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

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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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This activity investigates how you might make squares and pentominoes from Polydron.

Three Squares

Age 5 to 11 Challenge Level:

Daniel from Pewsey Primary, Kieren from St Luke's in Sway, Rebecca from The Grange School and Sports College, Tim and Tom from Stratton Upper School, Lewis from Beaupre Community Primary School and Maisy who learns at home, all agreed that three overlapping squares could make eight squares in total. Maisy sent in a picture which shows very clearly how the three squares are overlapped and where the eight resulting squares are:

overlapping to make 8

Maisy went on to suggest that if four squares are overlapped in a similar way, you can make sixteen squares:

four overlapping squares

Well done too to Jacob from St Edburgs who found this arrangement of the squares, but didn't quite count them all.

I wonder how many squares we could make from five overlapping squares, or six ...? What would you predict? Why? Perhaps you can test out your ideas.