Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

How many different rhythms can you make by putting two drums on the wheel?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

If you have only four weights, where could you place them in order to balance this equaliser?