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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.


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.


Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Taking a Die for a Walk

Age 5 to 11 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?