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 game of Countdown is  great way to start or end a lesson.


You can download an excellent free programs for the Numbers Game from Chris Farmer’s CSF Software site.

For a low tech solution print out the Make a number puzzles with solutions from Brain Food.
For other number puzzles see the Number page on Mathematics – Games.

For a new challenge why not try Coundown with Fractions from Nrich? See also the Nrich Countdown collection.

Desmos Delights!

Regular readers will know I am a huge fan of the wonderful Desmos graphing calculator.

Take a look at the newly designed home page for some brilliant examples.
Click on any of the graphs to explore further and have a look at the equations used.
I have found this instructive for learning more about the syntax one can use.

For example one can plot individual points: (click the image for the Desmos page)

…or restrict the range:

I thought I would create a slideshow for my students showing the different types of graph which they should be familiar with at GCSE (taken at age 15-16 in the UK).
Each slide links to a Desmos page where they can use the sliders to explore families of curves.

This has also been uploaded to Mathematics for Students.

Happy Easter

Happy Easter 2017! (Click the link and WolframAlpha will tell you more than you wanted to know about Easter Sunday!)

Since it’s a holiday we should be relaxing! A conversation on Twitter (click the link for an updated post on Twitter) this morning reminded me of the excellent Set Game – a daily puzzle which is provided by the new York Times for age 6 – adult.

For many more puzzles and games see one of the companion blogs to this on Strategy Games and Puzzles. 

Wishing you all a very Happy Easter.