Playing with Squares

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?