Mathematical Miscellany #22

Underground Maths R9452

Oxford MAT 2007, Q1d

On Mathematics for Students earlier this week, see the annual update on University Admissions tests. Many resources are available to help students prepare for the tests. Such resources are excellent for students aiming for high grades, not just those taking tests.

For a new Competitions page – note the link on the right-hand side. Check, for example, the poster competition from the excellent maths careers site and from MEI, Ritangle.

MEI & Maths Careers

ParallelNot a conventional competition, but to challenge your able mathematicians, try Parallel from Simon Singh. All materials and resources are completely free and teachers will have access to all the student scores from the Parallelograms which are automatically marked.

Students do earn points depending on their percentage score on each Parallelogram, which in turn earns mathematical badges. There will be prizes for schools and students linked to the badges in future. Keep an eye on Parallel for the latest news.

Maths GenieReturning to Mathematics for Students, I have updated the GCSE Revision Resources page. My students do like Maths Genie, which is excellent for both GCSE and Advanced level.

In case you have not seen my recent post on Advanced Level – Worked Examples, do check these superb resources from Hodder and from Maths Genie.

Hodder examples

Hodder – Solutions for My Revision Notes (Pure)

Advanced Level – Worked Examples

Hodder examples

Hodder – Solutions for My Revision Notes (Pure)

Looking at some A Level texts From Hodder, we see My Revision Notes for Pure Mathematics (MEI). Noting the link (on the left) to Answers and Full Worked Solutions, I was curious to see this document. Access to this resource requires registration (free) which I would highly recommend as this free resource is simply excellent. In 146 pages, the questions and fully worked solutions for each section are provided, the categories are ‘Target your revision’, ‘Exam-style’ and ‘Review’ questions. Whilst the document refers to the book, it is complete in itself. I do have and like this book, it is clear, attractively presented and written by very experienced authors. The companion Applied book, similarly has fully worked solutions.

Hodder texts

Hodder MEI A Level Texts

Note the five pages to scroll through to see the various texts; on page 2 you will find the AS Revision notes; again a pdf of full worked answers is available and also a complete set of Test yourself questions for each chapter in the book.

Hodder Test Yourself example

Hodder – Test Yourself example

The correct answer with reasoning is provided and also explanations as to why the other responses are incorrect.

Thank you to Hodder for providing such excellent and useful resources.

Maths Genie

Maths Genie

From Maths Genie, as well as all the excellent GCSE resources, we also have A Level worked examples. There are two AS Sample papers with worked solutions, Pure Mathematics and Statistics and Mechanics; also available are videos and examination questions by topic for both AS and A Level.

These resources have been added to the 16+ Resources series of pages.

Mathematics Competitions

October 2019

List of Mathematics Competitions – Wikipedia



Maths Careers Maths of Space Poster Competition 2019.
Closing date January 10th 2020.

MEI – Ritangle.
Registration for MEI’s Ritangle opened on October 7th. Ritangle is a competition for teams of students of A level Mathematics, the International Baccalaureate and Scottish Highers requiring no knowledge of mathematics beyond A level Mathematics.

There have been some great questions to challenge your older students in these Ritangle competitions. note the links to the questions and answers to the 2016-2018 competitions.

MEI Ritangle 2018 q1

MEI Ritangle – 2018, Question 1


Puzzle of the Week is a free international puzzle competition for schools. The new competition opened on 23rd September 2019. Though aimed at 11-16 year olds, anyone from a registered school can enter. The competition is very simple to run. Puzzles are published weekly on Mondays. School and student performances are recorded and leaderboards are published on the results page.

The Puzzle Library is a brilliant collection; all the previous puzzles are available with detailed answers including extensions and background information. The library is helpfully indexed by topic.
Puzzle of the Week

ParallelNot a conventional competition, but to challenge your able mathematicians, try Parallel from Simon Singh. All materials and resources are completely free and teachers will have access to all the student scores from the Parallelograms which are automatically marked.

Students do earn points depending on their percentage score on each Parallelogram, which in turn earns mathematical badges. There will be prizes for schools and students linked to the badges in future. Keep an eye on Parallel for the latest news.

Nrich publish problems regularly for which students can submit solutions; problems remain live for about 6 weeks. Nrich are inviting students to send solutions and will publish a selection of them, along with the name of each student and their school.

For more information, have a look at this Nrich article: I’ve Submitted a Solution – What Next?Nrich

The Math Contest 2.0.
Math Contest 2.0
The Math Contest, which was started in 1996 by David Rock and Doug Brumbaugh, is now sponsored by Casio Education and powered by The University of  Mississippi’s School of Education.

