pupil Text materials. This is because we feel that MEP Resources and the New Two-Tier Mathematics GCSE (1st August 2006)

i) The current Standard/Academic route covers the specifications for the Foundation tier and the Express/Special route covers the specifications for the Higher tier.
ii) We envisage yet further changes to the GCSE Mathematics course and will consider amendments to our resources once these changes have been confirmed.

However, we are updating all of the Practice Books with new GCSE questions as and when we require reprints of these books. The updates will also be available online. The new GCSE questions have been taken from AQA, Edexcel and OCR 2005 past papers and specimen papers for the new two tier GCSE course. The first Practice Book to be updated is the 7-12 Express/Special.

The Centre has now made online versions of all the IPMA primary tests and several of the MEP secondary tests. Pupils can take these tests using most web browsers, and their work is immediately marked. Results are displayed at the end of the test and also submitted to our own database for research purposes. The IPMA tests 4, 5 and 6 are also now available in shorter parts to bring them into line with the original paper versions of the tests. Tests 4 and 5 have two 40 minute sections and test 6 has three 40 minute sections. Complete versions of each of these tests are also still available. MEP and IPMA tests available on-line (27 July 2006)

For more information, see https://www.cimt.org.uk/projects/meptests/testinfo.htm
To enter an access code to take a test, go to https://www.cimt.org.uk/projects/meptests/

The diagnostic tests used in Year 7, Year 8 and Year 9 have been analysed so that scores in these tests can be converted into National Curriculum levels. These tables are now available on the Work out National Curriculum levels from diagnostic tests (updated 23 February 2004)
Book 7, Book 8 and Book 9 pages. You can link directly to the nine tables using the links below:

y7-test-levels-standard.pdf |y7-test-levels-academic.pdf |y7-test-levels-express.pdf
y8-test-levels-standard.pdf |y8-test-levels-academic.pdf |y8-test-levels-express.pdf
y9-test-levels-standard.pdf |y9-test-levels-academic.pdf |y9-test-levels-express.pdf

A new GCSE unit on the subject of proof has been added to the reorganised Additional GCSE Unit on Proof (29 January 2004)
GCSE page.
You can view the unit directly by clicking here.

A number of additional resources have been added to the reorganised Additional GCSE Sections available (29 January 2004)
GCSE page.
Most of these are new sections or exercises for Units 10, 13 and 14 in the GCSE course.
These have been highlighted in yellow on the Teacher Support Material section of the GCSE page (link above).

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Centre for Innovation in Mathematics Teaching - Mathematics Enhancement Programme

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SCHOOL CURRICULUM MATERIALS Click on the underlined links to access the detailed material for each part of the MEP course Year R to Year 6 Course Material The primary material includes a full Mathematics scheme of work for pupils in Reception through to year 6 (ages 5-11).

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The latest entries posted on Interwoven Maths

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PixiMaths | Free Maths Teaching Resources | Homepage | Oakham

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Welcome to PixiMaths where you will find an assortment of resources as well as SOWs and assessments for the new 9-1 maths GCSE.

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I'm excited to announce that on 17 September, my new book was published in the UK and around the world by Bridge Street Press. How To Make The World Add Up is my effort to help you think clearly about the numbers that swirl all around us.

Tim Harford is our most likeable champion of reason and rigour... clear, clever and always highly readable."
The Times, Books of the Year

Over the past 13 years of presenting More or Less I've come to realise that this clear thinking is only rarely a matter of technical expertise. Instead, it requires an effort to overcome our biases, set aside our preconceptions, and see beyond our emotional reactions. We need to be open-minded without being gullible, maintaining a healthy scepticism without lapsing into corrosive cynicism. Above all, we need to keep being curious.

A Financial Times Book of the Year "

I loved writing the book, trying to understand the heroes and villains of statistics, from Florence Nightingale to John Maynard Keynes. There are some strange cameos from an art forger, an erotic dancer, several alchemists and a whole phalanx of storks. I hope you'll like it too.

Characteristic lucidity, concealed intellectual depths, wry humour - and a big unifying idea - from one of our finest economic and statistical communicators."
The Independent

Tim Harford... has never been more needed. With a chatty style and a stream of good yarns, he offers a solid guide to sifting truth from statistical chaff."
The Sunday Times, Books of the Year

Rather than simply rebuffing statistical trickery, Harford's book implores us to look past the bluster - and our own biases...required reading"
Wired, best science and tech books of 2020

For anyone who wants to better understand the world around us, Tim Harford's rollicking tales of statistical success and failure are tough to beat."
Canberra Times

Harford is a gifted science communicator, a wonderful and sprightly writer. He's spent many years teaching millions of people to consume statistics critically - but with this book, he's doing something nobler: he's teaching us to consume statistics WISELY."
Cory Doctorow

[One of] Ten books from 2020 you must not miss... fascinating."

An entertainment for numerate readers and a user-friendly introduction to statistics for beginners."
Kirkus Reviews

An engaging guide to avoid being bamboozled by statistics."
Indo-Asian News Service

"An economist who literally wrote the book on communicating clearly with numbers boils down advice that will help you make better business and personal decisions."

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I'm excited to announce that on 17 September, my new book was published in the UK and around the world by Bridge Street Press. How To Make The World Add Up is my effort to help you think clearly about the numbers that swirl all around us.

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Centre for Education in Maths and Computing

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Centre for Education in Maths and Computing

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Mathematics and Computing Contests | University of Waterloo - CEMC

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Each year, educators order CEMC contests for over 300 000 students worldwide, reaching students in over 85 countries. Students cannot register for contests on their own. They must be registered by their school. If their own school is not participating, students can look for another local school that will allow them to join as a participant. Below are the steps that educators can follow to help their students participate in CEMC contests:

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​All You Need for German Math Olympiad (FAQ)

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​​All You Need for German Math Olympiad Home About Us Exam Conditions Awards / Medals Curriculum Sample Questions Downloads Frequently Asked Questions Announcements Contact Clandar

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an inclusive vision of what mathematics is, who it's for,
and why anyone should learn it

in bookstores now or order from

interview with QUANTA magazine
"what is human flourishing?"

-JAMES TANTON
Global Math Project

"This is perhaps the most important mathematics book of our time.
Francis Su shows mathematics is an experience of the mind and, most important, of the heart."

about

Mathematics for human flourishing

From Yale Press:

For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas.

​

In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires-such as for play, beauty, freedom, justice, and love-and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can-and must-be open to all.

Reflection & Action

Ways you can go deeper.

Notes with live hyperlinks to the bibliographic references in each chapter.

100 questions for reflection. Gather friends, read the book, discuss. #Math4HF

People and organizations that could flourish with your assistance.

about the author

Francis Su writes about the dignity of human beings and the wonder of mathematical teaching. He is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a former president of the Mathematical Association of America. In 2013, he received the Haimo Award, a nationwide teaching prize for college math faculty, and in 2018 he won the Halmos-Ford writing award for the highly-acclaimed speech that formed the basis for his book Mathematics for Human Flourishing. His work has been featured in Quanta Magazine, Wired, and the New York Times.

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Mathematics for Human Flourishing - Book Page

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Book reviews and press about Mathematics for Human Flourishing, as well as resources for reflection and action.

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“Inspiring and informative...deserves to be widely read.”—Wall Street Journal“This fun book offers a philosophical take on number systems and revels in the beauty of math.”—Science NewsBecause we have ten fingers, grouping by ten seems natural, but twelve would be better for divisibility, and eight is well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart presents arithmetic not as rote manipulation of numbers—a practical if mundane branch of knowledge best suited for filling out tax forms—but as a fascinating, sometimes surprising intellectual craft that arises from our desire to add, divide, and multiply important things. Passionate and entertaining, Arithmetic invites us to experience the beauty of mathematics through the eyes of a beguiling teacher.“A nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education...Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting.”—Jonathon Keats, New Scientist“What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind’s most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story...A wonderful book.”—Keith Devlin, author of Finding Fibonacci

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Maryam Mirzakhani (مریم میرزاخانی‎, 1977 - 2017) was an Iranian mathematician and professor at Stanford University. She was the first woman to receive the Fields Medal, the highest award in mathematics.

Mirzakhani worked at the intersection of dynamical systems and geometry. She studied objects like hyperbolic surfaces and complex manifolds, but also contributed to many other areas of mathematics.

When solving problems, Mirzakhani would draw doodles and diagrams on large sheets of paper, to see the underlying patterns and beauty. Her daughter even described Maryam's work as "painting". At the age of 40, Mirzakhani died of breast cancer.

Born in Adelaide, Australia, Terence Tao (born 17 July) is sometimes called the "Mozart of mathematics". When he was 13, he became the youngest ever winner of the International Mathematical Olympiad, and when he was 24, he became the youngest tenured professor at the University of California, Los Angeles.

Tao has received the MacArthur Fellowship, the Breakthrough Prize in mathematics, as well as the Fields Medal, the highest award in mathematics, for "his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory".

Together with Ben Green, Tao proved the Green-Tao theorem, which states that there are arbitrarily long arithmetic sequences of prime numbers.

In 2003, the Russian mathematician Grigori Perelman (Григо́рий Перельма́нborn, born 1966) proved the Poincaré Conjecture, which, until then, was one of the most famous unsolved problems in mathematics.

The complex proof was verified by 2006, but Perelman declined two big awards that came with it: the $1 million Clay Millennium Prize, and the Fields Medal which is the highest recognition in mathematics. In fact, he said: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."

Perelman also made contributions to Riemannian geometry and geometric topology, and the Poincaré Conjecture is still the only one of the seven Millennium Prize problems to have been solved.

Yitang Zhang (张益唐, born 1955) was born in China and is now a professor of mathematics at the University of California.

Zhang discovered that there is a number k less than 70 million, so that there are infinitely many pairs of prime numbers that are exactly k apart. This was a groundbreaking discovery in number theory, for which he received the MacArthur award in 2014.

This is similar to the Twin Prime conjecture, which states that there are infinitely many pairs exactly 2 apart (for example 11 and 13) - but no one knows if this is true.

The British mathematician Sir Andrew Wiles (born 1953) is best known for proving Fermat's Last Theorem, which, until then, was one of the most famous unsolved problems in mathematics.

