Why do this problem?
is a lovely practical way for children to investigate common multiples and to gain familiarity with their tables. It also allows children to make and justify conjectures.
You could start by inviting everyone in the group to clap and count the two times table at the same time so that all the children understand what is happening.
Ask pupils to talk in pairs about their predictions for each combination first and then pool ideas from the whole group, listening out for good explanations. Then each pair can test out the counting and clapping to check the class response. Alternatively, you could split the group into two and clap as a whole, or one pair could demonstrate the combination each time.
Can you predict what you will hear?
Which numbers will be quiet? Why?
Which numbers will be fairly loud and which would be very loud? Why?
You could extend this activity by asking each pair to join with another pair. They could try the $2$, $3$, $4$ and $5$ times tables altogether. How long will they have to clap before they get to a number which is clapped loudly by all of them? Can they predict this before clapping?
It may be useful for learners to use a $100$ square to record multiples on prior to, or during, this activity.