6931 /www/nrich/html/content/id/6931/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <div style="float: right;"><mdo:image height="241" width="80" src="10Cubes.jpg" alt="10 cubes"></mdo:image></div> <div>Long ago, I made a string of ten graded cubes.</div> <div> </div> <div>Each edge of the smallest cube was one centimetre long. Each edge of the largest cube was ten centimetres long.</div> <div> </div> <div>I labelled each one with its volume in cubic centimetres.</div> <div> </div> <div>The challenge for you is to make a string of graded cubes. You might do better working in a team, so encourage your friends to help!</div> <div> </div> <div>We would love to hear how you made your own cubes and to see photos of them.</div> <div></div><br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <span class="editorial">Class 5AM from St Peter's School, Barcelona, worked on this problem in groups.</span> <a class="editorial" href="/content/id/6931/Next%20Size%20up%20-%20st%20peters.docx">Here</a> <span class="editorial">is their report.</span><br></br>  <br></br> <span class="editorial">Yusuf from Columbia Primary School told us:</span><br></br> <br></br> We made our cubes using modular origami. We had to measure each piece of paper to make sure it was the correct size and that it would make the right sized cube. We worked out the volume of each cube and wrote it on the side.<br></br>  <br></br> <span class="editorial">Kathy and Pete from Barley Hill Primary School decided to see what patterns they could find by making cuboids.</span><br></br>  <br></br> First we drew the nets of our cuboids.<br></br>  <br></br>  <mdo:image height="395" width="279" alt="small net" src="nextSizeUp1%20small.png"></mdo:image><mdo:image height="389" width="278" src="nextSizeUp2%20small.png" alt="small net 2"></mdo:image><br></br> We noticed that the volume of our first set where we just added one square to the length of the rectangle went up by $1$ each time. The volume of our second set went up by $4$ each time. This is different to the set of cubes in the problem which went up different amounts each time because we only changed one length of our shape.<br></br>  <br></br> <span class="editorial">Here is a picture of their graded cuboids.</span><br></br> <mdo:image height="408" width="244" alt="cuboid" src="cuboids%20small.jpg"></mdo:image><br></br> <span class="editorial">Well done for sending in your pictures.</span><br></br> <span class="editorial"> </span> <br></br> <span class="editorial">There are lots more shapes you could make - you could see what happens to the volume if you change more than one side of a cuboid.</span><br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Next Size Up</h2> <br></br> <div style="float: right;"><mdo:image alt="10 cubes" height="241" src="10Cubes.jpg" width="80"></mdo:image></div> <div>Long ago, I made a string of ten graded cubes.</div> <div> </div> <div>Each edge of the smallest cube was one centimetre long. Each edge of the largest cube was ten centimetres long.</div> <div> </div> <div>I labelled each one with its volume in cubic centimetres.</div> <div> </div> <div>The challenge for you is to make a string of graded cubes. You might do better working in a team, so encourage your friends to help!</div> <div> </div> <div>We would love to hear how you made your own cubes and to see photos of them.</div> <div> </div> <br></br>  </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/6931&amp;part=">This problem</a> is fundamentally a practical one, which involves careful measuring and drawing. But by making a string of graded cubes for themselves, children&#39;s understanding of length and volume will be deepened far more than through just calculating volumes of hypothetical cubes. The problem could be used as a group or team activity where learners cooperate and work together for a common purpose. </div> <br></br> <h3>Possible approach</h3> <div>You could begin by showing the group the string of cubes pictured in the problem and invite them to talk in pairs about what they see. Open up the discussion so that the whole group participates and eventually comes to a consensus about what is pictured.  You can then introduce the challenge to make a set of cubes for themselves.</div> <div> </div> <div>This problem could be a good way to introduce the idea of a net of a cube, or you could choose to set the challenge having already worked on nets. The group&#39;s prior experience of nets will influence the way you facilitate the activity and the frequency with which you bring them all together to share progress.</div> <div> </div> <div>Invite groups of learners to work together on this task and try not to be too prescriptive in terms of the way they approach it and the materials they use. It might be worth ensuring that sharp pencils, rulers, thin card (preferably squared), glue and sticky tape are available, should a group require them. (<a href="/content/id/6931/1cmSqs.pdf">This squared sheet</a> for printing onto thin card might be useful.) Some groups might want to use the computer to create their net. Thin thread and a needle will also be needed to hang up the shapes.</div> <div> </div> <div>It might be that the whole class decides to distribute the work amongst the groups so that one or two sets are produced in total.</div> <br></br> <h3>Key questions</h3> <div>How will you make a cube from paper/card?</div> <div>What can you tell me about a cube?</div> <div>How do you know how big each cube will be?</div> <div>How will you share out the work?</div> <br></br> <h3>Possible extension</h3> Learners could make a string of other more ambitious shapes such as tetrahedra or octahedral although calculating the exact volume of these might be too tricky.<br></br> <h3>Possible support</h3> Some children will find this <a href="/content/id/6931/CubeNet.gif">net</a> a useful starting point.<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Using squared card or paper will help. <br></br> You could download <a href="/content/id/6931/1cmSqs.pdf">this squared sheet</a> and print it out on thin card. You will need several sheets to make the larger cubes. <br></br> How can you draw a net of a cube? You could look at <a href="http://nrich.maths.org/1140&amp;part=">this problem</a>. <br></br> <br></br></mdoxml> 5 4 0 1 0 0 0 The challenge for you is to make a string of six (or more!) graded cubes. Using, Applying and Reasoning about Mathematics Practical Activity Measures and Mensuration Volume and capacity 3D Geometry, Shape and Space Cubes 3D Geometry, Shape and Space Regular polyhedra 3D Geometry, Shape and Space 2D representations of 3D shapes Admin Upper primary mapping document