In 1637, Pierre de Fermat, wrote in the margin of a textbook that he had a wonderful proof that the equation a n n>2. Unfortunately, no one was able to find a proof - until Wiles, some 400 years later.+b n=c n has no integer solutions for

Wiles had been fascinated by the problem since the age of 10, and spent seven years working on it in solitude. He announced his solution in 1993, although a small gap in his argument took two more years to fix.

He was too old to receive the Fields medal, the highest award in mathematics, which has an age limit of 40. Instead, Wiles was awarded a special silver plaque for his work.

The problem asks for an algorithm to decide whether a given Diophantine equation (a polynomial equations with integer coefficients) has any integer-valued solutions.

William Paul Thurston (1946 - 2012) was an American mathematician and a pioneer in the fields of topology, manifolds and geometric group theory.

Thurston's Geometrization Conjecture is about describing the structure and geometry of different three-dimensional spaces. In 1982, he was awarded the Fields Medal for his study of 3D manifolds.

Paul Joseph Cohen (1934 - 2007) was an American mathematician who proved the continuum hypothesis, and that the axiom of choice is independent from the other Zermelo-Fraenkel axioms of set theory. He received the Fields medal for his work.

Alan Turing (1912 - 1954) was an English mathematician and is often called the "father of computer science".

During the Second World War, Turing played a critical role in breaking the Enigma code used by the German military, as part of the "Government Code and Cypher School" at Bletchley Park. This helped the Allies win the war, and may have saved millions of lives.

He also invented the Turing machine, a mathematical model of a general purpose computer, and the Turing test, which can be used to judge the ability of artificial intelligence.

Turing was gay, which was still a crime during his life, and meant that his groundbreaking accomplishments were never fully recognised. He committed suicide at the age of 41.

André Weil (1906 - 1998) was one of the most influential French mathematicians in the 20th century.

He was one of the founders of the Bourbaki group, a group of mathematicians working under the collective pseudonym Nicolas Bourbaki. The goal of the Bourbaki group was to unify all of mathematics with a formal, axiomatic foundation.

Weil believed that many problems in algebra and number theory had analogous versions in algebraic geometry and topology. These are known as Weil conjectures, and became the basis for both disciplines. They also have applications in fields like cryptography and computer science.

During the second World War, Weil fled to the United States and later joined the Institute for Advanced Study at Princeton University.

Kurt Gödel (1906 - 1978) was an Austrian mathematician who later immigrated to America, and is considered one of the greatest logicians in history.

At the age of 25, just after finishing his doctorate in Vienna, he published his two incompleteness theorems. These state that any (consistent and sufficiently powerful) mathematical system contains certain statements that are true but cannot be proven. In other words, mathematics contains certain problems that are impossible to solve.

This result had a profound impact on the development and philosophy of mathematics. Gödel also found an example of these "impossible theorems": the continuum hypothesis.

Mary Lucy Cartwright (1900 - 1998) was a British mathematician and one of the pioneers of Chaos theory. Together with Littlewood, she discovered curious solutions to a problem: an example of what we now call the Butterfly effect.

Elbert Cox (1895 - 1969) was the first African-American mathematician to receive a PhD. Universities in England and Germany refused to accept his thesis at the time, but Japan's Tohoku Imperial University did.

Cox taught at Howard University in the United States, he studied polynomial solutions to differential equations, generalised the Boole summation formula, and compared different grading systems.

Albert Einstein (1879 - 1955) was a German physicist, and one of the most influential scientists in history. He received the Nobel Prize for physics and TIME magazine called him the person of the 20th century.

Einstein triggered the most significant transformation in our view of the universe since Newton. He realised that classical, Newtonian physics was no longer enough to explain certain physical phenomenons.

At the age of 26, during his "miracle year", he published four groundbreaking scientific papers that explained the photoelectric effect and Brownian motion, introduced special relativity, and derived the formula E=m c 2, which states that energy ( E) and mass ( m) are equivalent.

G.H. Hardy (1877 - 1947) was a leading English pure mathematician. Together with John Littlewood, he made important discoveries in analysis and number theory, including the distribution of prime numbers.

In 1913, Hardy received a letter from Srinivasa Ramanujan, an unknown, self-taught clerk from India. Hardy immediately recognised his genius, and arranged for Ramanujan to travel to Cambridge where he was working. Together, they made important discoveries and authord numerous paper.

Hardy always disliked applied mathematics and expressed this in his personal account of mathematical thinking, the 1940 book A Mathematician's Apology.

Peano also developed a new, international language, Latino sine flexione, which was a simplified version of Latin.

The French mathematician Henri Poincaré (1854 - 1912) is often described as the last universalist, meaning that he worked in every field of mathematics known during his lifetime.

Poincaré is one of the founders of the field of Topology, and he came up with the Poincaré conjecture. This was one of the famous unsolved problems in mathematics, until it was proven in 2003 by Grigori Perelman

He also found a partial solution for the "three body problem", and discovered that the motion of three stars or planets in space can be completely unpredictable. This laid the foundation for modern Chaos theory.

Poincaré was the first to propose gravitational waves, and his work on Lorentz transformations was the basis upon which Albert Einstein built his theory of special relativity.

Charles Lutwidge Dodgson (1832 - 1898) is best know under his pen name Lewis Carroll, as the author of Alice's Adventures in Wonderland and its sequel Through the Looking-Glass.

However, Carroll was also a brilliant mathematician. He always tried to incorporate puzzles and logic into his children's stories, making them more enjoyable and memorable.

Richard Dedekind (1831 - 1916) was a German mathematician and one of the students of Gauss. He developed many concepts in set theory, and invented Dedekind cuts as the formal definition of real numbers. He also gave the first definitions of number fields and rings, two important constructs in abstract algebra.

While still in his teens, Galois proved that there is no general solution for polynomial equations of degree five or higher - simultaneously with Niels Abel.

Unfortunately, other mathematicians who he shared these discoveries with repeatedly misplaced or simply returned his work, and he failed his school and university exams while concentrating on much more complex work.

At the age of 20, Galois was shot in a duel (some say a feud over a woman), and later died of his wounds. During the night before his death, he summarised his mathematical discoveries in a letter to a friend. It would take other mathematicians many years to fully understand these letters, and realise the impact of his work.

Augustus De Morgan (1806 - 1871) was a British mathematician and logician. He studied the geometric properies of complex numbers, formalised mathematical induction, suggested quaternions, and came up with new mathematical notation.

The De Morgan laws explain how to transform logical relationships in set theory, for example A∩B‾A∪B‾=A‾∩B‾. =A‾∪B‾ and

William Rowan Hamilton (1805 - 1865) was an Irish mathematician and child prodigy. He invented quaternions, the first example of a "non-commutative algebra", which has important applications in mathematics, physics and computer science.

He first came up with the idea while walking along the Royal Canal in Dublin, and carved the fundamental formula into a stone bridge he passed: i 2=j 2=k 2=ijk=−1.

Hamilton also made significant contributions to physics, including optics and Newtonian mechanics.

Niels Henrik Abel (1802 - 1829) was an important Norwegian mathematician. Even though he died at the age of 26, he made groundbreaking contributions to a wide range of topics.

At the age of 16, Abel proved the binomial theorem. Three years later, he proved that it is impossible to solve quintic equations - by independently inventing group theory. This had been an open problem for over 350 years! He also worked on elliptic functions and discovered Abelian functions.

Abel spent his life in poverty: he had six siblings, his father died when he was 18, he was unable to find a job at a university, and many mathematicians initially dismissed his work. Today, one of the highest awards in mathematics, the Abel Prize is named after him.

In theory, these machines could automatically perform certain calculations stored on cards or tape. However, due to the high production costs, they were never fully completed during Babbage's lifetime. In 1991, a functional replica was constructed at the Science Museum in London.

August Ferdinand Möbius (1790 - 1868) was a German mathematician and astronomer. He studied under Carl Friedrich Gauss in Göttingen and is best known for his discovery of the Möbius strip: a non-orientable two-dimensional surface with only one side. (However, it was independently discovered by Johann Benedict Listing just a few months earlier.)

Many other concepts in mathematics are named after him, including the Möbius plane, Möbius transformations, the Möbius function μ n in number theory, and the Möbius configuration of two mutually inscribed tetrahedra.

Joseph Fourier (1768 - 1830) was a French mathematician, and a friend and advisor of Napoleon. In addition to his mathematical research, he is also credited with the discovery of the greenhouse effect.

While travelling to Egypt, Fourier became particularly fascinated with heat. He studied heat transfer and vibrations, and discovered that any periodic function can be written as an infinite sum of trigonometric functions: a Fourier series.

Adrien-Marie Legendre (1752 - 1833) was an important French mathematician. He studied elliptic integrals and their usage in physics. He also found a simple proof that π is irrational, and the first proof that π 2 is irrational.

Gaspard Monge (1746 - 1818) was a French mathematician. He is considered the father of differential geometry, having introduced the concept of lines of curvature on surfaces in three-dimensional space (e.g. on a sphere). Monge also invented orthographic projection and descriptive geometry, which allows the representation of three-dimensional objects using two-dimensional drawings.

During the French Revolution, Monge served as Minister of the Marine. He helped reform the French education system and found the École Polytechnique.

Maria Gaetana Agnesi (1718 - 1799) was an Italian mathematician, philosopher, theologian, and humanitarian. Agnesi was the first western woman to write a mathematics textbook. She was also the first woman to be appointed professor at a university.

Her textbook, the Analytical Institutions for the use of Italian youth combined differential and integral calculus, and was an international success.

Agnesi also studied a bell-shaped curve described by the equation y=a 3 x 2+a 2. This function is now called the Witch of Agnesi. The strange name might come from a pun in the Italian language, were the word "versiera" for "witch" sounds similar to the ropes used when sailing.

Émilie du Châtelet (1706 - 1749) was a French scientist and mathematician. As a women, she was often excluded from the scientific community, but she built friendships with renown scholars, and had a long affair with the philosopher Voltaire.

She applied her mathematical ability while gambling, and used her winnings to buy books and laboratory equipment, and made important advanced regarding the concepts like energy and energy conservation.

Around the age of 42, Du Châtelet became pregnant again. At the time, without adequate healthcare, this was very dangerous for women of her age. She was also working on a French translation of Newton's book Principia, which containes the basic laws of physics.

