6522
/www/nrich/html/content/id/6522/
5
2011-02-01T00:00:01
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<p>Look at this image for a short while before turning away.<br></br>
Can you:</p>
<ul>
<li>Recreate the image?</li>
<li>Describe the image?</li>
<li>Say some mathematical things about what you notice?</li>
<li>Think of some mathematical questions you would like to ask about it?</li>
</ul>
<p><a class="doclink" href="/content/id/6522/Baravelle.doc">Here</a> is a Word document containing the image.</p>
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<br></br>
<div style="text-align: center;"><mdo:image alt="Baravelle Spiral" height="551" src="baravelle.png" width="551"></mdo:image></div>
<div style="text-align: center;"> </div>
<p><span class="editorial">This image is taken from the NRICH Mathematics Posters CD called "Exploring Squares" published by Virtual Image. More details of this and the "Exploring Circles" CD can be found</span><a class="editorial" href="http://www.virtualimage.co.uk/html/exploring_squares_and_circles.html" style="font-style: italic;">here.</a></p>
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<h3>Why do this problem</h3>
The aim of using <a href="http://nrich.maths.org/public/viewer.php?obj_id=6522&part=">
this image</a> is to encourage discussion about the different ways
of seeing and pose questions that can form the focus of further
investigation.<br></br>
<br></br>
<h3>Possible approach</h3>
Look at the image for about a minute and then "hide it". Then share
ideas.<br></br>
<br></br>
Follow up by selecting one or two of the ideas for the group to
explore further, for example:<br></br>
<ul>
<li>Recreating the image</li>
<li>Finding what fraction of the whole the areas is shaded red,
blue and white.</li>
</ul>
<h3>Key questions</h3>
Can you continue the pattern inwards? Outwards?<br></br>
Can you give a convincing argument for the fractions of the whole
that you can see?<br></br>
<br></br>
<h3>Possible Extension</h3>
Consider summing infinite series.<br></br>
What are the ratios of the lengths of the sides of the
triangles?<br></br>
<br></br>
<h3>Possible support</h3>
Can you find the fractions and or recreate the shape by folding?
Some learners might like to try the problem <a href="http://nrich.maths.org/public/viewer.php?obj_id=2132&part=index">
Inside Seven Squares</a>. <br></br>
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Baravelle
What can you see? What do you notice? What questions can you ask?
Using, Applying and Reasoning about Mathematics
Visualising
Using, Applying and Reasoning about Mathematics
Questioning
2D Geometry, Shape and Space
Squares