Music to My Ears
Why do this problem?
This activity centres on factors and multiples in a very practical context, and introduces the idea of common multiples.
Possible approach
You could introduce the first rhythm yourself by clapping and clicking, and asking the questions orally. This will encourage children to listen carefully and think about how the beat number connects to the different actions. The important point here is that pupils will understand how the repeated pattern links with factors and multiples, and this will enable them to predict where certain actions will occur. Learners might articulate this in different ways, for example, by referring to numbers which are in certain 'times tables'. Of course, you can invite some children to physically demonstrate the rhythms so that the group's hypotheses are checked (at least for lower numbers of beats!).
Key questions
Possible extension
As an extension you could ask pupils to investigate and prepare an example of two rhythms to bring back as a challenge for the rest of the class, for example CCCT, CCCT, CCCT ... and CCT, CCT, CCT ... (where C is clap and T is tap). Here the Ts coincide on all multiples of 12. This problem has kept the ideas quite simple by only allowing one tap in a sequence and always at the end. This could be made more difficult by allowing the tap anywhere or having more than one tap.
Possible support
Clapping Times makes a good introduction to this problem which many learners would benefit from doing first.
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