Making Trains

4331 /www/nrich/html/content/id/4331/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Laura made a train with the Cuisenaire rods. <br></br> Her train was made from three rods which were all different colours. <br></br> It was the same length as three pink rods:<br></br> <br></br> <mdo:image width="340" height="30" alt="three pink rods" src="train1.gif"></mdo:image><br></br> <br></br> Laura's train looked like this:<br></br> <br></br> <mdo:image width="342" height="28" alt="black, red and green rods" src="train2.gif"></mdo:image><br></br> <br></br> Can you make a different train, the same length as Laura's, with three rods which are all different colours?<br></br> <br></br> Can you make one the same length using no colours that Laura used? <br></br> <br></br> Rob made a train that was the same length as Laura's using four differently coloured rods.<br></br> How did he do it?<br></br> <br></br> Charlene made a train which was as short as it could be using four differently coloured rods. Can you find a rod that is the same length as Charlene's train? <br></br> <br></br> Ben made a train using four differently coloured rods the same length as two black rods and a light green one: <br></br> <br></br> <mdo:image width="483" height="29" alt="2 black rods and a light green rod" src="train3.gif"></mdo:image><br></br> <br></br> He made it without using a white rod. How did he do it? <br></br> <br></br> You may like to use this interactivity to try out your ideas. Click on 'Rods' to choose your rods:<br></br> <br></br> <a href="/content/id/4331/cuisenaire.swf">Full Screen Version</a> <br></br> <mdo:flash height="400" width="550"><param value="/content/id/4331/cuisenaire.swf" name="movie" ></param><param value="7" name="flashplayerversion" ></param><param value="400" name="height" ></param><param value="550" name="width" ></param></mdo:flash><br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial"> Rukmini who goes to Dowanhill Primary sent us a very detailed solution to this problem - well done Rukmini! </p>I counted how many white rods would fit in Laura's train. Her train was 12 white rods long since it had 7 + 2 + 3 = 12. Yes, I can make trains with 3 different colours, of length 12.<br></br> <div style="clear: both;">First I took the longest rod Orange (10) but I couldn't do it. <br></br> <div style="clear: both;">I tried each size one after the other. <br></br> <div style="clear: both;">I could make the following 8 trains: <br></br> <div style="clear: both;">Blue + red + white = 9 + 2 + 1 = 12 <br></br> <div style="clear: both;">Brown + white + green = 8+ 1 + 3 = 12 <br></br> <div style="clear: both;">Black + pink + white = 7 + 4 + 1 = 12 <br></br> <div style="clear: both;">Black + green + red = 7 + 3 + 2 = 12 <br></br> <div style="clear: both;">Dark green + yellow + white = 6 + 5 + 1 = 12 <br></br> <div style="clear: both;">Dark green + pink + red = 6 + 4 + 2 = 12 <br></br> <div style="clear: both;">Yellow + dark green + white = 5 + 6 + 1 = 12 <br></br> <div style="clear: both;">Yellow + pink + green = 5 + 4 + 3 = 12</div> <div style="clear: both;"></div> <p style="clear: both;" class="editorial">In fact, the fourth one in your list, Rukmini, is the same as Laura's and the fifth and seventh are the same, I think. Do you agree?</p> <div style="clear: both;">After that I did not need to check as the same things would be repeated. That is we would get a train like green + brown + white which is the same as brown + white + green. <br></br> <div style="clear: both;">The train yellow + dark green + white was 12 long and did not use the same colours as Laura, but was just as long.</div> <div style="clear: both;"></div> <div style="clear: both;">Rob's train could have been: 6 + 1 + 2 +3 = 12 : dark green + white + red + green or 5 + 1 + 2 + 4 = 12: yellow + white + red + pink</div> <div style="clear: both;"></div> <div style="clear: both;">Charlene's train had the 4 shortest rods: 1 + 2 + 3 +4 = 10. Orange rod is of the same length, 10.</div> <div style="clear: both;"></div> <div style="clear: both;">Ben's train was 7 + 7 + 3 = 17 long. <br></br> <div style="clear: both;">He might have made: pink + yellow + dark green + red = 4 + 5 + 6 + 2 = 17 <br></br> <div style="clear: both;">green + brown + pink + red = 3 + 8 + 4 + 2 = 17 <br></br> <div style="clear: both;">green + black + yellow + red = 3 + 7 + 5 + 2 = 17</div> </div> </div> </div> </div> </div> </div> </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="">Making Trains<br></br> Laura made a train with the Cuisenaire rods.