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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?
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?
Which pairs didn't work?
Do you get a sense of why?
What do you notice about the numbers of teeth in each case?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.