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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!

### Cutting Corners

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

### Cut and Make

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

# Sorting Symmetries

##### Age 7 to 11 Challenge Level:

Many of you wrote to tell us that there were six ways of posting the triangle into the shape sorter. JC explained:

There are six ways to put the triangle into the hole. On the blue side, you can have the dot in the top angle, the bottom left or bottom right angle. It is the same on the flip, yellow, side!

Mike tackled the second part of the problem (using the diagrams below):

I will call these six symmetries A, B, C (along the top row) and D, E, F (along the bottom row).

If you turn triangle A 120 degrees clockwise you get to position B. If you then flip it vertically you go from B to F.

If you turn triangle A 120 degrees anticlockwise you get to position C. If you then flip the triangle you get to position E.

Philippa also noticed that you can do a whole turn before flipping:

If you turn triangle A 360 degrees clockwise or anticlockwise you get back to position A. If you then flip it you get to position D.

Well done everyone!