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

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Tiles on a Patio

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

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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?

My New Patio

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

We haven't received a solution for this problem yet - do let us know if you find anything out. Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried. Teachers - you might like to send in a summary of your children's work.


Here are a few of the possible solutions for a space in the top left hand corner.

BUT, Early in 2015 we received email  an email from Year 5 at Highfield C E Primary School in Southampton in the UK.
The solution was displayed as follows
Thank you for this excellent solution, please send in more solutions to otherchallenges.


Here are some answers when the space is near to the middle.


Here are some answers when the space is about half way down the left hand side.