Play with the wonderful Spirograph!
As a child my Spirograph was definitely a favourite toy so I was delighted to find this digital version, Inspirograph by Nathan Friend. Try altering the gears so that the fixed and rotating gear are the same size, or make one size a factor of the other, make the two sizes have a common factor, or not! Investigate.
You can change the colours too and create a work of Art!
For some more Spirograph resources including from the awesome Desmos graphing calculator see this post.