<br></br> Her train was made from three rods which were all different colours.<br></br> It was the same length as three pink rods:<br></br> <br></br> <mdo:image alt="three pink rods" height="30" src="train1.gif" width="340"></mdo:image><br></br> <br></br> Laura's train looked like this:<br></br> <br></br> <mdo:image alt="black, red and green rods" height="28" src="train2.gif" width="342"></mdo:image><br></br> <br></br> Can you make a different train, the same length as Laura's, with three rods which are all different colours?<br></br> <br></br> Can you make one the same length using no colours that Laura used?<br></br> <br></br> Rob made a train that was the same length as Laura's using four differently coloured rods.<br></br> How did he do it?<br></br> <br></br> Charlene made a train which was as short as it could be using four differently coloured rods. Can you find a rod that is the same length as Charlene's train?<br></br> <br></br> Ben made a train using four differently coloured rods the same length as two black rods and a light green one:<br></br> <br></br> <mdo:image alt="2 black rods and a light green rod" height="29" src="train3.gif" width="483"></mdo:image><br></br> <br></br> He made it without using a white rod. How did he do it?<br></br> <br></br> You may like to use this interactivity to try out your ideas. Click on 'Rods' to choose your rods:<br></br> <br></br> <a href="/content/id/4331/cuisenaire.swf">Full Screen Version</a><br></br> <mdo:flash height="400" id="/content/id/4331/cuisenaire.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/4331/cuisenaire.swf"></param> <param name="flashplayerversion" value="7"></param> <param name="height" value="400"></param> <param name="width" value="550"></param> </mdo:flash><br></br> <br></br> <br></br> <br></br> <br></br> <br></br> </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=4331&part=index">This problem</a> will help pupils to apply and improve their knowledge of number bonds and to develop systematic ways of working.</div> <br></br> <div>The link between the Cuisenaire rods and the number they represent could be made more explicit by showing the rods on $1$ cm squared paper. Ideally, this could be done in front of the whole class using OHT rods and a grid.</div> <br></br> <h3>Key questions</h3> <div>Which is the longest rod? Could you try with that one first?</div> <div>How about the next longest?</div> <div>How many white rods are there in Laura's train?</div> <div>How many different ways can you find to make a train the same length as Laura's, with three rods which are all different colours?</div> <div>How can you record what you have done?</div> <div>Would it help to use squared paper?</div> <br></br> <h3>Possible extension</h3> Those who find this easy could find all the three-colour trains in all lengths from $6$ to $20$ or try <a href="http://nrich.maths.org/public/viewer.php?obj_id=2724&part=index">Cuisenaire Counting</a>.<br></br> <h3>Possible support</h3> Suggest drawing round the Cuisenaire rods on $1$ cm squared paper and then colouring them.<br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Which is the longest rod? Could you try with that one first?<br></br> How about the next longest?<br></br> How many different ways can you find to make a train the same length as Laura's, with three rods which are all different colours?<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Same as Laura's but all different colours:<br></br> 9, 2, 1 (blue, red, white). <br></br> 8, 3, 1 (brown, light green, white). <br></br> 7, 4, 1 (black, pink, white). <br></br> 6, 5, 1 (dark green, yellow, white) - this one uses none of her colours.<br></br> 6, 4, 2 (dark green, pink, red). <br></br> 5, 4, 3(yellow, pink, light green). <br></br> <br></br> Rob's train: 1, 2, 3, 6 (white, red, light green, dark green). <br></br> <br></br> Same as Charlene's: 10 (orange). <br></br> <br></br> Ben's: 2, 3, 4, 8 (red, light green, pink, brown).<br></br></mdoxml> 2 4 1 0 0 0 0 Making Trains Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it? Using, Applying and Reasoning about Mathematics Working systematically Numbers and the Number System Comparing and Ordering numbers Calculations and Numerical Methods Addition & subtraction Mathematics Tools Cuisenaire rods Information and Communications Technology Interactivities