Du Châtelet was determined to finish the translation, as well as a detailed commentary with additions and clarifications, and often worked 18 hours per day. She died just a few days after giving birth to a daughter, but her completed work was published posthumously, and is still used today.

Christian Goldbach (1690 - 1764) was a Prussian mathematician and contemporary of Euler, Leibniz and Bernoulli. He was tutor of Russian Tsar Peter II, and is remembered for his "Goldbach Conjecture".

Abraham de Moivre (1667 - 1754) was a French mathematician who worked in probability and analytic geometry. He is most remembered for de Moivre's formula, which links trigonometry and complex numbers.

De Moivre discovered the formula for the normal distribution in probability, and first conjectured the central limit theorem. He also found a non-recursive formula for Fibonacci numbers, linking them to the golden ratio φ.

Pierre de Fermat (1607 - 1665) was a French mathematician and lawyer. He was an early pioneer of calculus, as well as working in number theory, probability, geometry and optics.

In 1637, he wrote a short note in the margin of one of his textbooks, claiming that the equation a n n>2, and that he had a "marvellous proof, which this margin is too narrow to contain". This became known as +b n=c n has no integer solutions for Fermat's Last Theorem, and one of the most famous unsolved problems in mathematics - until it was finally proven in 1994.

René Descartes (1596 - 1650) was a French mathematician and philosopher, and one of the key figures in the Scientific Revolution. He refused to accept the authority of previous philosophers, and one of his best-known quotes is "I think, therefore I am".

Descartes is the father of analytical geometry, which allows us to describe geometric shapes using algebra. This was one of the prerequisites, which allowed Newton and Leibnitz to invent calculus a few decades later.

He is credited with the first use of superscripts for powers or exponents, and the cartesian coordinate system is named after him.

Marin Mersenne (1588 - 1648) was a French mathematician and priest. Because of the frequent exchanges with his contacts in the scientific world during the 17th century, he has been called the "the post-box of Europe".

Today we mostly remember him for the Mersenne primes, prime numbers that can be written as 2 n−1. Most of the largest known primes are of this type. He also studied acoustics and the harmonics of a vibrating string, and wrote about theology and philosophy.

Galileo Galilei (1564 - 1642) was an Italian astronomer, physicist and engineer. He used one of the first telescopes to make observations of the night sky, where he discovered the four largest moons of Jupiter, the phases of Venus, sunspots, and much more.

Galileo, sometimes called the "father of modern science", also studied the motion of objects in free fall, kinematics, material science, and invented the thermoscope (an early thermometer).

He was a vocal proponent of Heliocentrism, the idea that the Sun was at the centre of our solar system. This eventually led to him being tried by the Catholic Inquisition: Galileo was forced to recant and spent the rest of his life under house arrest.

François Viète (1540 - 1603) was a French mathematician, lawyer, and advisor to Kings Henry III and IV of France. He made significant advances in Algebra, and first introduced the use of letters to represent variables.

Viète discovered the connection between the roots and coefficients of a polynomial, called Viète's formula. He also wrote books about geometry and trigonometry, including calculating π to 10 decimal places using a polygon with 393216 sides.

Pedro Nunes (1502 - 1578) was a Portuguese mathematician and astronomer. As Royal Cosmographer of Portugal he taught navigational skills to many sailors and explorers.

Nunes first noticed that if a ship always follows the same compass bearing, it won't travel on a straight line or great circle. Instead, it will follow a path called a rhumb line or loxodrome, which spirals towards the North or South pole.

Nunes also tried to calculate which day in the year has the fewest hours of sunlight, he disproved previous attempts to solve classical geometry problems like trisecting an angle, and he invented a system for measuring fractional parts of angles.

The Italian Gerolamo Cardano (1501 - 1576) was one of the most influential mathematicians and scientists of the Renaissance. He investigated hypercycloids, published Tartaglia's and Ferrari's solution for cubic and quartic equations, was the first European to systematically use negative numbers, and even acknowledged the existence of imaginary numbers (based on −1).

Cardano also made some early progress in probability theory and introduced binomial coefficients and binomial theorem to Europe. He invented many mechanical devices, including combination locks, gyroscopes with three degrees of freedom, and drive shafts (or Cardan shafts) that are still used in vehicles today.

Nicolaus Copernicus (1473 - 1543) was a Polish mathematician, astronomer and lawyer. During his life, most people believed in the Geocentric model of the universe, with Earth at the centre and everything else rotating around it.

Copernicus created a new model, where the sun is at the centre, and Earth moves around it on a circle. He also predicted that Earth rotates around its axis once every day. Afraid that it would upset the Catholic church, he only published the model just before his death - triggering what is now called the Copernican Revolution.

Copernicus also worked as a diplomat and physician, and made important contributions to economics.

Zhu Shijie (朱世杰, 1249 - 1314) was one of the greatest Chinese mathematicians. In his book Jade Mirror of the Four Unknowns, he showed how to solve 288 different problem using systems of polynomial equations and four variables (called Heaven, Earth, Man and Matter).

Zhu made extensive use of Pascal's triangle. He also invented rules for solving systems of linear equations - predating our modern matrix methods by many centuries.

Qin first developed a method for numerically solving polynomial equations, which is now known as Horner's method. He found a formula for the area of a triangle based on the length of its three sides, calculated the sum of arithmetic series, and introduced a symbol for "zero" into Chinese mathematics.

Qin also invented Tianchi basins, which were used to measure rainfall and gather meteorological data important for farming.

Leonardo Pisano, commonly known as Fibonacci (1175 - 1250) was an Italian mathematician. He is best known for the number sequence named after him: 1, 1, 2, 3, 5, 8, 13, ...

Fibonacci is also responsible for popularising the Arabic numerals (0, 1, 2, 3, 4, ...) in Europe, which was still using Roman numerals (I, V, X, D, ...) in the 12th century CE. He explained the decimal system in a book called "Liber Abaci", a practical textbook for merchants.

Jia Xian (賈憲, c. 1010 - 1070) was a Chinese mathematician during the Song dynasty. He described Pascal's triangle, more than six centuries before Pascal, and used it to calculate square and cube roots.

Hasan Ibn al-Haytham (أبو علي، الحسن بن الحسن بن الهيثم, c. 965 - 1050) lived in Cairo during the Islamic Golden Age, and studied mathematics, physics, astronomy, philosophy, and medicine. He was a proponent of the scientific method: the belief that any scientific hypothesis must be verified using experiments or mathematical logic - centuries before European scientists during the Renaissance.

Al-Haytham was particularly interested in optics and visual perception. He also derived a formula for the sum of fourth powers (1 4+2 4+3 4+...+n 4), and he studied the link between algebra and geometry.

Zu Chongzhi (祖沖之, 429 - 500 CE) was a Chinese astronomer, mathematician, writer, politician and inventor.

He calculated Pi accurately to 7 decimal places - a record which was not surpassed until 800 years later. To do this, he approximated a circle with a 24,576-sided polygon.

Zu also discovered the formula 4 3 πr 3 for the volume of a sphere. His precise astronomical observations allowed him to create a new, more accurate calendar and to predict solar eclipses. He also calculated that Jupiter takes almost 12 years to orbit the sun.

While we know today this model is incorrect, Ptolemy's scientific impact is indisputable. He developed trigonometric tables with many practical applications, which remained the most accurate for many centuries. He also created detailed maps of the Earth, and wrote about music theory and optics.

Heron of Alexandria ( Ἥρων ὁ Ἀλεξανδρεύς, c. 10 - 70 CE) was a Greek mathematician and engineer. He lived in the city of Alexandria in Egypt, and is one of the greatest "experimenter" of antiquity.

His inventions include windmills, pantograph, as well as a radial steam turbine called aeolipile or Hero's engine. Hero's formula allows you to calculate the area of any triangle, using just the length of its three sides.

Hipparchus of Nicaea (Ἵππαρχος, c. 190 - 120 BCE) was a Greek astronomer and mathematicians, and one of the greatest astronomers of antiquity.

Hipparchus made detailed observations of the night sky and created the first comprehensive star catalog in the western world. He is considered the father of trigonometry: he constructed trigonometric tables and used these to reliably predict solar eclipses. He also invented the astrolabe and solved different problems in spherical trigonometry.

Archimedes (c. 287 - 212 BCE) was an ancient Greek scientist and engineer, and one of the greatest mathematicians of all time. He discovered many concepts of calculus and worked in geometry, analysis and mechanics.

While taking a bath, Archimedes discovered a way to determine the volume of irregular objects using the amount of water they displaced when submerged. He was so excited by this discovery that he ran out on the street, still undressed, yelling "Eureka!" (Greek for "I have found it!").

As an engineer, he built ingenious defence machines during the siege of his home city Syracuse in Sicily. After two years, the Romans finally managed to enter, and Archimedes was killed. His last words were "Do not disturb my circles" - which he was studying at the time.

Euclid taught mathematics in Alexandria, but not much else is known about his life.

Aristotle (Ἀριστοτέλης, c. 384 - 322 BCE) was a philosopher in Ancient Greece. Together with his teacher Plato, he is considered the "Father of Western Philosophy". He was also the private tutor of Alexander the Great.

Aristotle wrote about science, mathematics, philosophy, poetry, music, politics, rhetoric, linguistics, and many other subjects. His work was highly influential during the Middle Ages and into the Renaissance, and his views on ethics and other philosophical questions are still being discussed today.

Aristotle is also the first known person to formally study logic, including its applications in science and mathematics.

Zeno of Elea (c. 495 - 430 BCE) was a Greek philosopher who his known for his famous paradoxes, which have fascinated mathematicians for centuries.

One example is the paradox of motion: imagine that you want to run a 100 meter race. You first have to run half the distance (50 meters). But before doing that, you have to run a quarter of the distance (25 meters). Before running a quarter, you have to run 1 8th, 1 16th, and so on. This is an infinite number of tasks, which means that you'll never arrive!

Pythagoras of Samos (c. 570 - 495 BCE) was a Greek philosopher and mathematician. He is best known for proving Pythagoras' Theorem, but made many other mathematical and scientific discoveries.

Pythagoras tried to explain music in a mathematical way, and discovered that two tones sound "nice" together (consonant) if the ratio of their frequencies is a simple fraction.