UK Maths Challenges


MEI Calculator Crunch

Calculator Crunch ran from 10th to 20th June, 2019. MEIMaths posted daily questions designed to develop important calculator skills for KS2–3 transition. The questions were designed to help Year 6s to be calculator-ready for secondary school and/or give extra practice to KS3 students. Note the extras – download lesson plans for Year 6 and 7. MEI are aiming to bring the Calculator Crunch back for 2020

Maths Careers – Competitions Archives

Maths Week England 2020 will run from 9th–14th November 2020
Maths Week England – 11th-16th November 2019
Maths Week England aims to “Raise the profile of Mathematics throughout England, you can see the full aims here. Note the various competitions running including a Secondary and Post 16 quiz featuring questions for every age group from Y7 to Y13 and also the resources available. MangaHigh, Sumdog and TimeTables Rockstars are running competitions using their software for all schools whether or not they subscribe and we also have MEI’s Ritangle competition and Desmos Art Competition. All the details are on the Maths Week England competition page.

The Royal Statistical Society’s Statistic of the Year 2018 has now closed. Over 200 nominations in total, an RSS record were received. The judging panel, chaired by RSS’s president, Professor Sir David Spiegelhalter, of eminent journalists, economists, statisticians and pollsters have announced the results. All the results, both International and UK are given and cover a variety of issues from key environmental issues to the number of Jaffa Cakes in the Christmas tube!

The 2017 winners are similarly fascinating.

WorldMathsDay 2018World Maths Day is over! 7th March 2018 was the big day.

Follow World Education Games on Twitter and/or Facebook.

We can still practise our tables with these resources. There are many games available to help you practice your tables:

From Transum Software comes Flash tables which will present you with random questions from your chosen tables and then show the answer at the speed you select. Also from Transum, see this great Tables Collection which has several activities to try.


Try this Tables Test from which you can play at different levels.

BBC Skillswise though written for adults has some useful activities for students.

For a real challenge try a Find the Factors puzzle from Iva Sallay.

Flashcards – Mathematics

Common Angles Subject Content

Quizlet common angles

In a Year 11 lesson, doing some revision for a mock examination, one of my students mentioned that she had created a set of flashcards on Quizlet for the exact values of the trigonometric functions students are required to know for GCSE Maths. This resulted in a round of applause from the class – I am very pleased that so many students use flashcards.

How we learn is something I regularly discuss with my students. Retrieval Practice is so important for learning, we need to work out how to get information out of our students – not just how to put it in! From The Learning Scientists see these valuable resources to support learning techniques including Retrieval Practice. Note the excellent downloadable materials on study strategies. Each strategy is backed up by research.

‘Ditch your highlighter and get busy with your flashcards’ as this article in Time, summarising the comprehensive report released on Jan 9th 2013 by the Association for Psychological Science concludes. The authors, led by Kent State University professor John Dunlosky, looked at various learning tactics and rated each from high to low utility.

The authors conclude that the most effective learning techniques are distributed study sessions (last minute cramming is not effective) and more practice testing, the use of flash cards can be very helpful with this.

Flashcards AlgebraI thought I would check Quizlet to see what is currently available for GCSE Mathematics. I noticed this for GCSE Foundation for example and another set for GCSE Revision; note that you can scroll down and see all the cards in the set. The quality clearly varies, I think I’ll get writing some sets myself to use in class – watch this space for more!

A first attempt! A set including images to test the common angles.
And a second – on Circle Theorems.
Quizlet common angles

Note that Quizlet includes the option to play games using the card sets.

Quizlet match game

Quizlet Match Game

Quizlet game

Quizlet Asteroid Game

Arithmagons and more…

Jonathan Payne - Arithmagons

Arithmagon Generator – Jonathan Payne

From Jonathan Payne, try this Arithmagon Generator. This is very simple to use and would be an ideal lesson starter. I like the option to use fractions, also to mix the question types as you see in the image. It is possible to choose missing sides, mixed or missing vertices.


This has been added to my Arithmagons collection which includes all the arithmagons you could ever want from the simplest to complex numbers and Calculus for older students!

Jonathan Payne - Missing AnglesAlso from Jonathan Payne, many more lovely question generators, try his Missing Angles question generator which has numerous options including Algebraic questions.
Jonathan’s collection of generators is here.

Jonathan Hall MathsbotOn the subject of question generators, we can turn to another Jonathan! Jonathan Hall’s has a wonderful collection of resources including question generators. His Differentiated Questions include numerous topics including several recent additions on Indices. These generators as you can see from the menu options can be customised to suit your class. They are also useful for student self-study.

Finally, from not a Jonathan, but John Tranter on Transum, this Custom Starter allows teachers to select the number of questions and the topics to include; scroll down the page and choose the topics you want from the Concept Selection.
Transum Revision

It is possible to save a particular selection of topics as the URL for your selection will be generated. It is also possible to drag the panels so your questions are displayed in the desired order.

The beginning of a lesson can be a good time to review previous learning, starters like these can be ideal. On the very important subject of reviewing previous learning, see Retrieval Practice.