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Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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.

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?

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?