5819
/www/nrich/html/content/id/5819/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
If I have these two shapes: <br></br>
<br></br>
<div style="text-align: center;"><mdo:image width="156" height="58" alt="yellow square, red equilateral triangle" src="OverL1.gif"></mdo:image></div>
<br></br>
<br></br>
and I overlap them a bit, I get this: <br></br>
<br></br>
<div style="text-align: center;"><mdo:image width="90" height="59" alt="overlapped so that triangle is half covered by square" src="OverL2.gif"></mdo:image></div>
<br></br>
<br></br>
The overlapped part looks like this:<br></br>
<br></br>
<div style="text-align: center;"><mdo:image width="33" height="60" alt="orange right angled triangle shape of overlap" src="OverL3.gif"></mdo:image></div>
<br></br>
<br></br>
Can you match these pairs of shapes with the shape you would get if
you overlapped them? <br></br>
<br></br>
<div style="text-align: center;"><mdo:image width="431" height="581" alt="pairs of shapes to match with shapes of overlap" src="OverL4.gif"></mdo:image></div>
<br></br>
<br></br>
You may like to use this interactivity to test your ideas after you
have tried imagining the overlap in your head.<br></br>
<br></br>
<a href="/content/id/5819/OverLap1.swf">Full screen version</a>
<br></br>
<mdo:flash height="400" width="550"><param value="/content/id/5819/OverLap1.swf" name="movie" ></param><param value="8" name="flashplayerversion" ></param><param value="400" name="height" ></param><param value="550" name="width" ></param></mdo:flash><br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><p class="editorial">We haven't received any solutions to this
problem yet. Perhaps you would like to have a
go?</p>
<p class="editorial">You could use the interactivity at the end of
the problem to try out your ideas. Please let us know
what you find out.</p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Overlaps</h2>
<br></br>
If I have these two shapes:<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="yellow square, red equilateral triangle" height="58" src="OverL1.gif" width="156"></mdo:image></div>
<br></br>
<br></br>
and I overlap them a bit, I get this:<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="overlapped so that triangle is half covered by square" height="59" src="OverL2.gif" width="90"></mdo:image></div>
<br></br>
<br></br>
The overlapped part looks like this:<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="orange right angled triangle shape of overlap" height="60" src="OverL3.gif" width="33"></mdo:image></div>
<br></br>
<br></br>
Can you match these pairs of shapes with the shape you would get if you overlapped them?<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="pairs of shapes to match with shapes of overlap" height="581" src="OverL4.gif" width="431"></mdo:image></div>
<br></br>
<br></br>
You may like to use this interactivity to test your ideas after you have tried imagining the overlap in your head.<br></br>
<br></br>
<a href="/content/id/5819/OverLap1.swf">Full screen version</a><br></br>
<mdo:flash height="400" id="/content/id/5819/OverLap1.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/5819/OverLap1.swf"></param>
<param name="flashplayerversion" value="8"></param>
<param name="height" value="400"></param>
<param name="width" value="550"></param>
</mdo:flash></div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>The main aim of <a href="http://nrich.maths.org/public/viewer.php?obj_id=5819&part=index">this problem</a> is to encourage children to try to picture images in their heads and, in this particular case, the image might be a dynamic one. However, in this context, they will also be applying knowledge of properties of shapes and using language associated with 2D shape and space.</div>
<br></br>
<div>Visualising is a skill which can be invaluable in solving problems and this problem provides a good context for practising it.</div>
<br></br>
<h3>Possible approach</h3>
<div>Rather than showing the image of the equilateral triangle overlapping the square in the first part of this problem, you could ask children to shut their eyes and imagine the triangle moving over the square. This will give them time to really focus on their own image, rather than being presented with someone else's straight away. Invite them to talk to a partner about what they can see in
their mind's eye - what shape is the overlap? - and then talk about it as a whole group.</div>
<br></br>
<div>At this point, you could then show the image or use shapes cut out of tissue paper or overhead transparencies. You could then ask the class to work on the problem in pairs, perhaps using cut-out shapes to test their hypotheses and using the interactivity to bring ideas together as a whole group.</div>
<br></br>
<div><a href="/content/id/5819/Overlaps.pdf">This sheet</a> of the shapes and overlaps might be useful.</div>
<br></br>
<h3>Key questions</h3>
<div>What are the two shapes you are thinking about?</div>
<br></br>
<div>Looking at the overlap are there sloping sides? Which shapes could they have come from?</div>
<br></br>
<h3>Possible extension</h3>
Learners could try <a href="http://nrich.maths.org/public/viewer.php?obj_id=5820&part=index">this</a> more complex version of this problem.<br></br>
<h3>Possible support</h3>
Suggest cutting out the shapes from <a href="/content/id/5819/Overlaps.pdf">this sheet</a> and drawing round them to make overlaps.<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">Try to "see" one shape moving over the other in your mind.<br></br>
If you want to work away from the computer, you could cut out the
shapes in two different colours of tissue paper or cut up two
overhead transparencies to test out your ideas. Or, you
could try drawing the two shapes overlapping. <br></br></mdoxml>
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Overlaps
What does the overlap of these two shapes look like? Try picturing
it in your head and then use the interactivity to test your
prediction.
Information and Communications Technology
Interactivities
2D Geometry, Shape and Space
Mixed triangles
2D Geometry, Shape and Space
Quadrilaterals
Using, Applying and Reasoning about Mathematics
Visualising