Clapping Times
Problem
Clapping Times printable sheet
For this activity, you'll need to work with a partner, so the first thing to do is find a friend!
Together, count from 1 up to 20, clapping on each number. When you clap on a number in the two times table, clap more loudly and say the number more loudly. Clap and speak quietly on the other numbers.
Now clap the five times table together up to about 30, so this time you are clapping more loudly and speaking loudly on the numbers in the five time table and quietly on the others.
If one of you claps the twos in this way and one of you claps the fives, at the same time, can you predict what you would hear?
Which numbers would be quiet?
Which numbers would be fairly loud and which would be very loud?
Now try it - what did you hear?
Were you right?
Choose another pair of tables and repeat what you have just done.
How about the twos and tens?
What about the fives and tens?
Each time, predict what you will hear before you clap - which numbers will be loud, which fairly loud and which quiet?
If you've enjoyed this activity and would like more of a challenge, try Music to my Ears.
Getting Started
Why will a number be quiet?
Why will a number be fairly loud?
Why will a number be loud?
You could use a number line or a number square to help you.
Student Solutions
Sam from Hitchin Boys' School, wrote in with a general solution to this problem:
My solution is that all the numbers that are a factor of neither of the numbers you use will be quietest.That's very clearly put, thank you Sam.
Teachers' Resources
Clapping Times
Clapping Times printable sheet
For this activity, you'll need to work with a partner, so the first thing to do is find a friend!
Together, count from 1 up to 20, clapping on each number. When you clap on a number in the two times table, clap more loudly and say the number more loudly. Clap and speak quietly on the other numbers.
Now clap the five times table together up to about 30, so this time you are clapping more loudly and speaking loudly on the numbers in the five time table and quietly on the others.
If one of you claps the twos in this way and one of you claps the fives, at the same time, can you predict what you would hear?
Which numbers would be quiet?
Which numbers would be fairly loud and which would be very loud?
Now try it - what did you hear?
Were you right?
Choose another pair of tables and repeat what you have just done.
How about the twos and tens?
What about the fives and tens?
Each time, predict what you will hear before you clap - which numbers will be loud, which fairly loud and which quiet?
If you've enjoyed this activity and would like more of a challenge, try Music to my Ears.
Why do this problem?
This activity 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.
Possible approach
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.
Key questions
Possible extension
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?