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/www/nrich/html/content/01/05/penta5/
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2011-02-01T00:00:01
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<p>Use the isometric grid paper below to find the following polygons.</p>
<ul>
<li>A rectangle</li>
<li>A rhombus</li>
<li>A trapezium</li>
<li>A parallelogram that is not a rectangle</li>
<li>An equilateral triangle</li>
<li>A right angled triangle</li>
<li>A scalene triangle</li>
<li>An isosceles triangle that is not an equilateral triangle</li>
<li>A pentagon</li>
<li>A hexagon</li>
<li>A heptagon</li>
<li>An octagon</li>
</ul>
<p>If you need to find a description of these polygons try looking at:<br></br>
<a href="http://www.mathleague.com/index.php?option=com_content&view=article&id=75:figuresandpolygons&catid=31:general">http://www.mathleague.com/index.php?option=com_content&view=article&id=75:figuresandpolygons&catid=31:general</a></p>
<p><mdo:image alt="Isometric grid paper." src="penta5.gif"></mdo:image></p>
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<p><span class="editorial">The pupils from</span> <strong style="font-weight: bold;" class="editorial">Moorfield Juniors</strong>
<span class="editorial">in Stockport sent in many solutions to this
problem. Well done to each of you. The first piece of work was
received from</span> <strong style="font-weight: bold;" class="editorial">Steven</strong> <span class="editorial">and</span>
<strong style="font-weight: bold;" class="editorial">Matthew</strong><span class="editorial">, who sent
along the following shapes that they were able to find and
recognise on the isometric paper.</span></p>
<p></p>
<p><span class="editorial">Many other shapes were found by
Moorfield's pupils, some of them were irregular and some were even
difficult to put a name to! They certainly demonstrated their
powers of observation.</span></p>
<mdo:image alt="" src="diagramp53.gif"></mdo:image> <br></br>
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<p class="editorial">Can you find any other examples of the shapes
that were named?</p>
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<h2>Where Are They?</h2>
<br></br>
<p>Use the isometric grid paper below to find the following polygons.</p>
<ul>
<li>A rectangle</li>
<li>A rhombus</li>
<li>A trapezium</li>
<li>A parallelogram that is not a rectangle</li>
<li>An equilateral triangle</li>
<li>A right angled triangle</li>
<li>A scalene triangle</li>
<li>An isosceles triangle that is not an equilateral triangle</li>
<li>A pentagon</li>
<li>A hexagon</li>
<li>A heptagon</li>
<li>An octagon</li>
</ul>
<p>If you need to find a description of these polygons try looking at:<br></br>
<a href="http://www.mathleague.com/help/geometry/polygons.htm">http://www.mathleague.com/help/geometry/polygons.htm</a></p>
<p><mdo:image alt="Isometric grid paper." src="penta5.gif"></mdo:image></p>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>Recognising shapes is relatively easy - it requires spotting perhaps just one or two key characteristics and matching to a name. Generating a shape given the name, as in <a href="http://nrich.maths.org/public/viewer.php?obj_id=1058&part=index">this activity</a> , is much more difficult for young children and requires much more attention to be paid. Using a grid helps children to
visualise the shapes and make connections between them. Talking with a partner helps to clarify definitions.</div>
<br></br>
<h3>Possible approach</h3>
<div>This is an activity that can be introduced to the whole class who then work in pairs. Using a large version of the grid, (either on an IWB or copying the grid paper (downloadable <a href="/content/01/05/penta5/iso.pdf">here</a> ) onto an OHT), tell the children that lots of different shapes are hidden, and ask if they can see any. Draw an equilateral triangle to illustrate. Ask what it is
called and invite a child to come out and draw another equilateral triangle, perhaps a different sized one. Explain that they don't have to go over the lines of the grid but they do have to join up the vertices.</div>
<br></br>
<div>Introduce the name of each of the shapes in turn, share understandings of what the shape is like and allow some time for the children to work in pairs to see how many different ones they can find. Bring the children together for each, or after each two or three, and invite them to illustrate for all to see. Does everyone agree? Encourage the children to name their shapes on their grid.</div>
<br></br>
<h3>Key questions</h3>
<div>What shapes can we see?</div>
<div>Can we draw more than one of each?</div>
<div>Are they the same or different?</div>
<div>How do we know this is a ...?</div>
<div>What makes it a ...?</div>
<br></br>
<h3>Possible extension</h3>
<div>Give some children <a href="http://www1.curriculum.edu.au/maths300/m300bits/000dotis.htm">triangular dotty paper</a> rather than isometric paper so that they have to visualise to a greater extent. Children who find this very easy could be challenged to see which shapes they could find on a square dotty grid. The free programme <a href="http://illuminations.nctm.org/ActivityDetail.aspx?ID=125">http://illuminations.nctm.org/ActivityDetail.aspx?ID=125</a> may be of interest to children who want to pursue isometric drawings further.</div>
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<h3>Possible support</h3>
<div>Children who find it difficult to see the embedded shapes may benefit from the <a href="/content/01/05/penta5/WhereAreTheyShapes.pdf">sheet of shapes</a>. If you have triangular pinboards and elastic bands these can be helpful too.</div>
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<mdoxml version="1.0">If you're having trouble finding some of the shapes, you could
print off <a href="/content/01/05/penta5/WhereAreTheyShapes.pdf">this
sheet</a>.<br></br></mdoxml>
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Where are they?
Use the isometric grid paper to find the different polygons.
2D Geometry, Shape and Space
Regular polygons
2D Geometry, Shape and Space
Other polygons
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