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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?


Age 7 to 11 Challenge Level:


picture of beadsThree beads are threaded on a circular wire and are coloured either red or blue.
Can you find all four different combinations?

You now repeat the following actions over and over again:

  • between any two beads of the same colour put a red bead
  • between any two beads of different colours put a blue bead
  • then remove the original beads.
Describe what will happen to each of the combinations.

Why do this problem?

This activity presents a very non-threatening challenge that could be used to get pupils thinking. It is one of those activities in which pupils will probably not have an instant idea of the solution and so encourage creative thinking.

Possible approach

It would be good to use a white board displaying the interactivity for pupils to come and try out. This could lead quickly to some good classroom discussions.

Key questions

Why do you think that?
Tell me about you thoughts?
What do you mean by (such things as "goes on and on")?

Possible extension

Pupils encouraged to explore changing some of the numbers of beads. They could also change a rule slightly.

Possible support

Some practical apparatus to make a system of beads of their own.