147 /www/nrich/html/content/99/03/letme2/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>The Red Express Train usually has five red carriages, but so many people wanted to catch it one weekend the station manager had to add two blue carriages.</p> <mdo:image alt="the old train" src="train1.gif"></mdo:image> <br></br> <p>At first she thought to put them both on the end, then at the front, then one on each end - but wasn't happy with any of those. So she thought about other ways to put the blue carriages into the train. How many ways can you find?</p> <mdo:image alt="some possibilities" src="train2.gif"></mdo:image> <br></br> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <span class="editorial">Amy sent us the ways she found to arrange the carriages. She was very systematic, so she can be sure that she has found all the arrangements. Can you see how she did this?</span> <br></br> <br></br> <div style="text-align: center;"><mdo:image width="629" height="68" src="carriages1.gif" alt="BBRRRRR"></mdo:image><mdo:image width="629" height="68" src="carriages2.gif" alt="BRBRRRR"></mdo:image><mdo:image width="629" height="68" src="carriages3.gif" alt="BRRBRRR"></mdo:image><mdo:image width="629" height="68" src="carriages4.gif" alt="BRRRBRR"></mdo:image><mdo:image width="629" height="68" src="carriages5.gif" alt="BRRRRBR"></mdo:image><mdo:image width="629" height="68" src="carriages6.gif" alt="BRRRRRB"></mdo:image><mdo:image width="629" height="68" src="carriages7.gif" alt="RBBRRRR"></mdo:image><mdo:image width="629" height="68" src="carriages8.gif" alt="RBRBRRR"></mdo:image><mdo:image width="629" height="68" src="carriages9.gif" alt="RBRRBRR"></mdo:image><mdo:image width="629" height="68" src="carriages10.gif" alt="RBRRRBR"></mdo:image><mdo:image width="629" height="68" src="carriages11.gif" alt="RBRRRRB"></mdo:image><mdo:image width="629" height="68" src="carriages12.gif" alt="RRBBRRR"></mdo:image><mdo:image width="629" height="68" src="carriages13.gif" alt="RRBRBRR"></mdo:image><mdo:image width="629" height="68" src="carriages14.gif" alt="RRBRRBR"></mdo:image><mdo:image width="629" height="68" src="carriages15.gif" alt="RRBRRRB"></mdo:image><mdo:image width="629" height="68" src="carriages16.gif" alt="RRRBBRR"></mdo:image><mdo:image width="629" height="68" src="carriages17.gif" alt="RRRBRBR"></mdo:image><mdo:image width="629" height="68" src="carriages18.gif" alt="RRRBRRB"></mdo:image><mdo:image width="629" height="68" src="carriages19.gif" alt="RRRRBBR"></mdo:image><mdo:image width="629" height="68" src="carriages20.gif" alt="RRRRBRB"></mdo:image><mdo:image width="629" height="68" src="carriages21.gif" alt="RRRRRBB"></mdo:image></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>This <a href="http://nrich.maths.org/public/viewer.php?obj_id=147&amp;part=">activity</a> can be used as a first entry for young pupils in exploring a somewhat open problem in which ordinary addition or subtraction play no apparent part. I have found that it is also useful in helping pupils develop some perseverance skills.</div> <br></br> <h3>Possible approach</h3> <div>You may stick to the train situation but it may be that in the classroom environment there may be another parallel story. You may decide on setting out five small chairs of one colour and use two of a different colour in a straight line. Or, have five children of one gender and two of the other sitting behind each other. There may be other reources in which two can be added to five. The pupils that I have worked with have used two sets of cubes - $5$ of one colour and $2$ of another. There will likely be some opportunities of seeing different ways of approaching the challenge, there may also be different systems used for ensuring that all the possibilities are found.</div> <h3>Key questions</h3> <div>How are you finding ways of having the carriages?</div> <div>Have you got the correct number of carriages?</div> <div>What could you do next?<br></br> Do you thinkthere are other ways of putting them?</div> <br></br> <h3>Possible extension</h3> <div>Try extending the numbers used $5$ &amp; $3$, $6$ &amp; $3$ etc.<br></br> Go to <a href="http://nrich.maths.org.uk/1997">two on five</a> to explore a similar activity but now in more dimensions.</div> <br></br> <h3>Possible support</h3> <div>When the pupils are at their tables some may find it helpful to have coloured cubes or something similar to represent the carriages.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <br></br> <br></br></mdoxml> 2 3 1 0 0 0 0 Red Express Train The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages? Decision Mathematics and Combinatorics Combinations Using, Applying and Reasoning about Mathematics Working systematically