## Tuesday 15 May 2012

### Introduction

We were continuing our investigation into 2D shapes. Our next focus was on squares and what we could do with them.

### Challenge 1

How many different ways can you arrange 3 squares?
• Rule - they had to join by a complete side, not by corners or part of a side
Here's a solution as discovered by one of the students:

Significant discussion ensued about flips and turns.
Were these shapes all different or just translations of the same shape?

### Challenge 2

How many different ways can you arrange 4 squares?
• Same rules apply
This is what we got. Note that we had by now eliminated duplications of the same shape in different orientations.

### Challenge 3

Now try it with 5 squares.

A bit more difficult but we think we found them all

### Challenge 4

Find the pattern.

If 1 square can have 1 solution
2 squares has 1 solution
3 squares has 2 solutions
4 squares has 5 solutions
5 squares has 12 solutions....

What comes next?

#### 1 comment:

1. 6 squares = 27 solutions

Any comments you would like to make?