He also founded a school in Italy where he and his students worshipped mathematics almost like a religion, while following a number of bizarre rules - but the school was eventually burned down by their adversaries.

The Ishango Bone is possibly the oldest mathematical artefact still in existence: it was discovered in 1950, in the Democratic Republic of Congo in central Africa, and is named after the region where it was found. It is dates back to the Upper Paleolithic period of human history, and is approximately 20,000 years old.

The bone is 10 cm long and contains a series of notches, which many scientists believe were used for counting. The grouping of the notches might even suggest some more advanced mathematical understanding, like decimal numbers or prime numbers.

In ancient Mesopotamia, almost 10,000 years ago, scribes and merchants started using small, three-dimensional clay objects as counters, to represent certain quantities, units or goods. Thousands of these were found on archaeological sites across the Middle East, like these from Tepe Gawra in Iraq (from around 4000 BCE):

The cone, sphere and flat disc were used to represent small, medium and large measures of grain. The tetrahedron probably measured the amount of work done in one day.

These two tablets from Susa in Iran were created around 3200 BCE and used a more advanced technique: the counters were pressed into the clay while it was still soft, to create a record:

Again, the triangular and circular impressions represent smaller and larger measures of grain. The patterns across the rest of the tablet were the official seals of the scribes.

These simple markings actually laid the foundations for cuneiform, one of the first writing system in history.

This is the oldest known clay tablet with mathematican computations - it was created around 2700 BCE in Sumer, one of the earliest civilisations that flourished in the Middle East.

It shows a multiplication table in cuneiform, which may have been used by student scribes to learn mathematics.

This tablet shows a multiplication table that was created around 2600 BCE in the Sumerian city of Shuruppak. It is one of the oldest mathematical tablets we have ever discovered.

The table has three columns. The dots in the first two columns represent distances ranging from around 6 meters to 3 kilometres. The third column contains the product of the first two, which is the area of a rectangle with the given dimensions.

Sumer was a region of ancient Mesopotamia in the Middle East. They invented Cuneiform as one of the earliest writing systems, by pressing small, wedge-shaped markers into clay tablets like this one. They also developed the base-60 number system.

This Babylonian clay tablet, called Plimpton 322, was created around 1750 BCE in Sumeria, during the reign of Hammurabi the Great.

The exact purpose of the tablet has been debated by archeologists. Some think that it was a "teachers aid", designed to help generate right-angled triangles. Others think it may be a very early trigonometry table.

This circular tablet from the Yale Babylonian Collection, called YBC 7289, was created around 1800 - 1600 BCE in ancient Babylon. It shows the geometric diagram of a square with its diagonals.

The cuneiform numerals indicate that one side of the square is 30 units long, and show how to find the length of the diagonal: units.

The tablet shows that Babylonian scribes knew Pythagoras' theorem, more than 1000 years before Pythagoras was even born. They were also able to calculate square roots and had an estimate for accurate to 6 decimal places. It is the highest computational accuracy ever seen in the ancient world!

While this simple tablet may have just been a practice exercise by a novice scribe, its mathematical and historical importance is enormous.

These two clay tablets from the Yale Babylonian Collection were created between 1800 and 1600 BCE, and contain exercises by student scribes, to calculate the area of different geometric shapes.

Tablet YBC 7290 shows how to calculate the area of a trapezium, by multiplying the average of the bases and the average of the sides.

Tablet YBC 11120 shows how to calculate the area of a circle, using the approximation

The Rhind Papyrus is one of the most famous mathematical documents from ancient Egypt. It was written around 1550 BCE by a scribe called Ahmose, who is maybe the earliest contributor to maths in history, whose name we still know today.

The papyrus is around 2 meters long and contains 84 problems about multiplication, division, fractions, and geometry. It was probably used as a kind of "textbook" by other scribes.

One of the most notable sections is a table. This shows how you can write rational numbers of the form where n is an odd number, as sums of unit fractions.

The papyrus is named after Scottish antiquarian Alexander Henry Rhind, who purchased it in Luxor, Egypt. Today, most of its remains are located at the British Museum in London.

Menna was a chief scribe in ancient Egypt, and in charge of measuring the size of fields for farming, inspected crop yields, reporting to the Pharaoh's central field administration, and calculating taxes.

The wall paintings in his tomb show the different measuring and calculating techniques used more than 3,000 years ago. For example, in the first row, you can see how long distances were measured using ropes with knots at regular intervals.

The tomb was built around 1420 BCE in the Valley of the Kings.

Here you can see a set of 21 Bamboo Strip that were created around 2300 years ago in China. When arrenged correctly, they form a multiplication table in base 10, written in ancient Chinese calligraphy.

While earlier civilisations like the Babylonians created multiplications tables in base 60, this is by far the oldest known decimal multiplication table - and it looks very similar to what we still use today.

Around 300 BCE, Euclid of Alexandria wrote The Elements, collection of 13 books that contained mathematical definitions, postulates, theorems and proofs, and covering topics like geometry and number theory.

It is one of the most famous books ever written, and one of the most influential works in the history of mathematics. Copies were used as textbooks for thousands of years and studied all around the world, with thousands of new editions published

No original copies of the Elements still exist today. This small papyrus fragment dates back to around 100 AD, and may be a part of the oldest existing copy of Euclid's work.

A palimpsest is a scroll or parchment from which the text has been washed or scraped off so that it can be reused. This method was common in the Middle Ages - even for documents by brilliant scientists and mathematicians.

Archimedes of Syracuse lived in the 3rd Century BCE and was one of the greatest mathematicians in history. A Greek copy of some of his work, created around 1000 CE in Byzantium, was later overwritten by Christian monks in Palestine. More recently, forgers added pictures to increase the value of the documents.

In 1998, scientists started studying the Archimedes Palimpsest, and used X-rays, ultraviolet and infrared light to uncover the hidden original text.

The Suàn shù shū (筭數書), which means Book on Numbers and Computation, is one of the oldest mathematical manuscripts from China. It was written around 200 BCE and consists of 200 strips of bamboo.

There are 69 problems, each with a solution, covering topics like arithmetic, fractions, integer factorisation, geometric sequences, inverse proportions, unit conversion, and error handling. Geometry problems show how to find the area of circles and rectangles, as well as the volume of three-dimensional solids, while assuming that

The inscription on this stone includes the oldest known use of the number zero: it dates back to the Khmer civilisation in Cambodia, around the year 683 CE.

Part of the text contains the number 605. Can you spot the dot that represents the zero? The inscription was only recently rediscovered by Amir Aczel.

Many ancient civilisations, like the Greeks and Romans, did not have a "zero" in their numeral system. From Cambodia, the concept was passed to India, where the Hindu-Arabic numeral system originated. From there, it spread to the Middle East and Europe, and we still use it today.

Some ancient American civilisations like the Maya also used zero in their calendars, but their numbers systems did not survive colonisation.

The title of the book Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa'l-muqābala (الْكِتَابْ الْمُخْتَصَرْ فِيْ حِسَابْ الْجَبْرْ وَالْمُقَابَلَة, short just __Al-Jabr__‎) translates to The Compendious Book of Calculations by Completion and Balancing.

It was written by the Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī around 820 CE, and established Algebra as a new area of mathematics. In fact, the name algebra derived from the word al-ğabr in the title of the book.

Al-Khwārizmī is often called the father of algebra. In the book, he shows how to solve linear and quadratic equations, how to calculate the area and volume of certain geometric shapes, and he introduces the concept of "balancing" when solving equations.

Maqalah fi al-jabra wa-al muqabalah, which means Demonstration of Problems in Algebra, is a manuscript written by the Persian mathematician Omar Khayyam, around 1100 CE.

Khayyam managed to classify and solve all cases of cubic equations, using the intersection of conic sections. For example, on this page he shows how to solve equations of the form using the intersection of a circle and a hyperbola.

He also explored a triangle of binomial coefficients. In Iran, this triangle is called the Khayyam triangle, while in Europe and America it is more commonly known as Pascal's traingle.

The Lilāvatī is the first volume of a series of books written by Bhāskara II, one of the greatest mathematicians and astronomers in medieval India. It was published around 1150, when he was 36 years old.

Bhāskara wrote the book for his daughter, and the title actually means "playful". He writes about problem-solving, number sequences, Pythagoras' theorem, combinatorics, and many other topics.

These two pages show a problem about a pet peacock standing on a column, which can be solved using Pythagoras' theorem.

In the following volumes, Bhāskara also writes about algebra and astronomy. The combined work is called Siddhānta-Śiromani, which is Sanskrit for Crown of Treatises.

Very few Mayan documents have survived until today: one of them is the Dresden codex. It was created in the 13th century and describes Mayan mathematics and astronomy.

The Mayan number system had base 20 - using both fingers and toes for counting. Every digit from 1 to 19 consists of circles (representing 1) and horizontal lines (representing 5). Can you work out what all the numbers on this page are?

The Dresden Codex was used as a divination almanac, to record the date of astronomical events important for certain rituals. This fragment may contain the dates of eclipses of the planet Venus.

The Liber Abaci, Latin for Book of Calculation, was published in 1202 by Leonardo Fibonacci, the son of an Italian merchant. Together with his father, he spent his youth travelling around the Mediterranean.

He studied mathematics from Islamic scholars and learned about new ideas like algebra and the Hindu-Arabic numerals, both of which greatly simplified business transactions. When he returned to Italy, Fibonacci wrote a book about everything he learned.

He first introduced our current number system to Europe, which was still using Roman numerals at the time, and explained how to convert between both systems. In later chapters, he explains how to calculate profit and interest, how to approximate irrational numbers, how to determine whether a number is prime, and many other topics in mathematics. Most famously, he shows how rabbit populations might grow using the numbers 1, 1, 2, 3, 5, 8, ... These numbers are now known as Fibonacci numbers.

The Siyuan Yujian (四元玉鉴), which means Jade Mirror of the Four Unknowns, is a masterpiece of Chinese mathematics, published in 1303 by Zhu Shijie. It consists of four individual books and 288 different problems.

Zhu shows how to solve problems using systems of polynomial equations with up to four unknown variables, 天 (Heaven), 地 (Earth), 人 (Man) and 物 (Matter). He explains how to eliminate variables and how to find the side length of two and three-dimensional shapes given their volume or area.

