2858 /www/nrich/html/content/id/2858/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br>Two children are playing with three balls, one blue, one red and one green.<br></br> <br></br> They toss up the balls, which run down a slope so that they land in a row of three.<br></br> <br></br> How many different ways could the balls land?<br></br><br></br>You might like to use the interactivity below to explore the problem.<br></br> <br></br> <a href="/content/id/2858/MusicalChairs.swf"> Full Screen Version</a> <br></br> <mdo:flash height="400" width="550"><param name="movie" value="/content/id/2858/MusicalChairs.swf" ></param><param name="flashplayerversion" value="7" ></param><param name="height" value="400" ></param><param name="width" value="550" ></param></mdo:flash><br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">We received many solutions to this problem, but Charles from Clear Water Bay School in Hong Kong, Alex from Longsands School and Maria from Wimbledon High Junior School took the trouble to explain how they worked it out. Charles says:</p> The answer is $6$.<br></br> <div style="clear: both;">If the green ball is in the first place, there are two combinations i.e. red ball second, blue ball third or blue ball second, red ball third.<br></br> <div style="clear: both;">That gives us two ways if the green ball lands in the first place.<br></br> <div style="clear: both;">It is the same with the other two balls. Therefore, $3 \times 2 = 6$ ways.</div> <p style="clear: both;" class="editorial">Here are the ways that all three of them listed:</p> <div style="clear: both;">green, red, blue<br></br> <div style="clear: both;">green, blue, red<br></br> <div style="clear: both;">blue, red, green<br></br> <div style="clear: both;">blue, green, red<br></br> <div style="clear: both;">red, blue, green<br></br> <div style="clear: both;">red, green, blue</div> </div> </div> </div> </div> </div> </div> </div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Three Ball Line Up</h2> <br></br> Two children are playing with three balls, one blue, one red and one green.<br></br> <br></br> They toss up the balls, which run down a slope so that they land in a row of three.<br></br> <br></br> How many different ways could the balls land?<br></br> <br></br> You might like to use the interactivity below to explore the problem.<br></br> <br></br> <a href="/content/id/2858/MusicalChairs.swf">Full Screen Version</a><br></br> <mdo:flash height="400" id="/content/id/2858/MusicalChairs.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/2858/MusicalChairs.swf"></param> <param name="flashplayerversion" value="7"></param> <param name="height" value="400"></param> <param name="width" value="550"></param> </mdo:flash></div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/2858&amp;part=">This problem</a> is a good context in which to encourage learners to work systematically and to be able to convince someone else that they have found all the possibilities.</div> <div> </div> The interactivity will help children to get a feel for the problem.<br></br> <h3>Key questions</h3> <div>If red landed in the middle, how could the blue and green fall?</div> <div>Where else could red land if it wasn&#39;t in the middle?</div> <div>Can you use this idea to find all the ways?</div> <div>How will you remember the ways you have found so far?</div> <br></br> <h3>Possible extension</h3> Encourage children to use four balls/counters.<br></br> <h3>Possible support</h3> <div>Pupils would benefit from having three differently-coloured counters to use while tackling this problem.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> If you are not using the interactivity, perhaps you could find three differently coloured balls, counters or cubes to try out some ideas. Or you could just use coloured pencils and draw three spots.<br></br> <br></br> If red landed in the middle, how could the blue and green fall?<br></br>Where else could red land if it wasn't in the middle? Can you use this idea to find all the ways?<br></br></mdoxml> 2 4 1 0 0 0 0 Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land. Information and Communications Technology Interactivities Using, Applying and Reasoning about Mathematics Working systematically Decision Mathematics and Combinatorics Combinations Collecting Data Data collection