As a child a favourite toy was my Spirograph with which I could generate endless pretty curves! Speaking of my favourite toy, there is a wonderful electronic version available.

The Nrich problem ‘Making Maths: Planet Paths‘ challenges students to draw some planet paths using a Spirograph. In case there is no Spirograph to hand they give instructions for making a simple one.


Spirograph – Desmos

Alternatively try an online version. Try Spirograph on the Desmos Graphing calculator.

This applet from wordsmith.org (requires Java) allows you to have the moving circle either inside or outside the fixed circle. You can alter various parameters and experiment.

From mathplayground.com comes this very clear and easy to use applet (the moving circle is outside the fixed circle).

Spirograph - Autograph Activity

Spirograph – Autograph Activity by Owen Elton

Owen Elton has written an excellent Spirograph Autograph activity (see Simon’s comment below) and also available on the Autograph player a very impressive 3D Spirograph!

For GeoGebra fans there are various applets available, including this which allows colour changes.

A little problem – solutions

If you have just read ‘A little problem for the holidays…

The clue is to stop thinking about the Maths and find your inner child!

Let’s reorder the numbers, does that help?

Why has 8809 been assigned a value 6 and 0000 a value 4?
What about all the numbers assigned a value of zero?

Scroll down for the answer …….





The value assigned to 2581 should be 2 as there are two closed loops!

A little problem for the holidays….

My son sent me the following problem which I have since discovered has been doing the rounds on the Internet.
I cannot find the original source – thank you whoever originally posed the problem!

This problem can be solved by pre-school children in five to ten minutes, by programmers in an hour and by people in higher education ….well, check it yourself!

I’m pleased to say despite my various Maths degrees I solved the problem quickly!
I obviously have the mind of a pre-schooler!
You can find a hint then check the answer here.

I present the problem as posed everywhere – though it looks like a misuse of the = sign!

The problem reminded me of some fun sequences to try with your students!
Get them thinking outside that box!

Try these ….

2, 3, 3, 5, 10, 13, 39, 43, 172, 177, …

2, 12, 1112, 3112, 132112, 1113122112, ….

For the answers and several more puzzles see Puzzle Sequences from the Online Encyclopedia of Integer Sequences.
See also this post on Sequences for further resources.

More puzzles resources.

Sumdog – practise with those directed numbers….

….and other arithmetic skills.

Sumdog provides free numeracy games at 10 different levels. For a great way to practice adding and subtracting with negative numbers, play these games at level 10.  There is a complete list of topics at each level here. Students can choose from several games.

I like the way that the various skill levels can be restricted; the site is aimed at students aged 6 to 14 (having said that some of my Year 11 (age 15-16) students looked like they were rather enjoying themselves recently) so I want my secondary age students to practise the skills at the upper end of the age range and have currently restricted them all to levels 8, 9 and 10. It is possible to set up competitions which I have done very successfully with Year 10 as one of our many Enrichment Week activities. See the Teachers’ page, also the help section for teachers.

Sumdog are creating a library of videos to help teachers get the most out of Sumdog.

I have linked to information for students on the companion Mathematics blog for students.

You can choose to play as a guest or sign up (free) so you can save your scores and see how you improve over time. The games are all completely free to use as are several other features for teachers.

You can follow the Sumdog blog for all the latest features.

Manga High – Prodigi Quizzes

Teachers here’s everything you need to know about getting started at Manga High.

Manga High seems well known for its games, it is also well worth investigating the excellent Prodigi quizzes available.

Hundreds of these are available offering excellent curriculum coverage. To access the resources select Challenges from the Activities menu.

The search facility offers teachers the opportunity to filter by curriculum area, age, level and whether a calculator is allowed; for example a simple search of Prodigi quizzes on Algebra gives the results as shown below. (A complete list of all quizzes is available here.)

Unlike the available games students cannot see the available Prodigi quizzes unless a teacher sets them as challenges (or you have a subscription). You can view very clear instructions on setting challenges on the Manga High website.