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'Shadow Play' printed from http://nrich.maths.org/
Why do this problem?
requires learners to visualise 3D shapes, and therefore consolidates knowledge of their properties. Pupils are also reminded that there is not necessarily one right answer in mathematics!
It is important for children to have had lots of experience of handling and talking about 3D shapes prior to this activity, and it would be helpful to have lots of 3D shapes to hand.
You could start off the activity by choosing a particular shape and telling children that you're going to shine a torch on it so that you can see its shadow. (Alternatively, hold a shape under the lamp of the overhead projector.) Ask children what shape they think the shadow will be and why. Give them time to talk to a partner before discussing it as a whole class. You could repeat this once
more with a different shape (or by shining the torch on a different face of the first shape) so that the group understands what is happening.
Then show them the pictures of the shadows in the problem and ask them to work in pairs or small groups to decide which shapes could make each shadow. You could give each group a torch to test their predictions.
In a plenary, share solutions and draw attention to those where more than one shape is possible. Are the children certain they have all the possibilities?
What shape is this shadow?
How might that help us to find a 3D shape that made it?
Is there only one possible shape?
What could the shadow of this shape look like?
Can you explain why?
Learners may be able to investigate other shadow shapes and list all the 3D shapes which could make these as well.
It would be useful for children to try Skeleton Shapes
before tackling this problem.