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Turning Cogs

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Turning Cogs


Pick two cogs in the interactivity below, place them near each other and turn one of them.
What happens?
(You can turn a selected cog by using the arrow keys on your keyboard or by using the green arrows on the interactivity.)

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Now pick a different pair and do the same thing again.

What do you notice about the direction in which the cogs turn each time?

Now pick two cogs with 5 "teeth".
Mark a "tooth" on each cog by selecting it and then pressing the blue button. You may like to line up the marked teeth so that they start next to each other.
Watch what happens to the teeth that are marked as the two cogs turn.
What can you say about the way that the marked tooth of one cog fits into the gaps of the second cog?
 
Will this always be the case whichever two cogs you pick?

This challenging problem can be taken to different stages by different children, but offers a starting point for all. Pupils should be encouraged to play with the interactivity and explore what happens. Drawing their ideas together will enable the class to offer some hypotheses and then they can test out their ideas. The problem is in fact about common factors (in the number of "teeth"), but some children may be happy to stick to cogs of the same size.

If the interactivity is not available, you might like to print off this sheet of cogs and cut them out for the pupils to use practically, or for you to demonstrate on an OHP.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.