## Friday, 27 January 2012

### Pattern Blocks

Another maths "manipulative" (as they called them in the US - I'm not sure what the equivalent British term is). This time the pattern block, invented in the 60s, if something so simple can be said to be invented:

We got them out. Not just ours, but everybody's on the primary corridor. We'd been looking at Islamic patterns, and a good way to create our own was to use the blocks.

Luckily - because it would be hard to do it on paper - there's an online way to record, and extend what was done by hand with the blocks, and to save the images and publish them to the web.

We made the distinction between pattens that could potentially continue for ever, and ones that are growing from a centre but which perhaps can't be continued outwards indefinitely. There's something very compelling about those mandala-like patterns that grow from a centre and some of the class were reluctant to switch to a repeating and infinitely repeatable tessellation.

Next, we had a look at a few of the dodecagons it's possible to make with pattern blocks. Everyone made their own "badge", their own dodecagon.

(I liked the idea of making physical badges, and if the school had a badge maker I would have done it.)

We paused to look at the symmetries in the dodecagons. They have different numbers of lines of symmetry. Some with no reflective symmetry have rotational symmetry.

Three of the pattern blocks have areas that are multiples of the triangle's area. So that leads on to considering fractions. It's also worthwhile to look at the angles, seeing how many of each shape can fit around a point.

And finally, we touched briefly on the idea of a geometric proof. As these two dodecagons below have the same area:

how would you break the first up and remake it as the second? You'd have to swap a square for two thin rhombuses. So we've demonstrated the relative areas of these two.