To solve some of these problems, Zhu even used the numbers in Pascal's triangle, more than 300 years before Pascal was born!

Zhu also published a number of other mathematics texts, like the Suanxue Qimeng (New Arithmetic Enlightenment) in 1299. This textbook is written in verse, like many similar books at the time, which makes it wasy to memorise the arithemtic calculations.

Quipu are a recording system that was used by the Incan civilisation in South America around 1400 - 1560. They consist of many strings with small knots, all of which are attached to one larger rope. The type and position of the knots, as well as the colour of the strings, was used to record numbers, dates and maybe even text.

The Incans used a decimal number system like we do today. The position of a knot indicates the place value (ones, tens, hundreds, ...). Different types of knots (e.g. figure-8 knots and long-knots) represents the digit from 0 to 9.

When the Italian mathematician Luca Pacioli needed illustrations for his book De divina proportione (published in 1509), he asked Leonardo Da Vinci, a renown artist and former student.

Da Vinci created 60 different images of polyhedra. He often made a solid version, as well as a transparent version that only shows the edges, which was a completely new way to represent these 3-dimensional solids.

The Codex Mendoza is a description of the Aztec civilisation, which was commissioned in 1541 by Antonio de Mendoza. Its three sections explain the history and daily life of the Aztec people and list the different rulers and towns that were conquered.

The codex also contains examples of the Aztec calendar system, which you can see along the blue bar. Each of the symbols represents a date, and consists of a small image combined with several small circles.

The Aztec calendar used 20 day signs represented by a small image (crocodile, wind, house, lizard, snake, rabbit, water, etc.), together with up to 13 circles. This gives a cycle of 20 × 13 = 260 days.

Can you see which dates are be represented by the symbols on this page?

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Travel through time and explore the greatest mathematicians and biggest mathematical discoveries in history.

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The Approximate History of Maths - Clips - BBC Two

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A humorous animation looking at the development of mathematical knowledge through time.

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Maths Inspiration - Maths Speakers - Rob Eastaway, Matt Parker

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The list of speakers and MC’s that perform in Maths Inspiration

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IB Maths Resources from Intermathematics

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IB Maths Resources from Intermathematics

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IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides

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IB Maths Resources from Intermathematics

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IB Maths Resources from Intermathematics

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IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides

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This email address will only be used to email you this code. If you'd like me to email you more, you can subscribe here.

It's nearly Christmas and something terrible has happened: a saboteur has infiltrated the stables where Santa's reindeer are kept, and has caused all three of Santa's test flights to be unsuccessful. You need to help Santa have a successful test flight so that he can deliver presents before Christmas is ruined for everyone.

In order to have enough magical power to fly with the sleigh, all nine of Santa's reindeer must be fed their favourite food. The saboteur gave one or more reindeer the wrong food before each of the three test flights, causing the reindeer to be unable to take off.

Behind each day (except Christmas Day), there is a puzzle with a three-digit answer. Each of these answers forms part of a piece of information about the reindeer's favourite foods and what the reindeer were fed before the three test flights. You must use these clues to work out what each reindeer's favourite food is, then complete a test flight by feeding each reindeer the correct food.

You can use this page to attempt up to three test flights per day. An attempted test flight will be successful if and only if all nine reindeer are given their favourite food just before the flight.

Ten randomly selected people who solve all the puzzles, complete a successful test flight, and fill in the entry form behind the door on the 25th will win prizes!

The prizes will include an mscroggs.co.uk Advent 2021 T-shirt. If you'd like one of the T-shirts from a previous Advent, they are available to order on Spring.

The winners will be randomly chosen from all those who submit the entry form before the end of 2021. Each day's puzzle (and the entry form on Christmas Day) will be available from 5:00am GMT. But as the winners will be selected randomly, there's no need to get up at 5am on Christmas Day to enter!

You can find more information about this competition, in this blog post.

I am Matthew Scroggs. I like maths.

I currently a postdoctoral research associate in the Department of Engineering at the University of Cambridge. Before this, I did a PhD in the Department of Mathematics at UCL and before that I obtained a Master's degree in mathematics at the University of Oxford. Between Oxford and UCL, I worked as a maths teacher in a secondary school. During my PhD, I began working on the open source boundary element method library Bempp. During my postdoc at Cambridge, I began working on the open source finite element library FEniCSx. You can find more about my work on the academic page.

If you would like to reuse any of my content, please get in touch.

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It's nearly Christmas and something terrible has happened: a saboteur has infiltrated the stables where Santa's reindeer are kept, and has caused all three of Santa's test flights to be unsuccessful. You need to help Santa have a successful test flight so that he can deliver presents before Christmas is ruined for everyone.

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IYMC | International Youth Math Challenge

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An educational mathematics competition open to students from around the world: Unleash your problem-solving skills and expand your knowledge through diverse math problems. Participate in this year’s Qualification Round to win awards and prizes!

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Balance quest, maths sudokus and many, many more!

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1st Class Maths Instruction and Tuition.
Request a tutor or learn from my collection of free resources and instruction videos.

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Interactive Maths - The Interactive Way to Teach Mathematics

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Making use of the fantastic UKMT Individual Challenges, I have generated a page that randomly selects questions within specific parameters. You choose which age range you are aiming it at (Junior is...

