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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?

Two Squared

Age 7 to 11
Challenge Level

Cameron from Quenn of the Apostles School sent in the following;

Everything can be done, as hard as it may seem, except for the hexagon.
When I couldn't figure it out I asked my mum and she said that my answer was the best.
You will need to use three half cut hexagons and one full one.
You put the full hexagon in the centre, next you put two halves at the bottom making sure they fit, do the same to the top, next put the last two halves at the sides. See how there are still gaps? This is not possible without more hexagons.

We had separate solutions sent in from Fulham Cross Girls' School from the following pupils, Tianah, Iania, Hagar, Alaa, Rachea, and Jessica. Here are two of them:

Firstly, with your first shape, in your head or on a piece of paper build up your shape e.g four squars as a cube. Then see if it matches with your big shape and count how much shapes there was in your shape your big shape.

I think that you put the the small square inside the big square in any of the corners that's two squared. If you put the small rectangle in the top/bottom left/right corner that's two squared too.

Well done ALL of you!