5820
/www/nrich/html/content/id/5820/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
You may want to look at <a href="http://nrich.maths.org/public/viewer.php?obj_id=5819&part=index">
Overlaps</a> before you try this problem.<br></br>
<br></br>
Here are some pairs of shapes:<br></br>
<br></br>
<mdo:image width="505" height="168" src="OverL5.gif" alt="pairs of shapes"></mdo:image><br></br>
<br></br>
What overlap shape would you get if you overlapped them halfway
across each other?<br></br>
<br></br>
Here are some more pairs of shapes. What overlap shapes would you
get this time?<br></br>
<br></br>
<mdo:image width="494" height="158" src="OverL6.gif" alt="more pairs of shapes"></mdo:image><br></br>
<br></br>
Which of these overlap shapes did you find?<br></br>
<br></br>
<mdo:image width="305" height="129" src="OverL7.gif" alt="overlap shapes"></mdo:image><br></br>
<br></br>
You may like to use this interactivity to experiment after you have
tried to imagine what will happen in your head.<br></br>
<br></br>
<a href="/content/id/5820/OverLap2.swf">Full screen version</a>
<br></br>
<mdo:flash height="400" width="550"><param name="movie" value="/content/id/5820/OverLap2.swf" ></param><param name="flashplayerversion" value="8" ></param><param name="height" value="400" ></param><param name="width" value="550" ></param></mdo:flash><br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><p class="editorial">We haven't had any correct solutions to this
problem yet, but you can still send us your ideas - we'd love to
hear from you.</p>
<p class="editorial">You might like to use the interactivity to
test out your visualisations.</p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Overlapping Again</h2>
<br></br>
You may want to look at <a href="http://nrich.maths.org/public/viewer.php?obj_id=5819&part=index">Overlaps</a> before you try this problem.<br></br>
<br></br>
Here are some pairs of shapes:<br></br>
<br></br>
<mdo:image alt="pairs of shapes" height="168" src="OverL5.gif" width="505"></mdo:image><br></br>
<br></br>
What overlap shape would you get if you overlapped them halfway across each other?<br></br>
<br></br>
Here are some more pairs of shapes. What overlap shapes would you get this time?<br></br>
<br></br>
<mdo:image alt="more pairs of shapes" height="158" src="OverL6.gif" width="494"></mdo:image><br></br>
<br></br>
Which of these overlap shapes did you find?<br></br>
<br></br>
<mdo:image alt="overlap shapes" height="129" src="OverL7.gif" width="305"></mdo:image><br></br>
<br></br>
You may like to use this interactivity to experiment after you have tried to imagine what will happen in your head.<br></br>
<br></br>
<a href="/content/id/5820/OverLap2.swf">Full screen version</a><br></br>
<mdo:flash height="400" id="/content/id/5820/OverLap2.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param>
<param name="movie" value="/content/id/5820/OverLap2.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><a href="http://nrich.maths.org/5820&part=">This problem</a>, as in <a href="http://nrich.maths.org/5819&part=">Overlaps</a>, focuses on encouraging children to visualise - in this case to picture an image in their head. There are also valuable opportunities for them to apply their knowledge of properties of shape and to use appropriate vocabulary.</div>
<br></br>
<div>Visualising can be a very useful way of getting into a problem, as well as helping at other stages of the problem-solving process. Providing opportunities like this for your class to practise visualising will help them become familiar with its uses and to regard it as a legitimate skill to draw upon.<br></br>
</div>
<h3>Key questions</h3>
<div>What are the two shapes you are thinking about?</div>
<div>Looking at the overlaps where the sides are diagonal, which shapes could they have come from?</div>
<div>Can you imagine gradually moving one shape across the other one?<br></br>
</div>
<h3>Possible extension</h3>
Learners who need more of a challenge could try <a href="http://nrich.maths.org/962&part=">Quadrilaterals</a>.<br></br>
<br></br>
<h3>Possible support</h3>
Suggest trying this <a href="http://nrich.maths.org/5819&part=">simpler version</a> of the problem.<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">Can you imagine gradually moving one shape across the other one?<br></br>
If you're working away from the computer, it might help to draw the shapes, or cut some out from tissue paper or overhead transparencies.</mdoxml>
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Overlapping Again
What shape is the overlap when you slide one of these shapes half
way across another? Can you picture it in your head? Use the
interactivity to check your visualisation.
Information and Communications Technology
Interactivities
2D Geometry, Shape and Space
Pentagons
2D Geometry, Shape and Space
Circles
2D Geometry, Shape and Space
Hexagons
2D Geometry, Shape and Space
Equilateral triangles
2D Geometry, Shape and Space
Quadrilaterals
Using, Applying and Reasoning about Mathematics
Visualising