1014 /www/nrich/html/content/00/09/penta1/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Norrie is watching the aircraft warning lights on the tops of some tall buildings in the city. He sees two lights flash at the same time, then one of them flashes every $4$th second, and the other flashes every $5$th second.<br></br> How many times do they flash together during a whole minute?</p> <mdo:image alt="Flash" src="prob1.gif"></mdo:image> <br></br> <p>Norrie then watched a third light. He saw it flash at the same time as the other two, then flash every $7$th second. How many minutes before this light again flashes at exactly the same time as the other two?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <em>(Thank you to Norrie McKay and the lights over Tokyo Bay for this problem)</em> <p><span class="editorial">There were many correct answers sent in for this problem. As</span> <strong class="editorial" style="font-weight: bold;">Primary Maths Club</strong> <span class="editorial">(International School of Toulouse) pointed out, it helps if you start counting seconds from the first time the two lights flashed together (at zero seconds).</span></p> <p class="editorial">Some people thought about a number line, others looked for a number that both of the numbers of seconds (4 and 5) would divide into (common multiple). Here are two very well explained solutions.</p> <p><strong style="font-weight: bold;" class="editorial">Holly, Harriette, Caroline, Florence</strong> <span class="editorial">and Rebecca from The Mount School, York:</span></p> 1st light 0 - 4 - 8 - 12 - 16 - 20 - 24 - ......<br></br> 2nd light 0 - 5 - 10 - 15 - 20 - 25 - ........<br></br> <br></br> They flash at the same time every 20 seconds 0 - 20 - 40 - 60<br></br> That's four times in all.<br></br> <br></br> For two lights the pattern was every 20 seconds and 4 x 5 = 20<br></br> For the three lights it is going to be 4 x 5 x 7 = 140 seconds or 2 minutes 20 seconds<br></br> <br></br> <br></br> <p><span class="editorial">Christina from Marlborough Primary School</span> :</p> To work this out you need to find a multiple of both 5 and 4 which is 20. So the lights flash together every 20 seconds and to find out how many times they flash in one minute you need to do 60/20 = 3 which means that they flash together 3 times a minute.<br></br> <br></br> You need to find a multiple of 20 and seven to work out how many minutes before all of the lights flash together. 20 x 7 = 140 sec = 2 mins 20 sec<br></br> <br></br> <span class="editorial">Well done to all of the following people: Jesse, Edward, Daniel and Thomas from Tattingstone School who did some very good work with finding the multiples. Lily from Sotogrande International School, Daniel from Anglo-Chinese School, Singapore, Abigail, Charles and David from Moorgate Primary School, Staffordshire, Jason from Priory School, Thomas from St Francis School, Maldon and Ashley.</span> <br></br> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Flashing Lights</h2> <br></br> <p>Norrie is watching the aircraft warning lights on the tops of some tall buildings in the city. He sees two lights flash at the same time, then one of them flashes every $4$th second, and the other flashes every $5$th second.<br></br> How many times do they flash together during a whole minute?</p> <mdo:image alt="Flash" src="prob1.gif"></mdo:image><br></br> <p>Norrie then watched a third light. He saw it flash at the same time as the other two, then flash every $7$th second. How many minutes before this light again flashes at exactly the same time as the other two?</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=1014&amp;part=index">This problem</a> is a good way of introducing children to common multiples and it is also a useful context for looking at different recording methods.</div> <br></br> <h3>Possible approach</h3> <div>As a starter, you could split the class into two groups. One group will clap every $3$ beats and the other every $6$ beats, while you count the beats. Ask them to predict on which beats they will all be clapping. Try other rhythms in the same way e.g. $3$ and $4$. Can they explain why everyone will be clapping on certain beats? How would they work out which beats these were without clapping?</div> <br></br> <div>Then you could introduce the flashing lights context and ask children to work in pairs on it. After a short time, stop them briefly to share some of the different ways they are working and, in particular, to look at what they are writing down to help them. For example, some might list multiples, some might list consecutive numbers but highlight multiples in some way, some might colour numbers in the $100$ square ... You could talk about the advantages of each method discussed. In this instance, the recording is only for them. What might they do differently if they were recording their work for someone else to understand?</div> <br></br> <div>In the plenary, you can specifically introduce the vocabulary of common multiples if you haven&#39;t done so already.</div> <br></br> <h3>Key questions</h3> <div>When will the first light flash?</div> <div>When will the second light flash?</div> <div>So when will they flash together?</div> <div>What do you notice about the times when they flash together?</div> <div>How would you predict when they will flash together next?</div> <br></br> <h3>Possible extension</h3> <div><a href="http://nrich.maths.org/public/viewer.php?obj_id=5483&amp;part=index">Music to My Ears</a> would be a good problem for children to try next as it places greater emphasis on predicting when common multiples occur.</div> <br></br> <h3>Possible support</h3> <div>Some learners might find <a href="http://nrich.maths.org/public/viewer.php?obj_id=5482&amp;part=index">Clapping Times</a> a good problem to try before this one.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">When will the first light flash? <br></br> When will the second light flash? <br></br> So when will they flash together?<br></br> Could you predict when they would next flash together? How?<br></br></mdoxml> 2 3 0 1 0 0 0 Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute? Numbers and the Number System Factors and multiples Mathematics Tools 100 square Admin Upper primary mapping document