7300 /www/nrich/html/content/id/7300/ 1 2011-02-28T18:16:58 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p><em>This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)</em></p> <p><span style="font-style: italic;">It may be used to follow on from </span> <a href="http://nrich.maths.org/6119&amp;part=">Cubes Here and There</a>.<br></br>  </p> <br></br> <div style="text-align: center;"> <mdo:image alt="3 of Four" height="159" src="3%20of%20Four%20Layers%207300.jpg" width="360"></mdo:image></div> <div style="text-align: left;">Looking at the three models here you may see that they have a lot in common although they are obviously different.</div> <div style="text-align: left;">The things that are the same produce the rules.</div> <div style="text-align: left;">So the rules are;</div> <div style="text-align: left;">$1$/  Each colour stays at the same level in each model.</div> <div style="text-align: left;">$2$/ Cubes of the same colour are not separated - they stay together.</div> <div style="text-align: left;">$3$/ The numbers of cubes for each colour is fixed at $1, 2, 3$ and $4$.</div> <div style="text-align: left;">$4$/ The cubes sit squarely face to face with no twists or slides.</div> <div style="text-align: left;"> </div> <div style="text-align: left;">Your challenge is to create more shapes that follow the four rules.</div> <div style="text-align: left;">When you have done so, compare them and show similarities and differences.</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Four Layers</h2> <p><em>This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)</em></p> <p><span style="font-style: italic;">It may be used to follow on from </span> <a href="http://nrich.maths.org/6119&amp;part=">Cubes Here and There</a>.<br></br>  </p> <br></br> <div style="text-align: center;"> <mdo:image alt="3 of Four" height="159" src="3%20of%20Four%20Layers%207300.jpg" width="360"></mdo:image></div> <div style="text-align: left;">Looking at the three models here you may see that they have a lot in common although they are obviously different.</div> <div style="text-align: left;">The things that are the same produce the rules.</div> <div style="text-align: left;">So the rules are;</div> <div style="text-align: left;">$1$/  Each colour stays at the same level in each model.</div> <div style="text-align: left;">$2$/ Cubes of the same colour are not separated - they stay together.</div> <div style="text-align: left;">$3$/ The numbers of cubes for each colour is fixed at $1, 2, 3$ and $4$.</div> <div style="text-align: left;">$4$/ The cubes sit squarely face to face with no twists or slides.</div> <div style="text-align: left;"> </div> <div style="text-align: left;">Your challenge is to create more shapes that follow the four rules.</div> <div style="text-align: left;">When you have done so, compare them and show similarities and differences.</div> </div> <br></br> <h3>Why do this problem?</h3> This activity challenges the most able pupils in their spatial awareness abilities. It also enables them to have something before them to explore and compare.<br></br> <br></br> <h3>Possible approach</h3> As this is intended for the most able I would suggest printing out the activity and discussing together first of all.<br></br> You could get started by asking the group to give you instructions to make the second or third model. Then let them produce their creations.<br></br> <h3><br></br> Key questions</h3> Tell me about your shapes.<br></br> So what have you found when comparing them?<br></br> What can you now explore about these?<br></br> <h3><br></br> Possible extension</h3> Pose the question about balance, asking "Does it matter if the model is stable?".<br></br> You could encourage children to explore models containing an archway/bridge.<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Have you checked that your model obeys the rules?<br></br> How will you make sure that you don&#39;t repeat any?</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div style="text-align: center;"><mdo:image alt="3 of 4 layers" height="159" src="3%20of%20Four%20Layers%207300.jpg" width="360"></mdo:image></div> <br></br> Surface Area of first one (yellow through to green) $5+7+9+11=32$<br></br> Surface Area of middle one ( as above) $5+8+12+13=38$<br></br> Surface Area of right one ( as above) $5+8+12+13=38$<br></br> <br></br> <br></br> Temp place for notes<br></br> Why do this problem?<br></br> This activity challenges the most able pupils in their spacial awareness abilities. It also enables them to have something before them to explore and compare.<br></br> Possible approach<br></br> As this is intended for the most able I would suggest printing out the activity and discussing together first of all, then let them produce their creations.<br></br> Key questions<br></br> Tell me about your shapes.<br></br> So what have you found when comparing them?<br></br> What can you now explore about these?<br></br> Possible Extension</mdoxml> 5 5 1 1 0 0 0 Can you create more models that follow these rules? Using, Applying and Reasoning about Mathematics Practical Activity Using, Applying and Reasoning about Mathematics Investigations 3D Geometry, Shape and Space Cubes Mathematics Tools Interlocking cubes