IntroductionWe were continuing our investigation into 2D shapes. Our next focus was on squares and what we could do with them.
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?
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.
Now try it with 5 squares.
A bit more difficult but we think we found them all
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?