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Cross curricular links

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Move Text
"Dear Christos, I appreciate you for developing a helpful material for the use of IB Math teachers community. Thank you." "Hello Christos, Just to let you know that I am impressed by your website. Thanks for sharing it with us (IB community). Nice notes, great tips! Will be following you for sure, especially with the new changes to the curriculum." "Hey, Greetings from Japan! I am a relatively new IB teacher. I have taught math SL for a full year now and math HL for 6 months. I am really thankful for your website" "Dear Dr Christos Nikolaidis, Thank you so much for sharing your site and notes with us! They are very useful information for revision. Thank you for your generosity! May God bless you and your family for your kindness!" "Greetings! Thank you for clear notes that support this maths HL option. They have been a support to my own lessons." "Hi, I am an ex-IB student. I am really grateful to you because I found your resources very helpful" "Hi Christos, I want to thank you for all this wonderful material you have shared. It is amazing and I am truly grateful. I just want to know if it is ok for me to share this with my students to prepare for their IB exam in 25 days. You are an amazing person and I a totally grateful for your time and effort you have put into this " "Hi Chris, I am a high school math teacher at an American school in Kuwait. I am going to be teaching an IB-SL class first time ever next year. As I was searching for good IB math resources online, I came across your website. This is serious stuff. You seem to have really put in a lot of effort. Thanks very much for being so generous to have all this material available for everyone." "Hello Christos, I am an IB Math HL teacher from India. I have been using your worksheets for most of the topics. I often recommend my students to use your notes for revision." "Thank you so much for designing a user-friendly website site and wonderful worksheets. It is after a long time I have come across good stuff. Very thoughtful to design and upload test in doc form. It gives me an opportunity to customize the test." "Dear Christos, congratulations on your site!!! It is very well organized and usefull for both teachers and students! I will teach Math HL in Genoa from September: I downloaded your suggested plan. Thank you for your time and for your site again! "Hi Christos, My name is P... R... and I am an IB mathematics teacher at the Zurich International School. I've thoroughly enjoyed your materials and tests" "I just wanted to say thank you! My high school just became an IB school last year and I am teaching IB Math SL for the first time. I came across your website about a month into my school year last year and it has been life saving for me. I have been able to pace myself, plan better, and use your tests as guidelines. I was nervous that they were changing the course, but when I saw that you were adjusting, I was able to relax. Thank you for being the teacher that I go to for IB help! Thanks a lot! You are great! :) "Hi, Mr.Nikolaidis, I just want to tell you that I use your Math HL exercise to teach my student. So, I would like to thank you!! "Hi, I am a math teacher, I have been teaching AP and A Levels in the last 10 years, this is my first year teaching IB (SL level). I just want to thank you because you have no idea how much you are helping me and my students with the lecture notes and exercises that you're posting." "Hi Christos, just to say I am an IB teacher in Brighton, England and me and my students absolutely love your site. Thank you so much for providing this amazing resource. It's so incredibly useful" "Hi Christos, What you have created is as beautiful as Maths itself. I refer and use your material to teach my students." "Hi! I'm an IB Coordinator & Science Educator from the United States. Thank you so much for your fantastic website!" "Dear Christos, I have found your amasing website. Thank you. "I am also an IB math teacher. I absolutely love your website and vast resources available, thanks for sharing it. "Christos, Hi. You are very accomplished in mathematics. Thank you very much for your website content - it has been very helpful. You have obviously put in many days/months of work into preparing your notes and examples. I have suggested your web site to my students to consolidate their understanding of the topics" "My exams are currently coming up, and I just want to thank you for all the resources that you have provided. They have helped me immensely." "Buen día Christos, saludos desde Perú, felicitarle por su pagina web muy interesante y útil para el trabajo pedagógico y la preparación de los estudiantes para los exámenes del IB." "Hello, I'm an IB student who is preparing for the upcoming Math HL exams. I just found your website and I just want to let you know that I really appreciate your work. Your lecture notes are amazing and it helped me so much. I am struggling so much especially with the optional calculus part and your notes really helped me to understand better. Thank you so much!!!!" "Hi Christos, I stumbled across your extensive resources at the start of this academic year when a departing teacher forwarded on your wonderful notes. Thanks for all your hard work!" "Thanks for these resources.... an outstanding addition to what I already do in the class..." "Hi Christos, I want to ask your permission for using your work (practice problems, etc) for my lesson activities" "Hello Christos, I would like to let you know that I appreciate every bit of information you shared in this website. Thank you so much for your immediate response and may the Lord bless you even more." "A heartfelt gratitude for creating these wonderful resources and sharing with us. I have been using your tests and exercises in my class for last one and half month and they are extremely helpful. I have shared your lecture notes with my students and they appreciated your hard work a lot." "Congratulations for such incredible work. I was a bit lost on coming up with a plan for MAA and your ideas were just a perfect fit. I attended an IB training last June and networking with some teachers. Our plan is a bit different but your ideas were just brilliant. Thank you for such a helpful and well-organized website." "I am a follower of your site and truly inspired by your sharing skills" "Thank you for the great resources! " "Hello Christos, Two teachers recommended your site. And I am glad they did, a high quality collection of material. Would you mind if I recommend your site in my workshops?" "Apres plusieurs années d enseignement des maths dans les lycees et collèges d Afrique je veux passer au système IB. Je vous remercie de ce que vous offrez sur votre site car pour le moment j ai aucun livre du programme, ni du PEI ni du PDD. Toute aide est bonne à prendre." "Hello Christos, Thank u for such wonderful arrangement of topics. These documents has really been a blessing." "Dear Mr Nikolaidis, I am a Math HL (old Syllabus) student, and I love using your lecture notes and exercises to study. They have been very helpful over the last year and a half. I can't thank you enough for putting them online." "Thank you for graciously sharing your intellectual property with everyone. I am co-teaching IB1 AI and knowing my colleagues, they too will be kind enough to reciprocate." "Thanks for offering a time-calculator on https://www.christosnikolaidis.com/en/time-calculator/" "Hi Christos, You are such a wonderful human being. I came across your math here. I can not believe it. You have made my work so easy. I can not thank you enough. You are so helpful. Thank you" "Hi Christos, I cannot begin to describe how much of a help your notes, exercises and tests and all the content that you have been posting has been to me. I am truly thankful for that." "Thank you so much for your phenomenal resource" "Hi, I wanted to thank you for uploading all of these tests here for free!" "Hi, I graduated IB in November 2019, in India. I increased my score to a 7 in Mathematics HL from a 5 and I would like to thank you for all the help your worksheets and tests have given me!" "Hi Christos, I am a teacher that is going to teach an IB MAA SL course this upcoming year for the first time, and found your site mentioned on an online thread. I just wanted to say thank you for making these documents public: it's awesome stuff." "Hi Sir, I am teaching DP math in my school for the first time, I was so clueless of what is the syllabus for SL and HL and I have combined class. Somehow I found your website through IB and after looking into it, I was so relieved and your content in the website is amazing." "Dear Mr Nikolaidis, I just wanted to thank you for all your wonderful material that you freely upload. I have been teaching for a while, but this is only my 2nd year in IB and I have found your notes incredibly useful! Thank you so very much!" "Hi Christos, Great job on the website. I love what you have to say about the unit plans. I think the unit plans are based on understanding by design, I do actually think that writing these unit plans is a useful exercise for inexperienced teacher who needs guidance on how to teach material for the first time. If the unit plans were that fundamental to teaching then we would have been provided with completed plans by the IB. Best regards, N... B..., Head of the Mathematics Department ..." "GOD BLESS YOU RICHLY ON BEHALF OF MY ENTIRE CLASS!" "What a wonderfull resources you made for students. Thanks for these resources." "Hello Christos, It a pleasure visiting your website which has a wealth of wonderful resources. I just started teaching the IB Maths A & I this semester and will continue to use this website." "Hey there, I have found your online resource for MATH AA HL and I think it is absolutely phenomenal and very very helpfull. I used your resource for a couple of my school tests and scored much higher than all my previous tests." "Hi I am a student in Shanghai, China. Currently studying in IB MATH HL Y1. I found your website in my DP Year 1 and it has been wonderful for my study. I really value your work." "Thank you for your work on the IB curriculum. I have used it for two years now with my students here in Gilbert, Arizona in the United States. Your work is thorough and well thought out." "Hi Christos, I am a British teacher teaching HL MAA in an International school in Brunei. Your website has been INVALUABLE - I can't thank you enough." "Dear Mr Nikolaidis, I take AA HL and have recently found your website which has greatly helped me to improve my math grades and enhance my understanding of so many topics. I'd just like to express my gratitude for the time and effort you've put into these resources, thank you so so much!" "Hi Mr. Nikolaidis! Thank you so much for your amazing lecture notes. They are extremely helpful. You make Math so much more fun and interesting. All the tests and exercises you have posted are very specific to the topics. Thank you so much for being so generous. I REALLY APPRECIATE IT SIR!" "Hi Chris, I live in Vancouver and work at ... School. I am going to teach Math Applications and Analysis HL or SL/HL for the first time as my school is offering this course for the first time starting in September 2021. I was hoping if I could use your notes and also if I could get some advise as well. I am also wondering if there are blank notes available that I could use for my students in the first year." "Hi, Christos, Thanks for making this website! We found it very useful as it is very difficult to find materials for the new AA & AI syllabuses, we hope that you can make more HL AI materials as these are extremely rare." "Hello sir, This is A... from India. I am new to IB curriculum. Thank you so much. The notes was really useful for me." "Hello there, I am R... M... and I hope you're doing well! I am a Math AI SL student. This website has helped me a lot in clearing my doubts while practicing a good number of questions from each topic. Thank you" "Good morning, I wanted to send my sincere thank you for the resources you have provided on this website. I have been an IB Math SL teacher for over 10 years now. I've worked through 2 curriculum reviews while also aligning with my provincial standards. This is our last year offering IB courses at our school, and with this being the first year of new exams, I have found your organized content to be a great tool for our exam prep. The students have been able to go to your lecture notes and use them as a great review of content, and we have used your example packages to work through questions as a class before they dive into practice papers. We did not order new textbooks for this year so your notes have been great for the students to read through knowing that everything is nicely organized in one place! I have the utmost respect for teachers who value sharing resources that not only help teachers be more effective, but ultimately help students succeed. Thank you again and have a great rest of your school year!" "Dear Christos, Thank you so much for this wonderful collection of review packets and tests for IB, I do highly appreciate it, they are fantastic!" "Dear Sir, A big kudos to your work!!" "Hi Mr. Nikolaidis, I want to thank you for your wonderful notes" "Thank you so much for posting your amazing resources! I am a soon-to-be first year teacher and was just told that I will be teaching AA SL. Feeling a little overwhelmed but am glad there are people like you who are supporting others" "I really appreciate your hard work, talent and dedication. Please keep it up from Ethiopia, Addis Ababa." "Dear Christos, Thank you so much for offering your materials online. I am planning to use your resources as a model for my AA HL class." "Hi Christos, Greetings! I am S..., working in an international school in Mumbai. I am new to DP curriculum. I came across your site and am so overwhelmed by the way IB mathematics is handled here. Your resources have been extremely useful to me. Thanks for everything and I truly appreciate all the effort that goes into creating so many resources. Cheers"

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IB mathemarics free resources, best ib math resources, IB lecture notes, IB exercise, IB tests, International Baccalaureate, Ibresources

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exam-mate is an exam preparation tool containing a bank of IGCSE past papers exam questions (Cambridge, Edexcel), A level past papers exam questions (Cambridge, Edexcel), past IB questions and mark schemes for a range of IGCSE, A level and IB diploma subjects.

Search for yearly IGCSE past papers exam questions (Cambridge, Edexcel), A level past papers exam questions (Cambridge, Edexcel)

Search for Topical IGCSE past papers exam questions (Cambridge, Edexcel), A level past papers exam questions (Cambridge, Edexcel), past IB questions and mark schemes

Search for Questions ,then build your own homework activity ,test or mock exam ,view and edit tests and mock exams you have created

Stay in Touch

Get latest updates and related news from exam-mate

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exam-mate is an exam preparation and exam builder tool, containing a bank of topical and yearly past papers. It covers Cambridge IGCSE Past Papers, Edexcel International GCSE, Cambridge and Edexcel A Level and IAL along with their mark schemes.

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The best resource for IB Mathematics just got better!

Voted #1 IB Mathematics Resource by IB Teachers & Students

IB Environmental Systems and Societies

Practice IB Exam Style Questions

Thousands of exam style questions, filtered by topic, sub-topic & difficulty. Detailed and easy to understand mark-schemes and video solutions for all questions. Practice & master IB exam style questions.

[Maximum mark: 6]

Consider an arithmetic sequence 2,6,10,14,...2,6,10,14,\dots 2 , 6 , 10 , 14 , ...

[Maximum mark: 6]

The table shows the first four terms of three sequences: u n v n w n w_n w . v_n v , and u_n u ,

State which sequence is

1. arithmetic;

2. geometric. [2]

[Maximum mark: 7]

1. Write down the quadratic expression 3 x 2+5 x−2(a x−b)(x+c)(ax-b)(x+c) ( a x − b ) ( x + c ) . 3x^2 + 5x - 2 3 + 5 x − 2 in the form [2]

2. Hence, or otherwise, find the coefficient of the term in x 9 x^9 in the expansion(3 x 2+5 x−2)5(3x^2+5x-2)^5 5 x − 2 .
of [5]

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Copyright - Revision Village 2024

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Revision Village | Ranked #1 IB Math Resource Online

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The #1 IB Mathematics Resource. Analysis & Approaches (AA) and Applications & Interpretation (AI). Practice Exams, Questionbank, Past Papers, Videos

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Exam paper questions organised by topic and difficulty. Our worksheets cover all topics from GCSE, IGCSE and A Level courses. Give them a try and see how you do!

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Math AA

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Math AA - analysis and approaches resources

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MadAsMaths.com :: Home

It is with great sadness that we announce the passing of creator/owner of the MadAsMaths website, Trifon Madas. This website will remain freely available for all its users, in his memory. However, please note that it will have a static format, there will be no further updates and the Contact form has been deactivated.

Free Resources for Students and Teachers of Mathematics.

In the 33 years of my involvement with mathematics I have produced, collected and accumulated a huge number of resources in many different forms.

I have used these resources with my teaching and lecturing, guiding several students into their mathematical careers.

Most of the material I have created is contained in this website and an overview is shown below.

Mathematical booklets, classified by topic, with a large number of questions and full solutions.

Practice papers with full solutions.

For the latest news click HERE .

The aim of this website is to give away mathematical resources, absolutely free!

It will give me immense pleasure to know that I have contributed to the education of yet more mathematicians, even if I did not personally meet them.

Enjoy !

[... and the homepage would not be complete without answering one of the most frequently asked questions ...

No, I do not post/help in TSR anymore because in my opinion it has little educational value, and is mostly run by talentless immature individuals ....]

SUBSCRIBE ON OUR BRAND NEW YOUTUBE CHANNEL!!!

Unfortunately I cannot put on the website past papers and solutions for examining boards or Universities due to copyright restrictions. I possess past papers for all A level boards and all modules, with some boards going back as far as the seventies. I will investigate ways into sharing these resources in the future.

