Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
A man paved a square courtyard and then decided that it was too
small. He took up the tiles, bought 100 more and used them to pave
another square courtyard. How many tiles did he use altogether?
Can you work out the area of the inner square and give an
explanation of how you did it?
A $2$ by $3$ rectangle contains $8$ squares. Can you see how?
A $3$ by $4$ rectangle contains $20$ squares. Can you see how?
A $4$ by $6$ rectangle contains $50$ squares. Can you see how?
What size rectangle contains exactly $100$ squares?
Is there more than one?
Can you find them all?
Can you prove that there are no more?
Click here for a poster of this problem.