2404 /www/nrich/html/content/id/2404/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>You are going to make three Robot Monsters. They are all $5$ cm wide.</p> <p>Here are their heads which all have blue backgrounds:</p> <table style="border-style: solid; border-width: 0pt; width: 100%;border:none;"> <tbody> <tr> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="first head" bgcolor="" height="87" src="RMhead1.gif" width="141"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="second head" bgcolor="" height="172" src="RMhead2.gif" width="140"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="third head" bgcolor="" height="113" src="RMhead3.gif" width="144"></mdo:image></p> </td> </tr> </tbody> </table> <p>Here are their bodies which all have yellow backgrounds:</p> <table style="border-style: solid; border-width: 0pt; width: 100%;border:none;"> <tbody> <tr> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="first body" bgcolor="" height="141" src="RMbody1.gif" width="143"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="second body" bgcolor="" height="199" src="RMbody2.gif" width="142"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="third body" bgcolor="" height="230" src="RMbody3.gif" width="142"></mdo:image></p> </td> </tr> </tbody> </table> <p>Here are their legs which all have green backgrounds:</p> <table style="border-style: solid; border-width: 0pt; width: 100%;border:none;"> <tbody> <tr> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="first legs" bgcolor="" height="171" src="RMlegs1.gif" width="143"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="second legs" bgcolor="" height="200" src="RMlegs2.gif" width="141"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="third legs" bgcolor="" height="229" src="RMlegs3.gif" width="143"></mdo:image></p> </td> </tr> </tbody> </table> <p>What is the tallest Robot Monster that you can make using one head, one body and one set of legs?</p> <p>What is the shortest one you can make using one head, one body and one set of legs?</p> <p>How tall would the Robot Monster be that was made from the three bits left over after you had made the tallest and the shortest?</p> <p>How many Robot Monsters which are all different heights can you make with the nine pieces (all with one head, one body and one set of legs)?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">We had a couple of very full solutions to this problem. Jack and Alex from Woodfall Junior School wrote:</p> <p>The biggest robot you can make is 22cm using 6cm head 8cm body and 8cm legs</p> <p>The smallest robot you can make is 14cm using 3cm head 5cm body and 6cm legs</p> <p>The bits that are left over using 4cm head 7cm body and 7cm legs that equals 18cm</p> <p class="editorial">They went on to say:</p> <div>There are 27 ways to make different monsters but only 9 different heights of monster altogether:</div> <br></br> <br></br> <table border="0" style="border-style: solid; border-width: 0pt; width: 80%;"> <tbody><tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> Head </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> Body </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> Legs </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> Total height </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 3 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 5 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 14 </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 3 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>5</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 15</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 3 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>5</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 16</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 3 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>6</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 16</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 3 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 17</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 3 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 7 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 18</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 3 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>6</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 17</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 3 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 8 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 7 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 18 </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 3 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 8 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 8 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 19 </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 5 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 17 </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>5</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 18</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>5</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>19</div> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>6</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 19</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>20</div> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 7 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 21</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>6</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 20</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 8 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 7 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 21 </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 8 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 8 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 22 </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 4 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 20</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 4 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 19</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 4 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 8 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 6 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 18 </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 4 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>8</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 19</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 4 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>7</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>6</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 17 </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 4 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 7 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 7 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 18 </p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 4 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>5</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 8 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 17</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 4 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>5</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 7 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 16</p> </td> </tr> <tr> <td valign="top" style="border-style: solid; width: 25%;"> <p style=""> 4 </p> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>5</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>6</div> </td> <td valign="top" style="border-style: solid; width: 25%;"> <div></div> <div>15</div> </td> </tr> </tbody> </table> <p>We tried to use a systematic order to make sure we found all 27 monsters. We found all the monsters with 3cm heads first, then 6cm, then 4cm. We did the same with the bodies and legs.