### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

### Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?

# Fitted

##### Stage: 2 Challenge Level:

If you are a teacher click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on ...

Nine squares with side lengths $1, 4, 7, 8, 9, 10, 14, 15$ and $18$ cm can be fitted together with no gaps and no overlaps, to form a rectangle.

What are the dimensions of the rectangle?

Once you've had a chance to think about it, click below to see how three different pupils began working on the task.

This is how Anna started:

Here is what Brendan tried:

Here is Chandra's initial approach to the problem:

Can you take each of these starting ideas and develop them into a solution?