927
/www/nrich/html/content/99/01/penta4/
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2011-02-01T00:00:01
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<div style="text-align: center;"><mdo:image width="189" height="178" alt="10 circles" src="10Circles.gif"></mdo:image></div>
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<div>Place the numbers 1 to 10 in the circles so that each number
is the difference between the two numbers just below it.</div>
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<tbody>
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<td style="text-align: center;">Example:</td>
<td align="center"><mdo:image width="92" height="89" alt="3 circles" src="561.gif"></mdo:image></td>
<td>6 - 5 = 1</td>
</tr>
</tbody>
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<td valign="middle"></td>
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<div>You could try this interactivity.</div>
<a href="Diff.swf"></a><br></br>
<a href="/content/99/01/penta4/Diff.swf">Full screen
version</a><br></br>
<mdo:flash height="400" width="550"><param value="Diff.swf" name="movie" ></param><param value="8" name="flashplayerversion" ></param></mdo:flash> <br></br></mdoxml>
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<p class="editorial">Craig from Brookdale Primary gave this
solution:</p>
<br></br>
<br></br>
<mdo:image height="174" width="227" alt="" src="fig1.gif"></mdo:image><br></br>
<p class="editorial">Perhaps you can find other ways of doing
it?</p>
<br></br>
<br></br>
<br></br>
<comment> soln.html </comment><br></br></mdoxml>
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<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=927&part=index">This problem</a> is a very challenging way of practising subtraction at the same time as being logical about arranging the numbers. The idea of 'difference' can be hard for children to grasp and this tricky problem is a way of coming to terms with it.</div>
<br></br>
<h3>Possible approach</h3>
<div>Read the question together and discuss what 'difference' between two numbers means. Try one or two examples like the 5 and 6 given in the problem, making sure that you begin with both the larger and the smaller number. For learners who have met negative numbers it is important to point out that for the purposes of this problem, the difference is always positive. For learners who need quick
success, or find puzzling out problems difficult, you could start with <a href="http://nrich.maths.org/public/viewer.php?obj_id=6227&part=index">this simpler problem</a>.</div>
<br></br>
<div>After the introduction learners could work in pairs on paper or with <a href="http://nrich.maths.org/public/viewer.php?obj_id=927&part=index">this interactivity</a> . Have rough paper available for jottings or use <a href="/content/99/01/penta4/Difference.pdf">this sheet</a> for working and recording. If you want a whole class to work on the problem at the same time, this <a href="/content/99/01/penta4/Differenceb.pdf">sheet</a> gives the pyramid of circles, the numbers from 1 to 10 to cut out and leaves space for adding another row of circles should this be required.</div>
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The plenary can be used to discuss whether there are different solutions, possibly using the interactivity.<br></br>
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<h3>Key questions</h3>
<div>Where could the largest number be? Why?</div>
Does thinking about odd and even numbers help you?<br></br>
<h3><br></br>
Possible extension</h3>
<div>Some children will be motivated to see if different arrangements can be found. They could also try using the numbers 1 -15 on five rows of circles!</div>
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<h3>Possible support</h3>
<div>Many learners will find it useful to start on <a href="http://nrich.maths.org/public/viewer.php?obj_id=6227&part=index">this problem</a> which has the numbers 1 - 6 on three rows of circles. Pupils could use numbered counters that can be moved about if they're not using the interactivity.</div>
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Think about where the highest number might go.<br></br>
You could use this <a href="/content/99/01/penta4/Difference.pdf">sheet of blank pyramids</a>
to try out your ideas.<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">Craig from Brookdale Primary gave this solution: <br></br>
<br></br>
<mdo:image width="227" height="174" src="fig1.gif" alt=""></mdo:image><br></br>
<br></br>
Perhaps you can find other ways of doing it?<br></br></mdoxml>
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Difference
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Using, Applying and Reasoning about Mathematics
Trial and improvement
Calculations and Numerical Methods
Addition & subtraction
Using, Applying and Reasoning about Mathematics
Working systematically
Information and Communications Technology
Interactivities