### 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.

### 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.

### Pebbles

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?

# Triangular Hexagons

##### Stage: 2 Challenge Level:

Well these are things that some of the children have found out and they've been put together for ease of exploring.

Using Equilateral Triangles that are two units along each side - 3 dots for each side.

 Dots Lines Triangles Around Inside Total Unit length Others 1/12 7 19 12 9 6 2/24 37 61 42 15 24 3/36 91 127 120 21 54 4/48 169 217 156 27 96

Well if you look at these sequences and explore them there's certainly a lot going on.

Then there are the patterns for equilateral triangles of 1 unit length sides.
One group of children were exploring the number of dots used in each successive size of hexagon and got: 1st 7
2nd 19
3rd 37
4th 61
5th 91
6th 127
They noticed that they are . . . . all PRIME !!!

Then one noticed that they were all related by taking one away and dividing by the order number. So 7 minus 1 divided by 1 is 6 And 19 minus 1 divided by 2 is 9 etc. and he got the sequence
6 9 12 15 18 21