What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

How many triangles can you make on the 3 by 3 pegboard?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?