5482
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2011-02-01T00:00:01
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For this activity, you'll need to work with a partner, so the first
thing to do is find a friend!<br></br>
Together count from $1$ up to $20$, clapping on each number, but
clapping more loudly and speaking loudly on the numbers in the two
times table, and quietly on the other numbers.<br></br>
Now clap the five times table together up to about $30$, so this
time you are clapping more loudly and speaking loudly on the
multiples of five and quietly on the others.<br></br>
<br></br>
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?<br></br>
Which numbers would be quiet?<br></br>
Which numbers would be fairly loud and which would be very
loud?<br></br>
<br></br>
Now try it - what did you hear?<br></br>
Were you right?<br></br>
<br></br>
Choose another pair of tables and repeat what you have just
done.<br></br>
How about the twos and tens?<br></br>
Why not try the fives and tens?<br></br>
Each time predict what you will hear before you clap - which
numbers will be loud, which fairly loud and which quiet?<br></br>
<br></br>
If you've enjoyed this activity and would like more of a challenge,
try <a href="http://nrich.maths.org/public/viewer.php?obj_id=5483&part=index">
Music to my Ears</a> .<br></br></mdoxml>
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<p class="editorial">Sam from Hitchin Boys' School, wrote in with a
general solution to this problem:</p>
My solution is that all the numbers that are a factor of neither of
the numbers you use will be quietest.<br></br>
<div style="clear: both;">The numbers that are factors of either
but not both will be the middle volume and the numbers that are
factors of both will be loudest.</div>
<div style="clear: both;"></div>
<p class="editorial" style="clear: both;">That's very clearly put,
thank you Sam.</p>
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<h2>Clapping Times</h2>
<br></br>
For this activity, you'll need to work with a partner, so the first thing to do is find a friend!<br></br>
Together count from $1$ up to $20$, clapping on each number, but clapping more loudly and speaking loudly on the numbers in the two times table, and quietly on the other numbers.<br></br>
Now clap the five times table together up to about $30$, so this time you are clapping more loudly and speaking loudly on the multiples of five and quietly on the others.<br></br>
<br></br>
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?<br></br>
Which numbers would be quiet?<br></br>
Which numbers would be fairly loud and which would be very loud?<br></br>
<br></br>
Now try it - what did you hear?<br></br>
Were you right?<br></br>
<br></br>
Choose another pair of tables and repeat what you have just done.<br></br>
How about the twos and tens?<br></br>
Why not try the fives and tens?<br></br>
Each time predict what you will hear before you clap - which numbers will be loud, which fairly loud and which quiet?<br></br>
<br></br>
If you've enjoyed this activity and would like more of a challenge, try <a href="http://nrich.maths.org/public/viewer.php?obj_id=5483&part=index">Music to my Ears</a> .</div>
<br></br>
<h3><span style="font-weight: bold;">Why do</span> <span style="font-weight: bold;">this problem</span><span style="font-weight: bold;">?</span></h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=5482&part=index">This activity</a> 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.</div>
<br></br>
<h3>Possible approach</h3>
<div>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.</div>
<br></br>
<div>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.</div>
<br></br>
<h3>Key questions</h3>
<div>Can you predict what you will hear?</div>
<div>Which numbers will be quiet? Why?</div>
<div>Which numbers will be fairly loud and which would be very loud? Why?</div>
<br></br>
<h3>Possible extension</h3>
<div>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?</div>
<br></br>
<h3>Possible support</h3>
<div>It may be useful for learners to use a $100$ square to record multiples on prior to, or during, this activity.</div>
<br></br>
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Why will a number be quiet? <br></br>
Why will a number be fairly loud? <br></br>
Why will a number be loud?<br></br>
You could use a number line or a number square to help you.<br></br></mdoxml>
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<mdoxml version="1.0">A number that is in both the two and five times tables (is a common
multiple of both 2 and 5) will be clapped loudly. These are 10, 20
etc ie multiples of ten. A number that is in only one table will be
clapped loudly by one person. A number that is not in either will
be heard very quietly.<br></br></mdoxml>
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Clapping Times
If you count from 1 to 20 and clap more loudly on the numbers in
the two times table, as well as saying those numbers loudly, which
numbers will be loud?
Numbers and the Number System
Factors and multiples
Using, Applying and Reasoning about Mathematics
Practical Activity
Applications
Music
Numbers and the Number System
Common factors
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