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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
William T.,  Joshua, Josh and William”¨ from Park Lane Primary School”¨ sent in the following:

First we took the top corner and translated it to every peg on the board and wrote down all of the right angled triangles. Then we did the same with the other two corners and got an answer of 24.

Thank you for these pictures of the shapes you made. You could explore further by visiting our sister site Wild Maths where you'll find our Dotty Grids pathway.  Take a look at Areas on a Grid.