1002 /www/nrich/html/content/00/05/penta4/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>Stuart's watch loses two minutes every hour.<br></br> Adam's watch gains one minute every hour.<br></br> They both set their watches from the radio at 6:00 a.m. then start their journeys to the airport. When they arrive (at the same time) their watches are $10$ minutes apart.</p> <mdo:image width="66" height="76" src="fig1.gif" alt=""></mdo:image> <br></br> <p>At what time (the real time) did they arrive at the airport?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <strong class="editorial" style="font-weight: bold;">Jason</strong> <span class="editorial">from Priory Middle School, Dunstable says:</span> <p>The time where the 2 watches are 10 mins apart is 9:20.</p> <p>At 7 o'clock they're 3 mins apart<br></br> At 8 o'clock they're 6 mins apart<br></br> 9 o'clock, 9 mins.<br></br> For 1 minute you divide 1 hour by 3, as 20 is 3 times as small as 60.<br></br> Then you add 9:00 and 0:20 to make 9:20, which is when they are 10 mins apart.</p> <p class="editorial">Stuart and Mark (Lower Juniors at Cummersdale, Cumbria) also say 9:20. They used this technique:</p> <br></br> <p>Every hour the difference between the two watches increases by 3 minutes 3x3=9<br></br> That gives us 3 hours and then divide 60 into 3 to make 20 minutes<br></br> 3hours + 20mins = 3 20mins<br></br> 6:00 a.m. + 3hrs 20 mins = 9:20 a.m.</p> <p><strong><span class="editorial" style="font-weight: bold;">George</span></strong> <span class="editorial">(Rosebank Primary School, Leeds) drew diagrams to show his thinking:</span></p> <p>I knew that it would take them 3 hours and something because every hour they got three minutes apart. That meant that it will have minutes as well as hours. I knew that Stuart's and Adam's watches went three minutes apart every hour. Now I needed to know how many minutes apart the boys' watches go in one minute. For this I drew a scale.</p> <mdo:image alt="" src="fig0.gif"></mdo:image> <br></br> <p>Then I marked how much they'd be apart.</p> <mdo:image alt="" src="fig2.gif"></mdo:image> <br></br> <p>This showed me that it must be between 15 and 30 minutes. When I divided it into even smaller parts I got the answer.</p> <mdo:image alt="" src="fig3.gif"></mdo:image> <br></br> <p>This got me to the answer, which is 3 hours and twenty minutes.</p> <p><strong class="editorial" style="font-weight: bold;">Daniel</strong> <span class="editorial">(Anglo-Chinese School - Primary, Singapore),</span> <strong class="editorial" style="font-weight: bold;">Thomas</strong> <span class="editorial">(Tattingstone School) and</span> <strong><span class="editorial" style="font-weight: bold;">Timothy</span></strong> <span class="editorial">(Munsang College, Hong Kong) gave very similar explanations. The one below is Timothy's:</span></p> <p>Stuart's watch loses 2 min every hour and Adam's watch gains 1 min every hour,<br></br> so they are 1 + 2 = 3 min apart after the 1st hour and 3 more mins after every hour.<br></br> When they arrive at the airport, their watches are 10 mins apart, so they travel:<br></br> 10/3 hours = 60 x 10/3 = 200min = 3hours and 20mins<br></br> They start at 6:00am, so they arrive at 9:20am.</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Wonky Watches</h2> <p>Stuart&#39;s watch loses two minutes every hour.<br></br> Adam&#39;s watch gains one minute every hour.<br></br> They both set their watches from the radio at 6:00 a.m. then start their journeys to the airport. When they arrive (at the same time) their watches are $10$ minutes apart.</p> <mdo:image alt="" height="76" src="fig1.gif" width="66"></mdo:image><br></br> <p>At what time (the real time) did they arrive at the airport?</p> </div> <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=1002&amp;part=index">This problem</a> consolidates children&#39;s understanding of the passage of time and encourages them to work systematically towards a solution. There are many ways of approaching this problem so it would be worth drawing attention to this.</div> <br></br> <h3>Possible approach</h3> <div>This problem would make a good challenge activity for the end of a block of work on time. You could begin by posing a few quick questions to make sure the children understand what gaining and losing time means. For example, if I wind up my watch so it shows the correct time at 5pm, but it loses three minutes every hour, what time will it say when the real time is 7pm? 8pm ... etc?</div> <br></br> <div>You could present the problem itself orally to the group, perhaps writing up the key pieces of information on the board. Allow pairs or small groups to talk about how they might go about solving the problem without saying much more yourself at this stage. After just a few minutes, encourage learners to share some of their thoughts and then give them more time to work on the problem. Give each group a large sheet of paper so that they can record what they do and tell them that they will present their work to everyone at the end.</div> <br></br> <div>Once the pupils have reached a solution and have presented their results, their pieces of paper could be displayed on the wall.</div> <br></br> <h3>Key questions</h3> <div>What time will each watch say after an hour? Two hours ...?</div> <div>How far apart will the times on the two watches be after an hour? Two hours ...?</div> <br></br> <h3>Possible extension</h3> <div>You could challenge some children to make up their own version of the problem according to certain criteria, for example, if the watches were $10$ minutes apart on the hour, what could the amount that they gain/lose be?</div> <br></br> <h3>Possible support</h3> <div>Breaking the problem down to an hour at a time might help some learners.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">What time will each watch say after an hour? Two hours ...? <br></br> How far apart will the times on the two watches be after an hour? Two hours ...?<br></br></mdoxml> 2 4 0 1 0 0 0 Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport. Measures and Mensuration Time Mathematics Tools Clock Using, Applying and Reasoning about Mathematics Working systematically Admin Upper primary mapping document