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

Tiles on a Patio

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


Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

More Transformations on a Pegboard

Age 7 to 11
Challenge Level

You might find it useful to use one or more of the following:
Spotted paper in squares 
- Nail boards with elastic bands
- The on-screen interactive board
- Squared paper.

You could try finding all the different right-angled triangles by moving one point first, then moving a second point, then the third.
Why not try with the top left corner to start with? Where could this point move to?
How will you kow that you have them all?
Have you decided how to record your work?