7299 /www/nrich/html/content/id/7299/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <div style="text-align: left;">We have a cube which is a bit like a dice, with inky marks on each face.</div> <div style="text-align: left;">When it goes on paper it shows these numbers one by one.</div> <div style="text-align: center;"> <mdo:image height="63" width="268" src="numerals.jpg" alt="numerals"></mdo:image></div> <div style="text-align: left;">The cube just gradually rolls over (NO SLIDING) and prints the following (I've draw squares round each number):</div> <div style="text-align: left;"> </div> <div style="text-align: center;"><mdo:image height="447" width="338" alt="paper" src="paper.jpg"></mdo:image></div> <div style="text-align: left;">Your challenge is to find where the cube starts and what route it travels to print the numbers exactly as shown above.  You may find it useful to print off a copy of the grid on <a href="/content/id/7299/RollingThatCube.pdf">this sheet</a>.</div> <div style="text-align: left;"> </div> <div style="text-align: left;">Can you also say how each face of the cube looks?</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">This activity produced a few replies. Oliver from St. Anthony's sent in;</p> <br></br> R R D L L D D R R U L<br></br> <br></br> <p><span class="editorial">Tessa, Sally and Kensa from Sherwood State School  in Australia sent in their solution like this;</span></p> <br></br> $1, 4, 6, 2, 4, 5, 1, 2, 4, 5, 1, 4$<br></br>  <br></br> <p><span class="editorial">Hanako and Emilia at Vale Junior School, Guernsey sent in this word document;</span></p> <br></br> First we decided to make a cube to physically test our theories and ideas.<br></br> We spotted that there were two impossible routes. These were: the rotating $4$s down the middle and the $1, 4, 1$ combination going across. <br></br> These are impossible because you can't have two $4$s next to each other as there is only one four on the dice. The other is impossible as to get from $1$ to $4$, and then to $1$ again, you would have to double back on yourself.<br></br> Next, we had to think of a route that bypassed these two impossible combinations. We thought that we could start our route with the $4$ in the impossible $1, 4, 1$ combination so that we didn't have to complete the whole impossible combination.<br></br>  <br></br> <div style="text-align: center;"> <mdo:image height="203" width="156" alt="Roll Dice" src="Roll%20Dice.jpg"></mdo:image></div> <br></br> We checked that our theory was correct by rolling our cube along the grid. As we rolled it, we wrote the next number in the grid as a reflection on the next face of the cube. We tried starting at the top $1$ and the centre $4$ and we found that this route works both ways.<br></br>  <br></br> <p class="editorial">Thank you Hanaho and Emilia for explaining how you did it and what your thoughts were and well done all of you!</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Rolling That Cube</h2> <br></br> <div style="text-align: left;">We have a cube which is a bit like a dice, with inky marks on each face.</div> <div style="text-align: left;">When it goes on paper it shows these numbers one by one.</div> <div style="text-align: center;"> <mdo:image alt="numerals" height="63" src="numerals.jpg" width="268"></mdo:image></div> <div style="text-align: left;">The cube just gradually rolls over (NO SLIDING) and prints the following (I&#39;ve draw squares round each number):</div> <div style="text-align: left;"> </div> <div style="text-align: center;"><mdo:image alt="paper" height="447" src="paper.jpg" width="338"></mdo:image></div> <div style="text-align: left;">Your challenge is to find where the cube starts and what route it travels to print the numbers exactly as shown above.  You may find it useful to print off a copy of the grid on <a href="/content/id/7299/RollingThatCube.pdf">this sheet</a>.</div> <div style="text-align: left;"> </div> <div style="text-align: left;">Can you also say how each face of the cube looks?</div> </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This <a href="http://nrich.maths.org/7299&amp;part=">activity</a> is one which will particularly appeal to those pupils who enjoy problem solving or have  good spatial awareness. It may, therefore, be a useful activity for a whole class - as it will enable you to see more clearly which pupils work well on spatial challenges.  It also offers opportunities for learners to share different ways of approaching the task.</div> <br></br> <h3>Possible approach</h3> <div>Depending on the pupils&#39; experiences, it may be appropriate to start with them altogether with a practical simplified example. Using a large cardboard/foam cube with simple shapes on each of the six faces, like this ...</div> <div style="text-align: center;"> <mdo:image alt="simple" height="194" src="simple.jpg" width="193"></mdo:image></div> <div>... they could observe what happens as it rolls and try to predict what face will be at the bottom each time.</div> <div style="text-align: left;"> </div> <div style="text-align: left;">You could then present the challenge itself and give children time to work independently or in pairs.  A copy of the route can be found on <a href="/content/id/7299/RollingThatCube.pdf">this sheet</a>. Try not to direct the way they work as you may be suprised by the methods they create. </div> <div style="text-align: left;"> </div> <div style="text-align: left;">The plenary can then focus on their different approaches.  Allow time for all the different ways to be explained and then encourage pairs/small groups to discuss which method they might use if they were presented with a similar problem. Can they justify their choice?</div> <br></br> <h3>Key questions</h3> <div>When working with the simple cube above;</div> <div>What&#39;s happening here?</div> <div>What can you tell me about the one at the bottom when I roll it this way?</div> <div> </div> <div>When working on the actual challenge;</div> <div>How are you working this out?</div> <div>Will you be able to check that it&#39;s ok?</div> <br></br> <h3>Possible extension</h3> <div>When pupils have managed this activity in a confident way they may like to have a look at <a href="http://nrich.maths.org/7241&amp;part=">Inky Cube</a> which is similar but much harder. You could also give the pupils opportunities to create their own cubes and set challenges for each other.</div> <br></br> <h3>Possible support</h3> <div>Many pupils may need to have support in rolling a cube over carefully. Be aware though that some pupils who need support in the more numerical aspect of mathematics may not need any support in this spatial work.</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">How will you know what you have tried so far?<br></br> Are there any rolls that you know are impossible?<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image width="156" height="203" src="Roll%20Dice.jpg" alt="roll dice"></mdo:image><br></br>  <br></br></mdoxml> 5 3 1 1 0 0 0 My cube has inky marks on each face. Can you find the route it has taken? What does each face look like? Using, Applying and Reasoning about Mathematics Working systematically Decision Mathematics and Combinatorics Route inspection problems Admin Lower primary mapping document Admin Upper primary mapping document