163 /www/nrich/html/content/99/12/letme2/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Choose a box and work out the smallest rectangle of paper needed to wrap it so that it's completely covered.</p> <div><mdo:image width="109" height="49" src="Picture%202.jpg" alt="pic 2"></mdo:image><mdo:image align="center" alt="" src="fig1.gif"></mdo:image></div> <br></br> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <span class="editorial">Colet Court School worked on this problem and came up with a few ideas of what the solution might be</span>. <p><span class="editorial">Thomas and Ken-Ree thought the smallest rectangle can be found by drawing around the net of the box. Here are Ken-Ree's</span> <a href="/content/99/12/letme2/wrapping%20presents%20-%20Ken-Ree.docx" class="editorial">diagrams</a>.</p> <p><span class="editorial">Camille tried something similar but moved parts of the net around to get a smaller rectangle</span>.</p> <p><span style="font-style: italic;">I chose a box with 7.8cm length, 5.6 cm width and 3 cm height. Firstly, I started by turning the box on a sheet of white paper drawing around it every time to get a net. Next I cut it out. Then on another piece of paper, using what I cut out, I drew the rectangle just around its borders. On this rectangle I turned the piece of paper to see what I could move to another place to make the rectangle smaller. The final rectangle measured 14.3 cm by 14.5 cm</span>.</p> <p><span class="editorial">Well done to John from Nagoya International School who used algebra to work out this problem</span>.</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/public/viewer.php?obj_id=163&amp;part=">This activity</a> is excellent for introducing children to both surface area and to nets. It opens up the whole idea of nets that are not necessarily the ones that you would find in text books.</div> <br></br> <h3>Possible approach</h3> <div>To give more purpose to this investigation, you might like to show the children some special colourful wrapping paper to be used for preparing some boxes to be used in a display or some other appropriate purpose. Explain that because there is so little of this paper, they will first need to find out exactly how much is needed to wrap each box.</div> This activity is suitable for working in pairs (which of course will require less special paper at the end). Supply the children with lots of newspaper and a selection of boxes to choose from. Spend a little time in comparing the boxes. Ask them to predict which box they think will need the most wrapping paper, the least paper, two that might need the same amount etc. Encourage them to experiment with wrapping the boxes in various ways and to cut off parts of the sheet of newspaper, keeping it rectangular. Have the pairs demonstrate their solution to others and compare the shapes and areas of their papers. Discuss the predictions they made earlier. The piece of newspaper can then be used as a template for cutting the same rectangle from the special wrapping paper. Perhaps the children could first try to fit the templates together over the special paper in such a way that little is wasted.<br></br> <h3>Key questions</h3> <div>Tell me about the paper shape you have.</div> <div>Explain to me how each face of the Box is covered.</div> <br></br> <h3>Possible extension</h3> <div>An extension to the investigation would be to tie ribbons (or join bands of paper) around the parcels, then take them off and compare the lengths. First, ask the children to find a parcel they thought would use the same length of ribbon, one that would use less, the one that would take the longest piece etc.</div> <div> </div> <h3>For the exceptionally able</h3> Go to the Auditorium steps <a href="http://nrich.maths.org/7235&amp;part=">here</a>.<br></br> <h3>Possible support</h3> <div>Some pupils may need to simply cut out rectangles to match each face of the box and then experiment in ways of fixing them together so that they work.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Ideas like this could be encouraged and move away from the fixed idea that all should be rectangles - we can have triangles and even curves!<br></br> <div style="text-align: center;"><mdo:image width="312" height="143" src="Picture%201.jpg" alt="pic 1"></mdo:image></div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <br></br></mdoxml> 2 4 0 1 0 0 0 Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered. Measures and Mensuration Area Using, Applying and Reasoning about Mathematics Visualising Measures and Mensuration Surface and surface area Admin To be developed