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Turning Cogs

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

Kathryn from Ardingly College Junior School described the way the cogs move:

If you turn the cogs to the right they will move away from each other, but if you turn them to the left they will move towards each other. This is the same no matter which sized cogs you have.

Ollie and Tom, also from Ardingly College Junior School, put this a bit differently:

One cog moves one way and the other the other way.

Alternatively, you could say that one moves clockwise and the other anticlockwise.

Unfortunately we didn't have any solutions for the next part of the question. Have a look at our solution and test it for yourself:

 

 

With two identical cogs, the marked tooth on one cog will always go in the same gap on the other cog.

If the cogs differ in size by one tooth, then eventually, the marked tooth on the smaller cog will fit into each gap in the larger cog in turn.

If the number of teeth on each cog share a common factor, then a marked tooth on one cog will never go in all the gaps of the other cog.

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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