Tuesday, 15 May 2012

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?



No comments:

Post a Comment

Any comments you would like to make?