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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!

Taking Steps

Stage: 2 Challenge Level: Challenge Level:1
There are several solutions to this, depending on exactly what questions you choose to ask.

Katie, Thomas, Abigail, Melita and Ellisha from Saxmundham Primary said that with the raised bricks, the pattern continues by adding one brick to each row. They also said that they could see 24 sectors round a circle in the middle, and that the pattern wouid keep continuing with 24 sectors in each layer.

When it came to the circles, they said:
"First we thought we could see part of a big circle at the top of the picture. Then we saw nearly a whole circle and bits of some others. There were 4 medium circles. The medium circles had 7 small circles inside. We drew the whole pattern and counted 28 small circles. Altogether there were 33 circles."

Thomas from C.C.J.S looked at what might happen if there were different numbers of each item to start with, and said:
"However many sectors you start with, the same number would continue as the rings get larger.

If there were 9 small circles per large circle and 16 large circles (multiple of 4 to get the right shape for the circle) per very large circle then there would be 144 small circles per very large circle."

Well done everyone! Have a go for yourself, and if you discover anything interesting, e-mail us to tell us about it.