Super Shapes

1056 /www/nrich/html/content/01/05/penta3/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Each of the following shapes has a value: <table cellpadding="7" border="0"> <tbody> <tr> <td><mdo:image alt="green triangle" src="letmetri.gif"></mdo:image></td> <td>$= 7$</td> <td><mdo:image alt="orange rectangle." src="letmerec.gif"></mdo:image></td> <td>$= 17$</td> <td><mdo:image alt="red circle." src="letmecirc.gif"></mdo:image></td> <td>$= \; ?$</td> </tr> </tbody> </table> The value of the circle changes in each of the following problems. Can you discover its value in each problem, if the value of the shapes are being added together? <table border="0"> <tbody> <tr> <td>(a)</td> <td><mdo:image width="150" height="47" src="one.gif" alt=""></mdo:image></td> <td>$= 25$</td> </tr> <tr> <td>(b)</td> <td><mdo:image width="189" height="39" src="two.gif" alt=""></mdo:image></td> <td>$= 51$</td> </tr> <tr> <td>(c)</td> <td><mdo:image width="266" height="39" src="three.gif" alt=""></mdo:image></td> <td>$=136$</td> </tr> <tr> <td>(d)</td> <td><mdo:image width="133" height="33" src="four.gif" alt=""></mdo:image></td> <td>$=48$</td> </tr> <tr> <td>(e)</td> <td><mdo:image width="350" height="47" src="five.gif" alt=""></mdo:image></td> <td>$=100$</td> </tr> </tbody> </table> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Joanne wrote: In the first line the circle is worth 1. I worked this out by adding 17 and 7 together = 24 then add 1 =25 In the second line the circle is worth 20. I worked this out by adding together 17, 7, 7 =31 add 20 =51 In the third line the circle is worth 44. I worked this out by adding together 17, 17, 7 and 7 =38 In the fourth line the circle is worth 16. I worked this out by doing 48 divided by 3 =16 In the fifth line the circle is worth 27.5 I used the same method as the 1st, 2nd and 3rd lines. Christopher and Matthew explain further about the final answer: On the last one the total was 100. We had to add 17 + 7 + 7 + 7 + 7 = 45. This meant there was 55 left which we halved to get the answer 27 and a half. Matthew from Worth School agreed with the answers given above but has recorded his thinking differently: I looked at it as an equation. What Matthew already knows: Triangle = 7, Rectangle = 17 and he uses C = circle 1. If 17+C+7=25 then C =? This can be rearranged as: 25-(17+7)=C 25-24=C 1=C 2. If 17+7+7+C=51 then C=? This can be rearranged as: 51-(17+7+7)=C 51-31=C 20=C 3. If 7+7+17+17+C+C=136 then C=? This can be rearranged as: 136-(7+7+17+17)=2C 136-48=2C 88=2C 44=C 4. If C+C+C=48 then C=? This can be rearranged as: 48=3C 48/3=C 16=C 5. If 7+C+7+17+7+C+7=100 then C=? This can be rearranged as: 28+17+2C=100 45+2C=100 2C=100-45 2C=55 C=27.5 Thank you also to sets of Moorfield pupils, Niall and Adam , Steven and Matthew, Christopher, Elliot and Luke, Hannah, Amy and Emma, Thomas and Robert , as well as to Abi . From Ms Flynn's class in Ringmer County Primary in Sussex, we heard from Nick and Tom. Ellen, Stacie, Rosie and Natasha from St. Aldhelm's Combined School all sent in the mail their calculations to this set of problems. Carla and Georgia from Tattingstone Primary School in Suffolk both sent their work as email attachments. Well done also to Mithran . Each one of you put a lot of effort into your work and your explanations were clear and well thought-out. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Super Shapes</h2> Each of the following shapes has a value: <table style="" border=""> <tbody> <tr> <td><mdo:image alt="green triangle" src="letmetri.gif"></mdo:image></td> <td>$= 7$</td> <td><mdo:image alt="orange rectangle." src="letmerec.gif"></mdo:image></td> <td>$= 17$</td> <td><mdo:image alt="red circle." src="letmecirc.gif"></mdo:image></td> <td>$= \; ?$</td> </tr> </tbody> </table> The value of the circle changes in each of the following problems. Can you discover its value in each problem, if the value of the shapes are being added together? <table style="" border=""> <tbody> <tr> <td>(a)</td> <td><mdo:image alt="" height="47" src="one.gif" width="150"></mdo:image></td> <td>$= 25$</td> </tr> <tr> <td>(b)</td> <td><mdo:image alt="" height="39" src="two.gif" width="189"></mdo:image></td> <td>$= 51$</td> </tr> <tr> <td>(c)</td> <td><mdo:image alt="" height="39" src="three.gif" width="266"></mdo:image></td> <td>$=136$</td> </tr> <tr> <td>(d)</td> <td><mdo:image alt="" height="33" src="four.gif" width="133"></mdo:image></td> <td>$=48$</td> </tr> <tr> <td>(e)</td> <td><mdo:image alt="" height="47" src="five.gif" width="350"></mdo:image></td> <td>$=100$</td> </tr> </tbody> </table> </div> <h3>Why do this problem?</h3> <div><a href="http://nrich.maths.org/public/viewer.php?obj_id=1056&part=index">This problem</a> provides an opportunity for pupils to practise using addition and subtraction, and it reinforces their inverse relationship. The problem gives learners chances to explain their working and it also helps them become familiar with the idea of a symbol (in this case a shape) representing a number.</div> <h3>Possible approach</h3> <div>This problem would make a good starter. You could print off <a href="/content/01/05/penta3/SuperShapes.doc">this sheet</a> of the problem for children to work from and make sure that paper and/or mini-whiteboards are available for them to jot down any workings.</div> <div>It would be important to talk about the methods that learners have used in each case and so invite a few children to share their way of working. The method is likely to differ depending on which problem is being solved and you can use this as an opportunity for the group to reflect on why particular approaches were chosen in each case. Emphasise that the method used is entirely up to the individual, but you may discuss which could be the most efficient.</div> <h3>Key questions</h3> <div>How did you work this out?</div> <h3>Possible extension</h3> <div><a href="http://nrich.maths.org/public/viewer.php?obj_id=5714&part=index">Shape Times Shape</a> involves multiplication rather than addition and requires much more sophisticated reasoning.</div> <h3>Possible support</h3> <div>You could provide calculators if you want children to focus on the method rather than the arithmetic.</div> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">What do the other shapes add up to in each case? So, what is left for the circle or circles? </mdoxml> 2 3 0 1 0 0 0 Super Shapes The value of the circle changes in each of the following problems. Can you discover its value in each problem? Calculations and Numerical Methods Multiplication & division Calculations and Numerical Methods Addition & subtraction Algebra Introducing algebra Admin Upper primary mapping document