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Why do this problem?
presents an ideal opportunity for children to engage in some practical mathematics. By tackling this task, learners will develop their knowledge of the properties of these 3D shapes and you can also encourage them to offer clear explanations of their thinking.
If you have wooden or plastic models of any of the shapes (sphere, cylinder and cone) it would be good for the group to be able to handle them. You could encourage them to talk to a partner about what they notice about the three shapes, then open the discussion more widely amongst the whole group.
It would also be worth having a modelling clay version of each shape ready for you to use as you introduce the task. Show the group the sphere and ask the first question, "How would you cut it to make the largest circle?". Again, ask pairs to talk to each other first and then share ideas across the whole class. Listen out for children who try to explain how they know that
their cut will give the largest circle. At this point, you could invite some pupils to test their ideas by cutting your modelling clay sphere until the whole group is satisfied that they have found a way. You could ask whether there are any other ways of doing it.
After this they could work in pairs to answer the other questions asked in the problem itself. You might wish them to record their work in some way before testing their ideas using modelling clay, should they wish.
Children should be encouraged to describe a "stretched circle" or "circle-rectangle" rather than necessarily knowing the term "ellipse" but you may feel that this activity offers a good opportunity to introduce new vocabulary.
Tell me about what you're doing.
How could you make a circle from this shape?
How could you make a larger/smaller circle?
If you cut the shapes in different ways, what other shapes could you make?
If you make two cuts, what other shapes are possible?
How do you know that that cut/those cuts will give that shape?
Learners could go on to find different plane shapes in other solids such as a cube, tetrahedron and various pyramids.
Having some ready-made clay models of the shapes will support those children who want to try out different cuts but find it hard to create the shapes from scratch. You may need to emphasise that, before they make any cuts, learners must have convinced at least one other person that their cut will produce the desired effect.