Magazines

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.

Stairs

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.

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Taking a Die for a Walk

Stage: 1 and 2 Challenge Level:

It would be useful to have a real dice and some squared paper to record on.
You could begin by always starting with $1$ on top and making a certain number of rolls, for example. How many different paths can you make?
What do they have in common? What is different about them?