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Excellent for marking!

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Configuration

Help

This website helps you make sets of axes that you can print and use. You can configure various aspects of the axes, as explained below. When you print the page, you should only get the axes. The configuration pane, and this help panel, will not be printed. The axes themselves are created as SVGs so alternatively you could download the SVGs and import them into a program that understands SVG.

Page Setup

Page Size: The idea is that the axes fit on a page of this size so that you can print them to the size you want, but ...

Page Margins: ... it is quite hard to figure out the relationship between how big something is on the screen and whether it will print all on one page (and it appears to be very dependent on the browser). The "page margins" are subtracted from the page height and width so that if the axes appear on more than one page then you can shrink them slightly to get them on a single page. This can be an iterative process, so use "Print Preview" or "View as PDF" options in the print dialogue to check before printing. The units are pixels, which are quite small. In my experiments, with A4 paper, I found that 5 worked with Firefox while the margin needed to be 36 for Chrome.

Borders: This is the space around each set of axes. If you cut out the axes, this should be the space left around each one.

Page Orientation: Whether the page should be portrait or landscape.

N-Up: How many sets of axes to display on the page.

Number of Axes: How many distinct sets of axes to display on the page. If this is less than the number of sets of axes to display, the set will repeat as needed.
So to get 2 copies of the same axes, set "N-Up" to 2 and "Number of Axes" to 1. To get 2 sets of axes, but each appearing twice, set "N-Up" to 4 and "Number of Axes" to 2.

Current Axes: The rest of the options apply to a specific set of axes. This option controls which set of axes the displayed options apply to.

Axes Setup

Font Size: This is the font size for the labels on the axes.

Preserve aspect ratio: If this is checked then the two axes have the same scale. If not, they are scaled independently to best fit the available space.

Grid: If this is checked then a grid is shown.

Line width: This slider controls the width of the axes lines.

Mark length: This slider controls the length of the marker lines.

Mark width: This slider controls the width of the marker lines.

X/Y Axis

Minimum: The minimum value on the relevant axis.

Maximum: The maximum value on the relevant axis.

Marks every: How often to put marks (counting outwards from 0).

Labels every: How often to put labels, in number of marks.

Lastly, a note on copyright. As you create the axes, you have the copyright on them. I have the copyright on the code, but it is released under the MIT Licence so if you want to improve it, feel free. It is available on github.

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This website helps you make sets of axes that you can print and use. You can configure various aspects of the axes, as explained below. When you print the page, you should only get the axes. The configuration pane, and this help panel, will not be printed. The axes themselves are c…

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A game requiring you to devise a strategy far more complex than that required for the standard noughts and crosses game.

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In a post on Cognitive Science in the Classroom, I mentioned Knowledge Organisers, or to be more precise I mentioned Kris Boulton's "When shouldn't I use knowledge organisers?". Kris has written on why they are less applicable to maths. Certainly, I had not used knowledge organisers for Mathematics myself with one exception, I have used William Emeny's Angle Facts; as Kris Boulton says in his article, "Maths is super-dense with concepts, and processes, but really only very few facts." Noting topics where students do need to know more facts, he includes angle facts.

When I have used Will's angle facts, I have adapted it so some content is missing, particularly the section on basic angle facts, students can be given just the diagrams for example and asked to recall the basic angle facts. I have also asked students to recall as many basic angle facts before they see the list as in the organiser, so using it following retrieval practice or as a retrieval exercise.

As noted in this post on Knowledge Organisers from Durrington Research School, it is not about the knowledge organisers themselves but how they are used for planning, teaching and testing. Note the example shared of a Maths Knowledge Organiser, Year 10 Expressions, Foundation. I like the fact that key vocabulary is included here, the few key facts needed and of course by far the largest section - key concepts with examples.

To quote the Durrington blog, " Maths are using their range of knowledge organisers to support homework tasks. Firstly, the students can access their maths knowledge organisers are any time using our online system Connect. This means that students have scaffolding in place for when they are working outside of the classroom. Furthermore, every fortnight the maths team set a homework that is based on retrieval quizzing. The students are required to use the knowledge organisers to find the answers to upcoming quizzes and then actually sit the quiz in class on the due date for the homework. Students who score less than 12 out of 15 are then supported in making flashcards on the questions, again gaining the information from the knowledge organiser, and use these to retest until they are successful. This strategy demonstrates how knowledge organisers can be used to support learning through the testing effect.

Nicola Whiston has a superb collection of Knowledge Organisers which follow the White Rose Schemes of Learning, all are available on TES Resources, on TES editable versions are available as well as the free pdf resources. These are really attractive and I believe appeal to students. I think these are excellent to use in class alongside teaching a topic. They could also be used for retrieval practice.

You can hear Nicola talking about Knowledge Organisers with Tom Manners, In his interview, he was joined by Nathan Burns aka @MrMetacognition who has researched these in great detail, as well as Nicola Whiston (@Whisto_Maths) to discuss what maths knowledge organisers should contain and how we should use them effectively.

From Becky Reed a set of Knowledge Organisers for Edexcel GCSE (UK age 14-16). We have here another set of very clear and also attractive set of resources. Like the other resources here I think these are useful in class and for students to use at home also. There are several examples given which is really helpful.

Sarah Hall has a GCSE ('WJEC flavoured' )collection. Sarah's Knowledge Organiser resources can all be found (all free) on TES Resources. These have many clear illustrations and like others in the Knowledge Organiser collection, are very attractively presented.

For a collection of Cornell notes linked to topics found in the Maths curriculum see Mr Hawes Maths.

For A complete set of A Level Statistics and Mechanics Knowledge Organisers - see these resources from Lucyjc. These resources are available free on TES Resources: Statistics and Mechanics. All include Key Words and Definitions and What Do I Need to Know sections.

And for Pure Mathematics, we have from @misschakera a set for the first year of A Level.

Mrs D Maths has been writing Knowledge Organisers for A Level Maths, ( free on TES Resources). She has also started a Year 2 set of organisers, see Year 2 Functions and Graphs.

These organisers are included in the Knowledge Organisers collection which includes resources for KS3, KS4 and KS5 (ages 11 - 18).

If I want definitions, characteristics and examples (clarified with the use of non examples), then I could return to the Frayer model. (See Frayer Models.)

Searching for Mathematics Knowledge Organisers, I have come across some resources I wish to explore further, such as the Henry Box School on Knowledge Organisers where the school are sharing Knowledge Organisers for each subject, recognising the support parents can offer. From the Subjects menu, choose a subject and you will find this includes Knowledge organisers for Year 7 through to Year 11, see Maths for example.

CIMT's GCSE course includes Facts to Remember for each unit.

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In a post on Cognitive Science in the Classroom, I mentioned Knowledge Organisers, or to be more precise I mentioned Kris Boulton's "When shouldn't I use knowledge organisers?". Kris has written on why they are less applicable to maths. Certainly, I had not used knowledge organisers for Mathematics myself with one exception, I have used ...

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Tes provides a range of primary and secondary school teaching resources including lesson plans, worksheets and student activities for all curriculum subjects.

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team mathematics competition designed for middle and high school students conducted annually since 2003.

PLEASE NOTE: All contest times are given in UTC (GMT) form. Current Server Time:

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team mathematics competition designed for middle and high school students conducted annually since 2003. PLEASE NOTE: All contest times are given in UTC (GMT) form. Current Server Time:

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Increasing participation in Core Maths, AS/A level Mathematics and Further Mathematics

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Copy of Collection of Awesome Math Resources 2018

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Dr Oliver Mathematics | Mathematics | Further Mathematics

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Mathematics and Further Mathematics: don’t you just love them? Thought so!

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GeometricSparks is the fourth in a series of school mathematics blogs written for mathematics teachers and others in mathematics education. Each blog provides a commentary on 20 'weekly' sets of 5 'daily' tasks.

The first blog in the series is Algebradabra, with algebra tasks for secondary school students. The blog was later published in book form by the Association of Teachers of Mathematics (ATM).

You can find the blog here,
and information about the book here.

A STUDENT version of Algebradabra, containing just the 100 tasks, without commentary, is available from DEXTER GRAPHICS.

The second blog is Algeburble, with early algebra tasks for upper primary / lower secondary school students. The blog was also published in book form by ATM.

You can find the blog here,
and information about the book here.

The third blog is MultipliXing, with multiplicative reasoning tasks for secondary school students. The blog is in the process of being published in book form by ATM.

You can find the blog here.

I have also produced a set of over 100 fractions task. These come as a set of SLIDES and a TEACHER'S GUIDE, both available as pdf files from DEXTER GRAPHICS.

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GeometricSparks is the fourth in a series of school mathematics blogs written for mathematics teachers and others in mathematics education. Each blog provides a commentary on 20 'weekly' sets of 5 'daily' tasks. The first blog in the series is Algebradabra, with algebra tasks for secondary school students.

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MathsStarters is a collection of activities for the start, middle or end of maths lessons. Each activity can be used over and over with a new set of numbers each time.

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Sarah Farrell

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Maths Teaching Resources | Dr Austin Maths

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Dr Austin Maths is a free-to-use Maths teaching resources website, focussing on quality resources for KS4 IGCSE and GCSE Maths.

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This site includes screenshots of graphs that are likely to require some interpretation! They might be complicated, unhelpful or just plain bizarre. There will be a few articles about how they...

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https://www.ukmt.org.uk/competitions/team/primary-team-maths-resources

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Free resources for younger problem solvers

These digital resources are designed to support secondary schools running mathematics events for feeder schools. Any registered UKMT centre (including primary schools) may access the resources free of charge and use them as they wish.

How do I get access?

To download the Primary Team Maths Resources, you must be logged in as an approved user from registered UKMT centre. Please log in or create a new account if you do not already have one in order to access the resources below. The resources are not available to parents or private tutors.

What is in the pack of resources?

The resources are arranged into seven rounds, some of which are inspired by our Team Maths Challenge. Each round is designed for teams of four.

Group Round (Download sample Group Round)

Each team is given a set of questions, which they should divide up among themselves so that they can answer as many as possible in the allotted time.

Crossnumber
Download sample Crossnumber (PDF)
The team splits into pairs. One pair tackles the down clues and the other tackles the across clues.

