2343
/www/nrich/html/content/id/2343/
1
2011-02-01T00:00:01
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<mdoxml version="1.0"> <p>
Here are some pictures of 3D shapes made from cubes. Can you make these
shapes yourself?
</p>
<p>
What do they look like from different positions? Please send us
photographs or pictures of your models.
</p>
<p>
</p>
<p>
<mdo:image align="top" width="233" src="yellow_blocks.gif" alt="four yellow cubes" bgcolor="" height="105" /><mdo:image align="top" width="150" src="purple_blocks.gif" alt="four purple cubes" bgcolor="" height="149" />
</p>
<p>
<mdo:image align="top" width="128" src="red_blocks.gif" alt="five red cubes" bgcolor="" height="209" />
<mdo:image align="top" width="238" src="green_blocks.gif" alt="six green cubes" bgcolor="" height="169" />
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<p><span class="editorial">Thank you to Emma, Hannah, Shawnee and
Sophie from Oakwood Junior School Maths Club for the drawings you
did of the shapes. They explained that they made the shapes and put
them at different angles, then copied them onto isometric paper.
Here are some examples that Emma and Sophie drew for the first
shape:</span></p>
<table border="0" align="center" style="border-style: solid; border-width: 0pt; width: 100%;" id="tableedit1">
<tbody>
<tr>
<td valign="middle" align="center" style="border-style: solid; border-width: 0pt; width: 50%;">
<p><mdo:image width="200" height="129" align="top" bgcolor="" src="shape1emmasol.gif" alt="Emma's first shape "></mdo:image></p>
</td>
<td valign="middle" align="center" style="border-style: solid; border-width: 0pt; width: 50%;">
<p><mdo:image width="200" height="135" align="top" bgcolor="" src="shape1solsophie.gif" alt="Sophie's first shape"></mdo:image></p>
</td>
</tr>
</tbody>
</table>
<p><span class="editorial">Here is Sophie's drawing of the second
shape:</span></p>
<p align="center"><mdo:image width="200" height="96" align="top" bgcolor="" src="shape2sophiesol.gif" alt="second shape"></mdo:image></p>
<p align="left"> </p>
<p align="left"><span class="editorial">Emma drew the third shape
like this:</span></p>
<p align="left"> </p>
<p align="center"><mdo:image width="200" height="78" align="top" bgcolor="" src="shape3emmasol.gif" alt="third shape"></mdo:image></p>
<p align="center"> </p>
<p align="left" class="standard"><span class="editorial">Finally,
they both drew different versions of the fourth shape:</span></p>
<p align="left" class="standard"> </p>
<table border="0" align="center" style="border-style: solid; border-width: 0pt; width: 100%;" id="tableedit2">
<tbody>
<tr>
<td valign="middle" align="center" style="border-style: solid; border-width: 0pt; width: 50%;">
<p style=""><mdo:image width="150" height="177" src="shape4emmasol.gif" alt="Emma's fourth shape"></mdo:image></p>
</td>
<td valign="middle" align="center" style="border-style: solid; border-width: 0pt; width: 50%;">
<p style=""><mdo:image width="150" height="136" src="shape4sophiesol.gif" alt="Sophie's fourth shape"></mdo:image></p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td align="center"></td>
<td align="center"></td>
</tr>
</tbody>
</table>
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<mdoxml version="1.0"><div class="embed">
<h2>Building Blocks</h2>
<p>Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?</p>
<p>What do they look like from different positions? Please send us photographs or pictures of your models.</p>
<p> </p>
<p><mdo:image align="top" alt="four yellow cubes" bgcolor="" height="105" src="yellow_blocks.gif" width="233"></mdo:image><mdo:image align="top" alt="four purple cubes" bgcolor="" height="149" src="purple_blocks.gif" width="150"></mdo:image></p>
<p><mdo:image align="top" alt="five red cubes" bgcolor="" height="209" src="red_blocks.gif" width="128"></mdo:image> <mdo:image align="top" alt="six green cubes" bgcolor="" height="169" src="green_blocks.gif" width="238"></mdo:image></p>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>Working from 2D representations to 3D can be quite problematic at this level, and <a href="http://nrich.maths.org/public/viewer.php?obj_id=2343&part=index">this problem</a> gives children experience of doing just that, as well as then possibly transferring back to 2D. The activity provides a great opportunity to develop children's familiarity with positional language, for example behind,
in front, to the left, to the right, above/on top, below/underneath etc.</div>
<br></br>
<h3>Possible approach</h3>
<div>For this activity, you'll need plenty of multilink cubes. Display the picture on the screen of the interactive whiteboard, or project it onto an ordinary board. You could start with one of the shapes, for example the yellow one, and ask children to describe it. Encourage them to talk about the number of cubes used and their relative positions. Some learners might say it looks like an 'L'
shape.</div>
<br></br>
<div>Ask children to make the yellow shape, individually or in pairs, and they can compare the shapes to check they're the same. Depending on your class' experiences, you could then challenge them to draw their shape on <a href="http://www1.curriculum.edu.au/maths300/m300bits/000dotis.htm">isometric paper</a> , sketch their shape on plain paper, or just put their shape on the table in front of
them so that it looks different from the picture in the problem.</div>
<br></br>
<div>The other shapes could be tackled in similar ways and you could take some photographs of the results for display alongside a print-out of the problem itself.</div>
<br></br>
<h3>Key questions</h3>
<div>How many cubes will you need for that shape?</div>
<div>Can you describe how they are joined together?</div>
<br></br>
<h3>Possible extension</h3>
<div>Some pupils might like to try <a href="http://nrich.maths.org/public/viewer.php?obj_id=1148&part=index">The Third Dimension</a> problem which is much more challenging and requires drawing on isometric paper.</div>
<br></br>
<h3>Possible support</h3>
<div>It may be useful to have each of the shapes made up yourself prior to the lesson so that you could show them to the group. Children are likely to find it easier to replicate a shape if they can see a 'real' version rather than just a picture.</div>
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<mdoxml version="1.0"> <p>
Try using multilink cubes.
</p>
<p>
Try starting at one end of the shape and adding a cube at a time.
</p>
<p>
You can look at each shape from above or from the sides.
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Here are some pictures of 3D shapes made from cubes. Can you make
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