217
/www/nrich/html/content/02/03/letme1/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p>Can you split each of the shapes below in half so that the two
parts are exactly the same?</p>
<table cellpadding="20" border="0">
<tbody>
<tr>
<td><mdo:image src="rectangle.gif" alt=""></mdo:image></td>
<td><mdo:image src="shape2.gif" alt=""></mdo:image></td>
</tr>
<tr>
<td><mdo:image src="shape3.gif" alt=""></mdo:image></td>
<td> <mdo:image height="190" width="190" src="fourthpic.gif" alt=""></mdo:image></td>
</tr>
</tbody>
</table>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p>Esin aged 7 from Mef School in Turkey sent these two
solutions:</p>
<table cellpadding="20">
<tbody>
<tr>
<td><mdo:image alt="" src="esin1.gif"></mdo:image></td>
<td><mdo:image alt="" src="esin2.gif"></mdo:image></td>
</tr>
</tbody>
</table>
<br></br>
<p>Dost, also 7 from the same school, sent alternative answers:</p>
<table cellpadding="20">
<tbody>
<tr>
<td><mdo:image alt="" src="dost1.gif"></mdo:image></td>
<td>
<div><mdo:image alt="" src="dost2.gif"></mdo:image></div>
<div style="text-align: left;"></div>
</td>
</tr>
</tbody>
</table>
<table width="100%" cellspacing="0" cellpadding="0" border="0" id="tableedit3">
<tbody>
<tr>
<td>
<p>Perhaps you can find another way to split each of these
shapes?</p>
<p>We have also received this solution from Elizabeth, who goes to
Warren Road Primary School, Orpington, Kent.</p>
<p><mdo:image width="203" height="191" src="hong_solution_01.gif" alt=""></mdo:image></p>
<p>Can you find a way of splitting the fourth shape?</p>
</td>
</tr>
<tr>
<td align="center"></td>
</tr>
</tbody>
</table>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Happy Halving</h2>
<br></br>
<p>Can you split each of the shapes below in half so that the two parts are exactly the same?</p>
<table style="" border="">
<tbody>
<tr>
<td><mdo:image alt="" src="rectangle.gif"></mdo:image></td>
<td><mdo:image alt="" src="shape2.gif"></mdo:image></td>
</tr>
<tr>
<td><mdo:image alt="" src="shape3.gif"></mdo:image></td>
<td><mdo:image alt="" height="190" src="fourthpic.gif" width="190"></mdo:image></td>
</tr>
</tbody>
</table>
</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=217&part=index">This problem</a> consolidates children's understanding of halving in a spatial context and will help them to develop their powers of visualisation.</div>
<br></br>
<h3>Possible approach</h3>
<div>A precursor to this activity might be to show the group a square and ask them to split it in half in their "mind's eye". By discussing where they have imagined the "cutting line", the children will discover that there is more than one way to do this. From this point, you can talk about whether or not the two halves look the same each time. It is important pupils are clear that, in this
problem, the halves must look identical to each other.</div>
<br></br>
<div>It may be useful for the pupils to have a <a href="/content/02/03/letme1/HappyHalving.doc">sheet of the shapes</a> . Alternatively, they could use a pegboard or geoboard to try out their ideas.</div>
<br></br>
<div>In the plenary, you could focus on how they know the two parts they have created are definitely identical halves. This might involve children describing turning one part so that it fits on top of the other and some learners might want to practically do this by cutting out the two parts of each shape.</div>
<br></br>
<h3>Key questions</h3>
<div>Where could you try splitting the shape?</div>
<div>How do you know those two parts are identical halves?</div>
<div>What could we do to check?</div>
<br></br>
<h3>Possible extension</h3>
<div>Using the same size grid, children could create examples of shapes for a partner to split in half. <a href="http://nrich.maths.org/public/viewer.php?obj_id=990&part=index">This problem</a> offers some more shapes which children could try.</div>
<br></br>
<h3>Possible support</h3>
<div>Pupils could try <a href="http://nrich.maths.org/public/viewer.php?obj_id=1788&part=index">Halving</a> before having a go at this problem.</div>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
You could print off <a href="/content/02/03/letme1/HappyHalving.doc">this sheet</a> <a href="/content/02/03/letme1/halving.doc"></a>with the shapes drawn so
you can try out your ideas. Or you could make the shapes on a
pegboard.<br></br>
You might like to cut out the shapes first. Then you could try
cutting each shape and checking to see whether the two parts are
the same - perhaps you'll need to turn one of them round! <br></br>
<br></br></mdoxml>
2
5
1
0
0
0
0
Happy Halving
Can you split each of the shapes below in half so that the two
parts are exactly the same?
Using, Applying and Reasoning about Mathematics
Visualising
Fractions, Decimals, Percentages, Ratio and Proportion
Fractions
Mathematics Tools
Pinboard/geoboard
Using, Applying and Reasoning about Mathematics
Practical Activity
Admin
Lower primary mapping document