1000 /www/nrich/html/content/00/05/penta2/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Nina must cook some pasta for 15 minutes. The only way she has of measuring time is a 7-minute sand-timer and an 11-minute sand-timer.</p> <mdo:image width="183" height="124" alt="" src="fig1.gif"></mdo:image><br></br> <p>How can she use these timers to measure exactly 15 minutes?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">Lots of good answers sent in for this one! Well done everyone! There were three types of solutions.</p> <p><strong class="editorial">Method A. Turning the 7-minute timer three times</strong></p> <p><span class="editorial">Grace (Tao Nan School, Singapore) said this ...</span></p> <ol> <li>Turn both timers.</li> <li>When 7 minutes is past (she'll know by the timers), turn the 7-minute timer over.</li> <li>When the 11-minute timer finishes, turn the 7-minute timer over. When the 7-minute timer finishes, 15 minutes has passed.</li> </ol> <p>Why?<br></br> 11-7=4. This makes the leftover sand in the 11-minute timer 4 minutes.<br></br> In that case, when the 11 minutes are over, the 7-minute timer will have<br></br> 3 minutes worth of sand left. 7-3=4, so 11+4=15 minutes.</p> <p><span class="editorial">Will and Scott (Antingham Southrepps Primary, Norfolk) said:</span></p> We think that you should set the timers off at the same time ,<br></br> <br></br> <ul> <li>when the 7 timer runs out turn the 11 timer over ,</li> <li>when that one runs out turn the 7 timer over</li> <li>when the 7 timer runs out violla! 15 minutes.</li> </ul> <p><span class="editorial">And here's one from Anna (Braga, Portugal)</span></p> <ul class="noindent"> <li>We have a 7-minute sand-timer and an 11-minute sand-timer.</li> <li>First we have to turn around both of them at the same time.</li> <li>After 7 minutes (measured with the 7-minute sand-timer) we realise that we have 4 minutes left in the 11 one.</li> <li>At this time we must turn the 7-minute sand-timer and let the 11 go.</li> <li>At the moment the 11-minute sand-timer is finished we have 3 minutes left (4 minutes passed) on the other sand-timer.</li> <li>The last step consists in turning the 7-minute sand-timer upside-down and let the 4 minutes pass.</li> <li>This way Nina measured 15 minutes and she got her pasta deliciously cooked!</li> </ul> <p><span class="editorial">George (Rosebank Primary School, Leeds) sent in a good explanation too.</span></p> <p><strong>Method B: Delay the start of cooking</strong></p> <p><span class="editorial">Alistair (Tao Nan School, Singapore) sent in this solution:</span></p> Firstly start both the 7-minute and the 11-minute timer.<br></br> 7 minutes later, the 7-minute timer will have run out of sand.<br></br> Turn the cooker on at that point.<br></br> 4 minutes later, the 11-minute timer will have run out of sand. Turn it over.<br></br> <br></br> <p>Since 4 + 11 = 15, turning off the cooker when the 11-minute timer runs out of sand will cook the pasta for exactly 15 minutes!</p> <p><span class="editorial">Tom, Robert and Carly (Histon Junior School, Cambridge) say:</span></p> <br></br> Nina should start both the timers at the same time.<br></br> <br></br> <ul class="noindent"></ul> <div>When the 7 minute timer stops, then put the pasta in</div> <div>then the 11 minute timer will only have 4 minutes left,</div> <div>so when that timer finishes she should turn the timer back over.</div> <div>Then when those 11 minutes have gone by the pasta has been cooked for 15 minutes.</div> <ul class="noindent"></ul> <ul class="noindent"></ul> <div>11 - 7 = 4</div> <br></br> <div>4 + 11 = 15</div> <br></br> <br></br> <p class="editorial">Daniel (Anglo-Chinese School - Primary, Singapore) thought about it the same way and sent in another good table. Thomas, Kimberley, Catherine, Matthew and Justin, all of Tattingstone School, each explained the same idea in their own way. Well done - they were all very clearly written.</p> <p><strong>Method C: Stop the timer</strong></p> <p><span class="editorial">Celia (Roundwood Primary, Harpenden, Hertfordshire) found another way:</span></p> <p>Start by turning over the 7 timer and the 11 timer together.<br></br> When the 7 timer stops, turn the 11 timer on it's side, because it has 4 mins. on it.<br></br> START COOKING<br></br> Immediately turn up the 11 timer and use the remaining 4 mins.<br></br> Then use it again (11 mins.)<br></br> 11 + 4 =15<br></br> You have done 15 mins.<br></br> FOOD'S ON THE TABLE.</p> <div class="noindent" style="margin-left: 2em;"></div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/public/viewer.php?obj_id=1000&amp;part=index"> This problem</a> requires children to combine addition, subtraction and logical thinking.</div> <br></br> <br></br> <h3>Key questions</h3> <div>How are you going to start?</div> <div>How much longer does the 11-minute timer take than the 7-minute timer?</div> <br></br> <h3>Possible extension</h3> <div>Challenge children to find at least two more ways of solving the problem.</div> <br></br> <h3>Possible support</h3> <div>You could suggest some starting points and ask children to work from there.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">How are you going to start? <br></br> How much longer does the 11-minute timer take than the 7-minute timer?<br></br></mdoxml> 2 3 0 1 0 0 0 Development list sfh10 Steve - Development