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Reasoning about the number of matches needed to build squares that share their sides.

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Tangram Paradox

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Peg Rotation

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Here we have a kind of peg board. The holes go all the way through so the pegs may be seen from the top or underneath.


You'll see the 4 blue pegs.
Now the peg board is either:
  • flipped over - north to south, OR east to west, OR north-east to south-west, OR north-west to south-east;
  • or it is rotated clockwise or anticlockwise.

Can you find out which movements could produce the four next views?

You could make some of your own and get your friends to see if they can find how you've moved it to make your next picture.
Try now to put 4 pegs in so that when you do a move with the board it still looks the same.

Now I've made a triangular board to do the same things.
Here's the starting view:

How has it been moved to show these views?

Hope you've had fun exploring these.
Can you think up ways of changing what I've done so that you can explore further?