Shuttle
Download sample Shuttle (PDF)
Working in pairs, teams attempt sequences of four linked problems, where the answer to question one feeds into question two, and so on.

Relay
Download sample Relay (PDF)
This round combines teamwork and speed and involves contestants moving around the room.

Speed Test
Download sample Speed Test (PDF)
A quick-fire round where contestants aim to answer any many questions as possible correctly in the allotted time.

Logic
Download sample Logic round (PDF)
The contestants organize themselves as they wish in order to solve a challenging logic puzzle.

Make a Number

Contestants try to make target numbers using a set of six numbers and the standard arithmetic symbols.

Can you help us?

If you or someone you know has benefited from our activities then please consider making a donation.

Find out more about volunteering with us.

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Free resources for younger problem solvers These digital resources are designed to support secondary schools running mathematics events for feeder schools. Any registered UKMT centre (including primary schools) may access the resources free of charge and use them as they wish.

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https://sites.google.com/site/mathteammatics/home/competition-problems

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There are four events to Math-Team-Matics - so really it's a Quadrathalon.

The structure of the competition is:

Team Challenge - open-middle problem that requires collaboration to solve within the time limit.

Individual Challenge - multiple choice problems trying to get at a different perspective than the usual quiz.

Relay Race - quick numerical problems that require the data from the runner before you.

Quiz Bowl - mix of turn-based and toss-up questions pitting one team against another.

Final Quiz Bowl - top two teams in each division face off in a winner takes all match.

Math content that is fair game for the competition is K-8 mathematics, plus high school algebra and geometry.

Here are some sample problems for the different phases. In the competition there will be an emphasis on fun and challenge.

Team Challenge SampleHow many numbers from 1 to 20 can you compute using the digit 9 exactly three times and any mathematical operation +, -, x, /, sqrt, factorial, decimal point, etc, but no other numbers or digits. You have to use 9s as digits, not necessarily the number 9, so 9, 99, 9.9, etc. are all fair. Extension: 21-30!

2016 Dodecagon Tiling (thanks to Henri Picciotto)

2015 MacMahon Squares Problem & Squares sheet

2014 Truchet Polygons

2013 Cubic Stairs Pattern

Individual Test (Multiple choice)To make this collaborative, we drop the high and the low scores, make a team score with credit for any problem anyone on the team answered correctly, then average that with the three middle scores.

Example: Ten liters of a 30% acid solution are obtained by mixing a 25% solution and a 50% solution. How many liters of the 25% solution must be used? (A) 1 (B) 1.5 (C) 2 (D) 5 (E) 8

2016 Individual Challenge

2015 Individual Challenge

2014 Individual Test

2013 Individual Questions (pdf)

Relay Race What is the sixth whole number factor of 144, counting from least to greatest? What is the answer to number 1 multiplied by 2.5? If the answer to number 2 is the amount a consumer pays for a movie and a third of that amount is profit for the theater. How much is profit?

Alex runs a lap in 90 seconds. If Alex ran (answer to number 3) laps, how long will it take him (in minutes)?

Take the answer to number 4, double it, and then add the sum of the first three prime numbers.

If the answer to number 5 is the area of a face on a cube, what is the volume of this cube?

2016 Relay Questions

2015 Relay Questions

2014 Relay Questions (there was a mistake on one... )

2013 Relays Questions (pdf) (general agreement that John was overzealous on these, but he likes the strong theme to each set.)

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There are four events to Math-Team-Matics - so really it's a Quadrathalon. The structure of the competition is: Team Challenge - open-middle problem that requires collaboration to solve within the time limit. Individual Challenge - multiple choice problems trying to get at a different perspective

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AL practice papers

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These papers are legacy Edexcel Exam Papers, however they have been edited to reflect the new A Level Specifications. I have included new questions, not found in the old specs, so as to make it suitable for the new A level requirements. I've made Paper 1 Pure Practice Papers into an AS Pure Papers so that they can be used by students taking AS Pure Paper.

I've created those papers in the only intention of helping teachers to deliver the new A level specifications and helping students in their revision for their A level exams. They will supplement the existing practice papers out there and hopefully will provide a big relief for all teachers and students who have been asking for more practice papers!
I've used code J8 which means January 2008 (I've combined Jan 2008 C1, C2 & C3 paper into a single AS Pure Paper). Code M8 means May 2008; J9 means Jan 2009; M9 means May 2009 etc... : These papers have been solely edited by me and are for educational purposes only, and not for financial gain

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A Level Practice Papers 2019 Specs | Naiker

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These papers are legacy Edexcel Exam Papers, however they have been edited to reflect the new A Level Specifications. I have included new questions, not found in the old specs, so as to make it suitable for the new A level requirements.

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The copyright in all of this material belongs to the originators who created it.
trol = Teacher Resources on Line = trol
See for details about these resources, as well as other (general) matters.

All of the resources offered here can only be accessed by
The [size in kilobytes] of each unit is given as a guide to downloading times.

The material is made available here for downloading and dissemination for
NON-PROFIT MAKING PURPOSES ONLY. Go to Cleave Books main Index

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The copyright in all of this material belongs to the originators who created it. trol = Teacher Resources on Line = trol See for details about these resources, as well as other (general) matters. All of the resources offered here can only be accessed by The [size in kilobytes] of each unit is given as a guide to downloading times.

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DrFrostMaths provides an online learning platform, teaching resources, videos and a bank of exam questions, all for free.

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Free Maths Rich Tasks on Mr Barton Maths

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A short introduction task to using algebra tiles for the distributive law. I have refrained from suggesting this task is about "expanding brackets". Instead, the task can be used with that focus or for factorisation using a common factor. I like to introduce both ideas within close proximity - a real manifestation of 'interleaving'. A key theme in mathematics is doing and undoing. Considering both the doing and undoing process in close proximity can help pupils to develop deeper understanding of both and how they are linked.
Download PDF Here
Credit: @Chrismcgrane84

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A short introduction task to using algebra tiles for the distributive law. I have refrained from suggesting this task is about "expanding brackets". Instead, the task can be used with that focus or for factorisation using a common factor. I like to introduce both ideas within close proximity - a real manifestation of 'interleaving'.

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https://www.purposefulmaths.com/algebra

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We are revising in year 10 and the topics of revision are Similarity including scaling units of area and volume, Trigonometry and Pythagoras and Indices. I decided that I wanted students to practice Trigonometry and Pythagoras whilst working on changing units of measure in area and volume problems.

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The Corbettmaths Conundrums - daily mathematical puzzles

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Materials that will assist you in your professional development and support you in teaching for mastery with confidence

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Foundation Mini Tests

One page tests to prepare for the the GCSE foundation exam:

Grade 5 (Foundation) Mini Tests

One page tests to prepare for the the GCSE foundation exam:

Grades 4-6 (Higher) Mini Tests

One page tests to prepare for the the GCSE higher exam:

Grades 7-9 (Higher) Mini Tests

One page tests to prepare for the the GCSE higher exam:

Old specification tests

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Maths Genie - Resources - Predicted GCSE Revision Papers

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One page tests to prepare for the the GCSE foundation exam: One page tests to prepare for the the GCSE foundation exam: One page tests to prepare for the the GCSE higher exam: One page tests to prepare for the the GCSE higher exam: Old specification tests

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A selection of our favourite mathematical puzzles and problems. Most are simple to explain, but the solutions require clever and unconventional thinking.

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Matt Parker has launched Matt Parker's Maths Puzzles! Once a week Matt will be making a puzzle video, in addition to his normal Stand-up Maths videos.

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Julia Robinson Maths Foundation Activities

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Julia Robinson Maths Foundation Activities

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JRMF puzzles are unique compared to other math games you'll find. We design problems with low-floors so everyone can get started by the simple act of trying something and with high-ceilings that lead to challenging mathematics.

Play them in person with friends, or virtually at home.

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Math puzzles for all ages and skill levels. JRMF puzzles are "low-floor, high-ceiling," meaning students as young as 6 and as old as 100 can find our math fun and challenging. Play them in person with friends, or virtually at home.

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A magazine for the mathematically curious. Issue 17 now available: Penguins, prison and PDE patterns feature in our new issue. Plus all your favourite puzzles & columns.

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Hey folk! Here are links to all of the #MathArtChallenge…challenges. :) Please feel free to share widely. This dropbox folder has lots of videos/pictures, too. Also, if you have an idea for a…

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Unleash your creativity with the world's best virtual manipulatives!

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Screen capture of the Rosenshine Masterclass slides in five key videos plus an introduction.

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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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Welcome to the Year 11 maths course for this unusual Easter term. The material that we will cover in the first part of the course is designed primarily to get you in to the mindset of an A Level mathematician, where the demands on your algebraic skills and your capacity to think independently are much greater than at GCSE. Along the way, you will also practise some of the skills used in the GCSE course, but also - I hope - think about some of the content in a deeper, less procedural fashion. Expect to be challenged and to have to think about the problems and techniques. There will be teachers on-line to help you during timetabled slots - and do also discuss questions with one another - but you must try to engage with the material and puzzle some things out for yourself. Always try the questions before looking at the solutions - looking at what someone else has done is not the same, and won't give as much satisfaction, as working it out on your own.

Later on, there will be a focus on the maths used in everyday contexts. You will have noticed the increased public awareness of mathematical modelling because of the coronavirus outbreak, and we'll look at some of the techniques behind modelling the spread of epidemics. There will also be some modelling in other contexts and a focus on some financial maths - you'll learn how to calcuate your mortgage repayments and what APR means.

Most of the written work will be self-checked with written or video solutions, but there will be some assignments to submit for marking. I hope you enjoy the course!

Paddy MacMahon

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Welcome to the Year 11 maths course for this unusual Easter term. The material that we will cover in the first part of the course is designed primarily to get you in to the mindset of an A Level mathematician, where the demands on your algebraic skills and your capacity to think independently are much greater than at GCSE.

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Find powerpoints, topic tests and other teaching resources for the 9-1 GCSE Maths made by crashMATHS. Suitable for AQA, Edexcel and OCR.

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Free Maths resources for KS2 Primary Maths - assessments, Maths practice lessons & CPD resources by Third Space Learning.

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Topic specific fluency, reasoning and problem solving questions

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This Starter is called Refreshing Revision because every time you refresh the page you get different revision questions.