Auditorium steps
What is the shape of wrapping paper that you would need to completely wrap this model?
Age
7 to 14
Challenge level
Problem
The challenge follows on from Wrapping Presents.
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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.
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.
Draw the shape of that wrapping paper which would need to be cut out.
Describe how you went about it and say what you can about the paper shape.
Then ask yourself "I wonder what would happen if I ...?"
Student Solutions
ZaynabӬ from Parkhill Junior School wrote:Ӭ
First of all I calculated how many squares there were of each colour.
Working out how many squares there were in the top part was the hardest as I had to make sure that I didn't overlap the squares.
In total there were:
Outer sides: 128 squares
Bottom: 64 squares
Top: 192 squares.
Within the top section, the colours were as follows:
Orange: 40
Green: 40
Purple: 64
I reduced the scale factor, and divided everything by 4. That way I could make a reasonably sized model. I drew it onto squared paper, then recreated it to make sure everything fit. I did this so that I could visualise it, as if I were really wrapping the auditorium.
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Matthew from Dulwich College Suzhou in China sent in this picture:
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Saksham from Hounslow Town Primary School sent in this picture:
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Thank you for these good solutions that probably tested your visualising skills.
Teachers' Resources
Why do this problem?
It acts as a further extension to Wrapping Presents. It's an activity that is intended to give opportunities for those pupils to explore deeply using their intuition, flair and risk-taking skills.
Possible approach
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.