Spirograph
Have you ever heard about a thing called "Spirograph" ?
Actually it is a toy for kids, but it has a nice mathematical background.
How it works: You take a pencil, put it through a small hole in the inner circle, while you make the inner circle roll around the inside of the outer circle continuously.
What is going to happen then? You will find it out by doint this worksheet.
Important (!) before you start playing:
-To delete the trace in the application, simply press "Strg + F".
If you are working with a Mac, press "Command + F".
Now play with the construction below and work through the points at the bottom of the page.