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Can you make five differently sized squares from the interactive tangram pieces?


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?


Age 7 to 11
Challenge Level

Do you have any Polydron in your school?
Here are some questions about the square Polydron.

You can see in the picture that a square can be made in two different ways.
  • How much bigger is the one made from 4 right angled isosceles triangles than the one made from just one square Polydron?

Polydron is great for connecting and folding pieces together. 
Using only square Polydron you can can easily click them together to make other shapes.
If you connect five squares together we call it a pentomino.
There are 12 different ones.
  • Can you find them all?
  • Do all your pentominoes have the same perimeter length?
  • How many pentominoes have line symmetry?
  • Rotational symmetry?

What if you could fold them up?
  • How many of the pentominoes will fold up and clip together to make 'lid-less' boxes? Why not discuss first which will fold up and which won't, before trying to fold them?