7185
/www/nrich/html/content/id/7185/
1
2011-02-01T00:00:01
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"Ip dip sky blue! Who's 'it'? It's you!"<br></br>
<br></br>
Have you ever used this rhyme to decide who is 'it' in a game?<br></br>
<br></br>
If you were playing a game with one friend and you wanted to be chosen to be 'it', would you start the rhyme pointing at yourself or your friend?<br></br>
<br></br>
If there were three of you, how would you position yourself so that you were sure you'd be chosen?<br></br>
<br></br>
How about with four of you? Five ...? Six ...? Seven ...? Eight ...? Nine ...? Ten ...? And so on?<br></br>
<br></br>
How would you predict where you should stand to be chosen for any number of players?<br></br>
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<p class="editorial">Tommy from Oswald Road Primary School gave a
very clear general way of describing where you would want to stand.
He wrote:</p>
<br></br>
If there are $8$ or more players, be $8$th.<br></br>
If there are fewer than $8$ players, keep subtracting the number
of players from $8$ as many times as you can, but don't get to $0$
or less. The remainder you are left with is the position you should
be in.<br></br>
<br></br>
<p><span class="editorial">Well done, Tommy. Amanda from Knights
Templar wrote this in a slightly different way and explains where
the number $8$ has come from:</span></p>
<br></br>
If the number of people is less than $8$ (the number of words) then
you do $8$ - the number of people $= n$. You position yourself
where $n$ is said, so if $ n = 5$ you would make sure you were
$5$th. If the number of people is more than the amount of words
($8$) then you just go $8$th as then the last word would end on
you.<br></br>
<br></br>
<p><span class="editorial">Thanks to both of you and to Ed,
Llewellyn and Alistair from St Peter's. I wonder how you reached
these conclusions? It would be interesting to know what you had
tried to get you this far.</span></p>
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<h2>Ip Dip</h2>
<br></br>
"Ip dip sky blue! Who's 'it'? It's you!"<br></br>
<br></br>
Have you ever used this rhyme to decide who is 'it' in a game?<br></br>
<br></br>
If you were playing a game with one friend and you wanted to be chosen to be 'it', would you start the rhyme, pointing at yourself or your friend?<br></br>
<br></br>
If there were three of you, how would you position yourself so that you were sure you'd be chosen?<br></br>
<br></br>
How about with four of you? Five ...? Six ...? Seven ...? Eight ...? Nine ...? Ten ...? And so on?<br></br>
<br></br>
How would you predict where you should stand to be chosen for any number of players?<br></br>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/7185&part=">This problem</a> offers the opportunity for children to work on some mathematics that might be meaningful to them and therefore engaging. At a basic level, it involves counting, but it is a good context in which children can be encouraged to identify and explain patterns using their knowledge of factors and remainders.</div>
<br></br>
<h3>Possible approach</h3>
<div>You could start by having a pair of volunteers standing up together so that everyone can see them. Ask the children to imagine that they are going to play a game of tag, or something similar. How would they choose who was going to be 'it' i.e. the person to do the chasing? Take some suggestions, which might involve some rhymes that are currently popular. You could choose to
go with one of these, or introduce the "Ip dip ..." rhyme with which some might already be familiar. (The important point at this stage is that the rhyme identifies the person to be 'it' straight away, having said it only once.)</div>
<div> </div>
<div>Say the chosen rhyme together a few times so that everyone feels they know it well and then indicate that you're going to find out who is going to be 'it' from the two volunteers. Say the rhyme while pointing to the children alternately. You could then pose the question about who you would start the rhyme on if you wanted to be chosen. Give the whole group a chance to
talk in pairs about this, then test out their ideas. You can then encourage pairs to work together to discover where you would position yourself if there were three of you ... four ... five etc.</div>
<div> </div>
<div>It may be appropriate to stop everyone after some time to share ideas so far. This might involve some pairs explaining how they are approaching the problem and sharing some possible ways of recording what they're doing.</div>
<div> </div>
<div>In the plenary, you can agree on solutions for the different numbers of people but also encourage children to talk about what they notice and to explain why where possible. How could they predict where to stand if there were seven people, for example, or ten people or a hundred people? Some might find it tricky to articulate where to stand for fewer than eight people, but a few
demonstrations with larger numbers will mean they are able to explain where to be for eight or more relatively easily. Can they tell you why eight is the 'key' number?</div>
<br></br>
<h3>Key questions</h3>
<div>What numbers of people have you tried? What did you find out?</div>
<div>How are you going about this problem? Tell me what you've done.</div>
<div>How will you remember what you've found out?</div>
<div>Do you notice any patterns?</div>
<div>Can you explain the patterns?</div>
<br></br>
<h3>Possible extension</h3>
<div>Some children may like to try with another version of this rhyme which makes the analysis much more tricky: "Ip dip sky blue! Who's 'it'? Not you!" so that a person is 'knocked out' each time and the only person left is 'it'. What happens when there are two people? Three? Four etc? Can they see any patterns emerging? Can they explain why the
patterns occur? Similarly, learners might like to test out the best places to be positioned for a rhyme of their choice.</div>
<br></br>
<h3>Possible support</h3>
<div>Having counters or other objects available to represent people might help some children. </div>
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How will you remember who is 'it' for different numbers of
people?<br></br>
You could use something like counters or cubes to represent
people.<br></br></mdoxml>
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<mdoxml version="1.0">Ip dip sky blue! Who's 'it'? It's you!<br></br>
<br></br>
Two players - second person is chosen.<br></br>
Three players - second player chosen.<br></br>
Four players - fourth player chosen.<br></br>
Five players - third player chosen etc<br></br>
<br></br>
Number of words in rhyme is 8.<br></br>
For number of players = 8 or fewer, divide 8 by the number of
players. If there's no remainder, the last person is chosen.
