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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?

Lawn Border

Age 5 to 11
Challenge Level

I was trying to imagine what my lawn would look like with a nice paved border around it. So I used some tiles that were all the same size but different colours, to build a little model. This is how it looked:


Make some kind of model or picture of your own that shows the same sizes.

Look at the number of tiles for different parts.

I wondered what my border would be like if I changed some of the tiles. I made it like this:


What do you notice has changed?

I decided I'd make some more changes to my model garden. I did this.


How does this compare with the last one?

I made one last model with some different tiles. Here it is. I liked this one.


Have a good look now at the numbers of the different tiles in different places for each of my models.

If I use $12$ tiles to make a lawn, how many tiles would I need to make a border?

How many differently shaped lawns can you make with $12$ tiles?

Do you need a different number of border tiles to go around each lawn shape?

Can you make models to show what the different gardens would look like?