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__Introduction__

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

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__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?*

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__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.

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__Challenge 3__

Now try it with 5 squares.

*A bit more difficult but we think we found them all*

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__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?

6 squares = 27 solutions

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