GeoGebra Resources & more…

Tidy UpSummer holidays provide an opportunity for updates and tidying up.

There are many references to GeoGebra resources on this blog. A reminder here of some of the excellent collections available. I will make sure these resources are added to the relevant pages of resource collections over the next few weeks.


Edexcel – GCSE Higher

For A Level (16+) see this Edexcel’s useful guide for teaching A Level Maths with Geogebra.

The following Pearson collections accompany their textbooks but the examples are clearly shown and will be valuable for exploration for students who do not have the books.

Velocity time graph

Pearson – Mechanics

GeoGebra Institute of MEI.

An annual job, is to make sure links to grade boundaries and results statistics for GCSE and A Level are available in one place, hence my Results 2019 page. All links have been checked and I will make sure this is kept up to date.

Ofqual have just published, “We’ve got an app for that!” Ofqual has interactive apps which will allow you to compare your own results with the national and regional picture. These interactive apps include over time results for GCSE and A level subjects, results by county for a range of subjects and graphs that show the extent of variation in the results of individual schools and colleges over time.

The interactive graphs using the 2019 GCSE and A level results data will be available from the morning the results are issued, Thursday 15 August 2019 – release of AS and A level results to candidates and Thursday 22 August 2019 – release of GCSE results to candidates.

Ofqual app example

Puzzle Time…

Area MazeIt’s holiday time, an appropriate time to look at some puzzles!

On my Apps page, you will find Area Maze from puzzle inventor Naoki Inaba. Alex Bellos told the story in his Monday Guardian column. This is available as an App on Android and iOS.

Naoki Inaba’s website is in Japanese, but it’s an interesting exericse to look at the images of the puzzles and solutions and try and work out what the puzzles are all about!

You can find pdf versions of his work in the Math Puzzle Room and the The Real Puzzle Room and happily Sarah Carter on her excellent Math=Love blog has been very busy! Her own interest in the puzzles led to her translating puzzles and putting them into a more user friendly format for use in the classroom.

I do like these Step Puzzles. Step Puzzles
Sarah has given a clear explanationof these puzzles which I think are an excellent resource for teaching Sequences and Series. The original documents, puzzles and solutions are on Naoki Inoba’s website can be found in the pdf version of The Math Puzzle Room.

Simple Puzzle

Mobile Puzzles

For some more puzzles, have a look at these great mobile puzzles.


Or try an old faourite, The Set Game from the New York Times, select How to play for the rules. Note the various difficulty levels from Basic 1 through to Advanced 2.

OCR Maths have published some great puzzles.

See also, of course Catriona Shearer and  Ed Southall.
Shearer & Southall

And don’t forget Radio 4s Puzzle for Today.
Answers to puzzles for today are provided for a limited time.

Underground Mathematics – Review Questions

Underground Maths Mapping Review Questions

When is 6x7=42 a counter example.There are many Underground Mathematics Resource Types. I do like the Review Questions which in the words of the Underground Maths Team:

These are questions designed to test students’ understanding of one or more topics and to exercise their problem-solving skills. In many cases they can also be used as a classroom resource to help teach concepts and methods. They are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking. The hints and solutions are designed to explain the reasoning and highlight connections as well as giving the answer. In many cases, alternative methods or solutions are presented.

Read about the use of Review questions in the classroom on this Teacher Support page. The fact that these questions are designed to test understanding of one or more topics, exercise problem-solving and proof skills and help students make connections make them ideal for use in the A Level classroom. They can be used to introduce a topic or are also ideal for review, something which should be a regular part of linear courses.

You can browse all the Review questions or narrow your search by question type; note the O/AO-level questions which are questions from old papers. One can also search by line (Number, Geometry, Algebra, Functions or Calculus) and by Station.

The Underground Maths team put together a spreadsheet that offers resource suggestions for each of the content statements in the DfE specification.  Scroll down the page for the spreadsheet. 

For each content statement, Underground Maths have suggested up to three rich resources and up to three Review questions. Each suggestion is hyperlinked to take you directly to the resource on the Underground Mathematics site. Resources that are particularly good at supporting the overarching theme of Mathematical modelling have been highlighted.

I have used many of the Review Questions successfully, something I will continue to do. My spreadsheet here gives the review questions by title rather than just number for each section of the subject contents. My starting point is the suggested review questions, most of which I have included; these are personal favourites. I can later add any additional suggestions.
Underground Maths Mapping Review Questions
The latest copy of the spreadsheet on this page on Underground Maths which is one of a series of pages on A Level Teaching Resources.



Mathematical Miscellany #30

To begin this collection, two items where you need to act swiftly!

Jonny Griffiths Further RISPS

Jonny Griffiths investigative activities for the pure A Level Mathematics classroom are well known. He has now published Further Risps, forty rich tasks for the pure Further Mathematics classroom.

For just a few days, Jonny Griffiths is halving the cost of the Further Risps pdf ebook from £7.50 to £3.75.

I thoroughly enjoyed his excellent session for London Maths, ATM and MA London Branch on Saturday 11th May, where teachers enjoyed working on these activities. Two editions are available – a hard copy or pdf version. On this page you can see two trial activities, Further Risps 1 and 2.

The pdf not only provides the forty problems but also full teachers notes for each. The notes for each task begin with the topic or topics covered, identify the type of task, for example, introductory and state any preliminary knowledge required. This is a valuable resource for teaching Further Mathematics.

For A Level mathematics, Jonny has a wonderful collection of free RISPS, the details are included in my series of pages on A Level reources.

The second act swiftly item – a remnder from last week on A Level resources that you have until July 10th if you would like to download the 2019 AS & A Level Question Countdown sheets from crashMATHS, See AS Level Question Countdown and/or the A Level Countdown. Each set provides 10 worksheets of mixed questions with 7 questions on each sheet, 5 are pure questions and 2 are applied. The pure section of the worksheets includes a mix of basic, problem and modeling questions.Whilst written in the style of Edexcel, the subject content is the same for all examination boards.

CrashMaths Countdown

Jonathan Hall has added an Arithmagon generator on his wonderful Mathsbot site. As always with Jonathan’s resources you have choices to create the resource you want.
Jonathan Hall Mathsbot
This has been added to my Arithmagons collection where you will find all the Arithmagons you could ever want from the simplest to complex numbers and Calculus for older students!

From Ontario Math see these HTML5 mathies tools which  are designed for use in desktop or mobile browsers. A search on Google Play apps for mathies found them all. Mathies are also available on ios.
mathies apps

On the mathies tools site you will find full details and tips for use. With Notepad for example you can sketch diagrams, import pictures, create graphs on one of four backgrounds: grid, isometric dot, lined or blank. The app includes built-in line, shape and text annotation objects, including number lines, rulers, grids and polygons. It is possible to copy and rotate any annotation object. A tip sheet provides a clear summary of  all the features.

mathies Algebra Tiles

Mathies – Algebra Tiles

The Algebra Tiles app comes with support including a series of examples, this page provides complete documentation.

Penrose Triangle

A lovely activity for the end of term perhaps, try a lesson on Impossible Objects from  Clarissa Grandi on her marvelous Artful Maths (scroll down  to the third lesson, Impossible Objects).

All the Resources you need are provided, including a presentaion containing a selection of images of ‘impossible objects’; and very clear printable instructions for constructing three different types. The instructions are taken from the 1985 SMP 11-16 booklet ‘Impossible Objects’ a direct link to the instructions is provided.

Note that you can access SMP materials through These materials certainly bring back memories, I have SMP O and A Level Maths!

Workers of Zen

Workers of Zen

Speaking of the end of term, fast approaching for UK schools, there are several suggested activities on this page.