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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?

Through the Window

Age 7 to 11
Challenge Level
We had these submissions from Colwich Primary School:

Ben and Will 

There are six windows shown and you could put them in pairs of windows which have the same perimeter but different areas, or the same areas but different perimeters. 

We chose to work with the £150 and £140 windows which have the same perimeter, but different areas. 

For the £150 window, A = 9 and P = 12.  For the £140 window, A = 8 and P = 12. 
This showed us that 1 square of A = £10. 

For the £140 window, this means that A = £80 and P = £60, which means that 1P = £5. 

So the answer is that a piece of glass costs £10 for every square of area, plus £5 for every square edge.

We checked our answers on all the other pieces of glass, and it worked every time.

Thank you very much for these submissions.