2782
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2011-02-01T00:00:01
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Choose four of the numbers from this list: $1, 2, 3, 4, 5, 6, 7, 8, 9$ to put in the squares below so that the difference between joined squares is odd.<br></br>
Only one number is allowed in each square. You must use four different numbers.<br></br>
What can you say about the sum of each pair of joined squares?<br></br>
What must you do to make the difference even?<br></br>
What do you notice about the sum of the pairs now?<br></br>
<br></br>
Here <a class="doclink" href="/content/id/2782/Ring%20a%20Ring%20of%20Numbers.doc">.doc</a> <a class="pdflink" href="/content/id/2782/Ring%20a%20Ring%20of%20Numbers.pdf">.pdf</a> are some sheets for recording your solutions.<br></br>
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<a href="/content/id/2782/4ring.swf">Full size version</a><br></br>
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<h5>This problem is based on an idea taken from "Apex Maths Pupils' Book 2" by Ann Montague-Smith and Paul Harrison, published in 2003 by Cambridge University Press. To find out more about this book, and order a copy go to the <a href="http://www.cambridge.org/uk/education/primary_projectpage.asp?id=2502503">CUP website</a>.</h5>
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<p class="editorial">Oli from Oakmeeds School began the first part of this question where we had to make odd differences between pairs of numbers.</p>You need odd, even, odd, even as odd + even make odd. Each
pair has an odd and an even.<br></br><br></br><span class="editorial">Rukmini from Hopscotch Nursery also said:</span><br></br><br></br>
When the differences are all odd, the sums are all odd.
<br></br><span class="editorial"></span><br></br><span class="editorial">Rukmini then went on to say:</span><br></br>
<br></br>To make the differences even, you need the numbers 2, 4, 6, 8. Then the
sums are also even.
<br></br><span class="editorial"></span><br></br><span class="editorial">Absolutely right - well done to both Oli and Rukmini. What about the order of the numbers 2, 4, 6 and 8 in the ring? Does it matter? I'll leave you all to ponder on that.</span><br></br></mdoxml>
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<h2>Ring a Ring of Numbers</h2>
<br></br>
Choose four of the numbers from this list: $1, 2, 3, 4, 5, 6, 7, 8, 9$ to put in the squares below so that the difference between joined squares is odd.<br></br>
Only one number is allowed in each square. You must use four different numbers.<br></br>
What can you say about the sum of each pair of joined squares?<br></br>
<br></br>
What must you do to make the difference even?<br></br>
What do you notice about the sum of the pairs now?<br></br>
<a href="/content/id/2782/4ring.swf">Full size version</a><br></br>
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<param name="movie" value="/content/id/2782/4ring.swf"></param>
<param name="flashplayerversion" value="7"></param>
<param name="height" value="420"></param>
<param name="width" value="550"></param>
</mdo:flash><br></br>
<br></br>
<h5>This problem is based on an idea taken from "Apex Maths Pupils' Book 2" by Ann Montague-Smith and Paul Harrison, published in 2003 by Cambridge University Press. To find out more about this book, and order a copy go to the <a href="http://www.cambridge.org/uk/education/primary_projectpage.asp?id=2502503">CUP website</a>.</h5>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=2782&part=index">This problem</a> provides a context in which children can recognise odd and even numbers, and begin to think about their properties. It also offers practice of addition and subtraction.</div>
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<h3>Possible approach</h3>
<div>It would be good to have the interactivity on the interactive whiteboard, or projected onto a screen. Begin by placing any four numbers in the ring and asking questions about them, for example:</div>
<ul>
<li>Which pair of numbers has a total of ...?</li>
<li>Which pair of numbers has a difference of ...?</li>
<li>Which pair of numbers has the highest/lowest total?</li>
<li>Which pair of numbers has the greatest/least difference?</li>
</ul>
<div>These questions will help children become familiar with the vocabulary of the problem and so you can then lead into the main activity. Having asked the question, give pairs of children chance to find at least one way of making odd differences. They could be working at computers and/or using this sheet of blank circles <a class="doclink" href="/content/id/2782/Ring%20a%20Ring%20of%20Numbers.doc">.doc</a> <a class="pdflink" href="/content/id/2782/Ring%20a%20Ring%20of%20Numbers.pdf">.pdf</a> You could then test some of these using the interactivity, and record the arrangements that work on board. Once you have several ways on the board, invite learners to comment on what they notice. What do all the arrangements have in common? You can
work through the rest of the problem in a similar way, drawing the whole class together as appropriate.</div>
<br></br>
<div>It is important to encourage the children to explain why the arrangements of odd/even numbers produce these results. You could make drawings <a class="doclink" href="/content/id/2782/Ring%20a%20Ring%20Odd%20and%20Even.doc">.doc</a> <a class="pdflink" href="/content/id/2782/Ring%20a%20Ring%20Odd%20and%20Even.pdf">.pdf</a> using paired joined squares to help them understand.</div>
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<h3>Key questions</h3>
<div>What do you notice about the numbers in the ring when the difference between joined pairs is odd?</div>
<div>What do you notice about the numbers in the ring when the difference between joined pairs is even?</div>
<div>Can you explain why?</div>
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<h3>Possible extension</h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=2783&part=index">More Numbers in the Ring</a> allows children to investigate different numbers of numbers in the ring.</div>
<br></br>
<h3>Possible support</h3>
<div>Some learners might benefit from having counters or other objects to help with their addition and subtraction.</div>
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Try putting one of the numbers in any square to start with. What numbers could go on each side of it? <br></br>
When you add the numbers in two joined squares, what kind of number do you get?<br></br>
You might like to print off this <a href="/content/id/2782/ringaringsheet.doc">sheet of blank rings</a> to help you try out some different numbers.<br></br>
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For difference to be odd, must be alternately odd/even around
circle<br></br>
Sum always odd.<br></br>
<br></br>
For difference to be even, must be odd next odd or even next to
even which means that all must be odd or all even<br></br>
Sum always even<br></br>
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http://www.cambridge.org/uk/education/primary_projectpage.asp?id=2502503<br></br>
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Ring a Ring of Numbers
Choose four of the numbers from 1 to 9 to put in the squares so
that the differences between joined squares are odd.
Calculations and Numerical Methods
Addition & subtraction
Numbers and the Number System
Odd and even numbers
Information and Communications Technology
Interactivities
Admin
Lower primary mapping document