</p> <p class="editorial">Ruth from Swanborne House School commented:</p> <p>There are 9 possible monster heights between 14cm and 22cm (14/15/16/17/18/19/20/21/22). To prove that you could make all of them we drew a diagram of all the possible combinations, starting from the three heads. We found that once we had drawn the first head + body and leg combination for the 3cm head, we could work out the other combinations for the 3cm head quite easily, because only the body measurement varied. Then we found it was easy to adjust from this to the other two heads, and we didn't need to do the full diagram.</p> <p class="editorial">Here is the diagram that Ruth sent:</p> <p></p> <div style="text-align: center;"> <mdo:image width="500" height="348" src="ruthsol.jpg" alt="diagram of different ways of making robots"></mdo:image></div> <br></br> <p class="editorial">Two very good ways of solving this problem - well done!</p> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Robot Monsters</h2> <br></br> <p>You are going to make three Robot Monsters. They are all $5$ cm wide.</p> <p>Here are their heads which all have blue backgrounds:</p> <table style="border-style: solid; border-width: 0pt; width: 100%;" border=""> <tbody> <tr> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="first head" bgcolor="" height="87" src="RMhead1.gif" width="141"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="second head" bgcolor="" height="172" src="RMhead2.gif" width="140"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="third head" bgcolor="" height="113" src="RMhead3.gif" width="144"></mdo:image></p> </td> </tr> </tbody> </table> <p>Here are their bodies which all have yellow backgrounds:</p> <table style="border-style: solid; border-width: 0pt; width: 100%;" border=""> <tbody> <tr> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="first body" bgcolor="" height="141" src="RMbody1.gif" width="143"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="second body" bgcolor="" height="199" src="RMbody2.gif" width="142"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="third body" bgcolor="" height="230" src="RMbody3.gif" width="142"></mdo:image></p> </td> </tr> </tbody> </table> <p>Here are their legs which all have green backgrounds:</p> <table style="border-style: solid; border-width: 0pt; width: 100%;" border=""> <tbody> <tr> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="first legs" bgcolor="" height="171" src="RMlegs1.gif" width="143"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="second legs" bgcolor="" height="200" src="RMlegs2.gif" width="141"></mdo:image></p> </td> <td align="center" style="border-style: solid; border-width: 0pt; width: 33%;" valign="middle"> <p style=""><mdo:image align="top" alt="third legs" bgcolor="" height="229" src="RMlegs3.gif" width="143"></mdo:image></p> </td> </tr> </tbody> </table> <p>What is the tallest Robot Monster that you can make using one head, one body and one set of legs?</p> <p>What is the shortest one you can make using one head, one body and one set of legs?</p> <p>How tall would the Robot Monster be that was made from the three bits left over after you had made the tallest and the shortest?</p> <p>How many Robot Monsters which are all different heights can you make with the nine pieces (all with one head, one body and one set of legs)?</p> </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <a href="http://nrich.maths.org/public/viewer.php?obj_id=2404&amp;part=index">This problem</a> is one on measurement that really focuses on number work - addition, ordering numbers and combinations. Manipulating the pictures can also help pupils to explore the different combinations systematically.<br></br> <h3>Possible approach</h3> <div>You could start by showing the whole group the pictures in the problem on a computer. Young children will probably want to discuss these. Explain that each Robot Monster needs a head, a body and a pair of legs. You could ask how tall a picture of a robot would be using a certain combination of head, body and legs.</div> <br></br> <div>Then you could set the task in the problem. If the children can have pictures from <a href="/content/id/2404/robotM.doc">this sheet</a> they will find the activity more enriching. [If these pictures are printed onto card and laminated they will make a lasting resource.] It is helpful if the children can work in pairs so that they are able to talk through their ideas with a partner.</div> <br></br> <div>At the end of the lesson the group could discuss the tallest and shortest robots, and all the different combinations they have found. If you have made pieces printed onto card, these could be fixed onto the board so that this discussion can be illustrated.</div> <br></br> <h3>Key questions</h3> <div>If a Robot Monster is going to be as tall/short as possible, which head will you choose?</div> <div>If a Robot Monster is going to be as tall/short as possible, which body and set of legs will you choose?</div> <div>Can you think of a good way to find all the different heights you can make?</div> <div>Why not start with one head and look at all the different ways you could add body and legs to it?</div> <div>How are you going to record what you have found out?</div> <br></br> <h3>Possible extension</h3> Learners could make their own robot monsters in different sizes or try <a href="http://nrich.maths.org/public/viewer.php?obj_id=6227&amp;part=index">Find the Difference</a> or The <a href="http://nrich.maths.org/public/viewer.php?obj_id=2354&amp;part=index">Tall Tower</a>.<br></br> <h3>Possible support</h3> <div>Suggest using the pieces from <a href="/content/id/2404/robotM.doc">this sheet</a> and trying it out practically.</div> <div> </div> <div>Handouts for teachers are available here (<a href="/content/id/2404/Robot%20Monsters.doc">word document</a>, <a href="/content/id/2404/Robot%20Monsters.pdf">pdf document</a>), with the problem on one side and the notes on the other. </div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> You could use the pieces from <a href="/content/id/2404/robotM.doc">this sheet</a> and try it out practically. <p>If a Robot Monster is going to be as tall as possible, which head will you choose? So which body and set of legs will you add?</p> <p>To work out how many Robot Monsters you can make of different heights, why not start with one head and look at all the different ways you could add body and legs to it?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Head Body Legs Total height <br></br>3 5 6 14 <br></br>3 7 6 16 <br></br>3 8 6 17 <br></br>3 5 7 15 <br></br>3 5 8 16 <br></br>3 7 7 17 <br></br>3 7 8 18 <br></br>3 8 7 18 <br></br>3 8 8 19 <br></br>6 5 6 17 <br></br>6 7 6 19 <br></br>6 8 6 20 <br></br>6 5 7 18 <br></br>6 5 8 19 <br></br>6 7 7 20 <br></br>6 7 8 21 <br></br>6 8 7 21 <br></br>6 8 8 22 <br></br>4 5 6 22 <br></br>4 7 6 17 <br></br>4 8 6 18 <br></br>4 5 7 16 <br></br>4 5 8 17 <br></br>4 7 7 18 <br></br>4 7 8 19 <br></br>4 8 7 19 <br></br>4 8 8 20 <br></br>Tallest: head 6 cm, body 8 cm, legs 8 cm = 22 cm S<br></br>hortest: 3 cm + 5 cm + 6 cm = 14 cm. <br></br>Robot Monster made from bits left over: 4cm + 7cm + 7cm = 18cm <br></br>There are nine different heights Robot Monsters could be: 14cm, 15cm, 16cm, 17cm, 18cm, 19cm, 20cm, 21cm, 22cm <br></br><br></br></mdoxml> 2 3 1 0 0 0 0 Use these head, body and leg pieces to make Robot Monsters which are different heights. Numbers and the Number System Comparing and Ordering numbers Calculations and Numerical Methods Addition & subtraction Using, Applying and Reasoning about Mathematics Working systematically Decision Mathematics and Combinatorics Combinations Admin Lower primary mapping document