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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Paving the Way

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?

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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Squares in Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A $2$ by $3$ rectangle contains $8$ squares. Can you see how?

2 by 3 rectangle

A $3$ by $4$ rectangle contains $20$ squares. Can you see how?

3 by 4 rectangle

A $4$ by $6$ rectangle contains $50$ squares. Can you see how?

4 by 6 rectangle


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?

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