2156 /www/nrich/html/content/04/02/penta1/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>You have been given three shapes made out of sponge: a sphere, a cylinder and a cone.</p> <div id="spongeshapes"><mdo:image alt="sphere" src="sphere.png"></mdo:image><mdo:image alt="cylinder" src="cylinder.png"></mdo:image><mdo:image alt="cone" src="cone.png"></mdo:image></div> <p>You are going to make some shapes for printing out of these sponges.</p> <p>How would you cut the sphere to make the largest circle for printing?<br></br> How could you make the largest possible circle from the cylinder ... and the cone?</p> <p>Which shape would you use to make a very small circle for printing?</p> <p>If you cut the shapes in different ways, what other shapes for printing could you make?</p> <p>If you make two cuts, are other shapes possible?</p> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <br></br> <p class="editorial">Alex from Cutthorpe Primary School and Lucy from Caversham Primary sent in very clear solutions to this problem. Alex says:</p> <blockquote> <p>To make a large circle from the cylinder and cone just use the flat faces of these shapes.</p> </blockquote> <p class="editorial">Lucy adds:</p> <blockquote> <p>You would cut the sphere in the exact centre to get the largest possible circle from the sphere (the cut would have to be in the absolute exact centre).</p> </blockquote> <p class="editorial">She goes on to say:</p> <blockquote> <p>You would use the cone to make a very small circle for printing. You would cut it at the top of the point.<br></br> If you cut the cone straight down from the point, you would find that the face would now be a semi-circle and the new face would be a type of triangle.<br></br> If you cut the cylinder down from the face you would find that the face was a semi-circle and the new face would be a rectangle.<br></br> If you cut the sphere in any place the face would still be a circle.</p> </blockquote> <p class="editorial">With two cuts, Alex suggests that you could cut the rectangle you made earlier (from the cylinder) into a square.</p> <p class="editorial">Naomi, who is Home Educated, suggests that you could make the biggest possible circle by rolling the cone around on its side, keeping the vertex as the centre of the circle. What a great idea.</p> <p class="editorial">Thank you also to A from MLC in Australia who sent a full solution.  (He/she didn&#39;t give us a full name.)</p> <p class="editorial">Are there any other possibilities? Let us know if you find any.</p> <br></br> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Sponge Sections</h2> <p>You have been given three shapes made out of sponge: a sphere, a cylinder and a cone.</p> <div id="spongeshapes"><mdo:image alt="sphere" src="sphere.png"></mdo:image><mdo:image alt="cylinder" src="cylinder.png"></mdo:image><mdo:image alt="cone" src="cone.png"></mdo:image></div> <p>You are going to make some shapes for printing out of these sponges.</p> <p>How would you cut the sphere to make the largest circle for printing?<br></br> How could you make the largest possible circle from the cylinder ... and the cone?</p> <p>Which shape would you use to make a very small circle for printing?</p> <p>If you cut the shapes in different ways, what other shapes for printing could you make?</p> <p>If you make two cuts, are other shapes possible?</p> </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/2156&amp;part=">This problem</a> 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.</div> <br></br> <h3>Possible approach</h3> <div>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.   </div> <div> </div> <div>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.</div> <div> </div> <div>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.</div> <div> </div> <div>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.</div> <br></br> <h3>Key questions</h3> <div>Tell me about what you&#39;re doing.</div> <div>How could you make a circle from this shape?  </div> <div>How could you make a larger/smaller circle?</div> <div>If you cut the shapes in different ways, what other shapes could you make?</div> <div>If you make two cuts, what other shapes are possible?</div> <div>How do you know that that cut/those cuts will give that shape?</div> <br></br> <h3>Possible extension</h3> Learners could go on to find different plane shapes in other solids such as a cube, tetrahedron and various pyramids.<br></br> <h3>Possible support</h3> 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.<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Use some modelling clay to make the shapes yourself and try it out.</p> <p>For the sphere, you could imagine you were cutting an apple or orange.</p> <p>It might help to have a good look at each shape before you make any cuts!</p> <br></br></mdoxml> 5 4 0 1 0 0 0 You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing. 3D Geometry, Shape and Space Cross sections Using, Applying and Reasoning about Mathematics Visualising 3D Geometry, Shape and Space Cylinders 3D Geometry, Shape and Space Cones 3D Geometry, Shape and Space Spheres Using, Applying and Reasoning about Mathematics Practical Activity Admin Upper primary mapping document