Otherwise, the remainder is person chosen.<br></br>
For number of players greater than 8, want to be eighth
person!<br></br>
<br></br>
<br></br>
Ip dip sky blue! Who's 'it'? Not you!<br></br>
<br></br>
Eight words<br></br>
<br></br>
Two players:<br></br>
<br></br>
<table border="1">
<tbody>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>1</td>
<td>2</td>
<td>1</td>
<td>2</td>
<td>1</td>
<td>2</td>
</tr>
</tbody>
</table>
<div> </div>
<div>Player who is first is left.</div>
<div> </div>
<div>Three players:</div>
<div> </div>
<table border="1">
<tbody>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>1</td>
<td>2</td>
<td>3</td>
<td>1</td>
<td>2</td>
</tr>
<tr>
<td>3</td>
<td>1</td>
<td>3</td>
<td>1</td>
<td>3</td>
<td>1</td>
<td>3</td>
<td>1</td>
</tr>
</tbody>
</table>
<div> </div>
<div>Player who is number 3 is left, assuming rhyme continues from
last person</div>
<div> </div>
<div>Four players:</div>
<div> </div>
<table border="1">
<tbody>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>1</td>
<td>2</td>
<td>3</td>
<td>1</td>
<td>2</td>
</tr>
<tr>
<td>3</td>
<td>1</td>
<td>3</td>
<td>1</td>
<td>3</td>
<td>1</td>
<td>3</td>
<td>1</td>
</tr>
</tbody>
</table>
<div> </div>
<div>Player who is number 3 is left, assuming rhyme continues from
last person</div>
<div> </div>
<div>Five players:</div>
<div> </div>
<table border="1">
<tbody>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>1</td>
<td>2</td>
<td>3</td>
</tr>
<tr>
<td>4</td>
<td>5</td>
<td>1</td>
<td>2</td>
<td>4</td>
<td>5</td>
<td>1</td>
<td>2</td>
</tr>
<tr>
<td>4</td>
<td>5</td>
<td>1</td>
<td>4</td>
<td>5</td>
<td>1</td>
<td>4</td>
<td>5</td>
</tr>
<tr>
<td>1</td>
<td>4</td>
<td>1</td>
<td>4</td>
<td>1</td>
<td>4</td>
<td>1</td>
<td>4</td>
</tr>
</tbody>
</table>
<div> </div>
<div>Player who is number 1 is left, assuming rhyme continues from
last person</div>
<div> </div>
<div>Six players:</div>
<div> </div>
<table border="1">
<tbody>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>1</td>
<td>2</td>
</tr>
<tr>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>1</td>
<td>3</td>
<td>4</td>
<td>5</td>
</tr>
<tr>
<td>6</td>
<td>1</td>
<td>3</td>
<td>4</td>
<td>6</td>
<td>1</td>
<td>3</td>
<td>4</td>
</tr>
<tr>
<td>6</td>
<td>1</td>
<td>3</td>
<td>6</td>
<td>1</td>
<td>3</td>
<td>6</td>
<td>1</td>
</tr>
<tr>
<td>3</td>
<td>6</td>
<td>3</td>
<td>6</td>
<td>3</td>
<td>6</td>
<td>3</td>
<td>6</td>
</tr>
</tbody>
</table>
<div> </div>
<div>Player who is number 3 is left, assuming rhyme continues from
last person</div>
<div> </div>
<div>Seven players:</div>
<div> </div>
<table border="1">
<tbody>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>1</td>
</tr>
<tr>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>2</td>
<td>3</td>
</tr>
<tr>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>2</td>
<td>4</td>
<td>5</td>
<td>6</td>
</tr>
<tr>
<td>7</td>
<td>2</td>
<td>4</td>
<td>5</td>
<td>7</td>
<td>2</td>
<td>4</td>
<td>5</td>
</tr>
<tr>
<td>7</td>
<td>2</td>
<td>4</td>
<td>7</td>
<td>2</td>
<td>4</td>
<td>7</td>
<td>2</td>
</tr>
<tr>
<td>4</td>
<td>7</td>
<td>4</td>
<td>7</td>
<td>4</td>
<td>7</td>
<td>4</td>
<td>7</td>
</tr>
</tbody>
</table>
<div> </div>
<div>Player who is number 4 is left, assuming rhyme continues from
last person</div>
<div> </div>
<div>Eight players:</div>
<div> </div>
<table border="1">
<tbody>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>1</td>
</tr>
<tr>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
<div> </div>
<div>Four players is the same as three players</div>
<div>Eight players is the same as seven players</div>
<div> </div>
<div>When number of players is a factor of 8, player left is same
as the player left for one fewer number of players.</div>
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Ip Dip
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position
yourself so that you are 'it' if there are two players? Three
players ...?
Using, Applying and Reasoning about Mathematics
Investigations
Numbers and the Number System
Counting
Numbers and the Number System
Factors and multiples
Admin
Upper primary mapping document
Admin
Lower primary mapping document