7235
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2011-02-01T00:00:01
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<div style="text-align: left; font-style: italic;"><em>This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)</em></div>
<div style="text-align: left; font-style: italic;">The challenge follows on from <a href="http://nrich.maths.org/163&part=">Wrapping Presents.</a></div>
<div style="text-align: center;"><mdo:image width="422" height="368" src="auditori.jpg" alt="auditori"></mdo:image></div>
<div>Here's a model of a small auditorium. There are four squares at the bottom inside and there are three sets of steps to the top. To help to visualise it I've coloured each face of the cube blocks according to which way they are facing.</div>
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<div>Your challenge is to imagine that this is a small model that is a present for someone and so it has to be carefully wrapped up with paper. We do not want to waste paper so the wrapping needs to be from a cut shape so that each visable face (no matter where you are viewing it from) needs to be covered CLOSELY with ONE LAYER OF PAPER ONLY and there is to be just ONE piece of
wrapping paper.</div>
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<div>Draw the shape of that wrapping paper which would need to be cut out.</div>
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<div>Describe how you went about it and say what you can about the paper shape.</div>
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<div>Then ask yourself "I wonder what would happen if I ...?"</div>
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<h3><span style="font-weight: bold;">Why do this
problem?</span></h3>
<div>This <a href="http://nrich.maths.org/7235&part=">activity</a> is
specially designed for the highest-attaining pupils that you ever
come across. It acts as a further extension to <a href="http://nrich.maths.org/163&part=">Wrapping Presents</a>.
It's an activity that is intended to give opportunities for those
pupils to explore deeply using their intuition, flair and
risk-taking skills.</div>
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<h3>Possible approach</h3>
<div>As this is designed for the highest attaining, it might be
presented as on the website or in a one-to-one situation,
encouraging discussion between adult and pupil. This discussion
could determine what kind of start suits the learner, for example
it may be a model needs to be constructed, it may be a conversation
about imagining it in the head, it may be a $2$D
representation.</div>
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<h3>Key questions </h3>
Tell me about this/your thinking.<br></br>
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Auditorium Steps
What is the shape of wrapping paper that you would need to completely wrap this model?
Using, Applying and Reasoning about Mathematics
Visualising
3D Geometry, Shape and Space
Nets