## Thursday, 23 May 2013

### Triangle Mysteries

Here's a great pattern investigation, that got all of us in Year 5G thinking about patterns in a fresh way - fresh because we'd not come across anything quite like it before.

The activity comes from Steve Humble, and appears in the New York Times. We didn't look at the random aspect of it; we concentrated on what we could see in terms of patterns and rules.

The idea is to to start off with an empty grid like this:
opening it in Paint. Each hexagon in the top row is filled with blue, red or yellow.

Then for the second row these are the rules:
1. If the two hexagons above are the same colour as each other, then the hexagon below is that colour.
2. If the two hexagons above are different colours, then the hexagon below is the third colour.

Here are some of our patterns:

The patterns are great, but it was the thinking that was the most interesting part!

Here are some of our thoughts, our general statements, about the patterns. Some of them are not in fact true, some of them need investigation...

William: With some of them you turn them and you get the same pattern.

Sophia: There's often a triangle in the pattern.

Jessica: Sometimes you can guess what the colour will be at the bottom.

Chris: If you start with just red and yellow the bottom hexagon will be blue. (Is this always true??)

Christophe: The only one that doesn't have a triangle of colour in it is mine:
Florian: You never know what the colour will be at the bottom.

Jessica: You can tell if it's done correctly because usually there are downward-pointing triangles, never upward-pointing triangles.

Jessica: There is usually a pattern but not always.

Anna: The pattern still works when it is rotated.

Anna: Some of the shapes are symmetrical.

The next day, some of us had time to model a few triangle mysteries in other materials:

and in the playground -