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Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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Making Cuboids

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Counting Cogs

Age 7 to 14 Challenge Level:
Which pairs of cogs have you found that work?
Which pairs didn't work?
Do you get a sense of why?
What do you notice about the numbers of teeth in each case?