4782 /www/nrich/html/content/id/4782/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> You may like to use our Cuisenaire rod environment for the problem below. Here is the environment (just scroll down for the problem itself):<br></br> <br></br> <mdo:flash height="400" width="550"><param name="movie" value="/content/id/4782/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> Here are three pairs of rods. The ratio of all the pairs is 3 : 2. <br></br> <br></br> <div style="text-align: center;"><mdo:image width="180" height="153" src="Rat1.gif" alt="three pairs of rods in ratio 3:2"></mdo:image></div> <br></br> What is the ratio of the pair below?<br></br> <br></br> <div style="text-align: center;"><mdo:image width="40" height="153" src="Rat2.gif" alt="two rods"></mdo:image></div> <div> Using only single rods what pair can you find with the same ratio as the pair below? </div> <div></div> <div style="text-align: center;"><mdo:image width="42" height="86" alt="yellow and pink rods" src="Rat3.gif"></mdo:image></div> <div>Using only pairs of single rods what pairs can you find with the same ratio as those below?</div> <div> </div> <div style="text-align: center;"><mdo:image width="42" height="256" alt="orange+yellow:blue rods" src="Rat5.gif"></mdo:image></div> Using only pairs of single rods what pairs can you find with the ratio 9 : 6?<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <span class="editorial">Kerr, Lewis,Sophie and Holly from Dundonald School have been working on this problem. They saw that the ratio of the blue rod to the black rod is 9:7.</span> <br></br> <br></br> <span class="editorial">Well done to Isis (South Island School), Rohaan (Long Bay Primary) and Samantha (The Hamlin School) for completing this toughnut! Samantha explained how she manged to find a pair with the same ratio as the yellow and pink rods:,</span> <br></br> <br></br> &quot;The pink rod had 4 units and the yellow one had 5 units. This meant that they had a ratio of 4:5. I then needed to find a like ratio. This can be done by multiplying both numbers in the ratio by the same number. In this case the number had to be 2 because the longest rod is 10 units. So the 8 (brown colored) and the 10 (orange colored) rods would have the same ratio as the 4 (pink colored) and the 5 (yellow colored)&quot;<br></br> <br></br> <span class="editorial">She also found pairs with the same ratio as the combined yellow+orange, to the blue rod:</span> <br></br> <br></br> The ratio of yellow (5) + orange (10) to blue (9) is equal to the ratio 15 to 9. This ratio can be simplified to a 5:3 ratio by dividing both 15 and 9 by 3. Therefore, the <span style="font-weight: bold;">yellow and green rods</span> form an equal ratio to that of the yellow + orange to the blue. Another equal ratio would be 10 to 6. Therefore, the <span style="font-weight: bold;">dark green and orange rods</span> also form an equal ratio.<br></br> <br></br> <span class="editorial">Finally she noted that the rods with the same ratio as 9:6 have already been given!</span> <br></br> &quot;The ratio of 9:6 can be simplified to the ratio 3:2. The possible combinations with rods for that ratios are shown at the start of the question!&quot; <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Rod Ratios</h2> <br></br> You may like to use our Cuisenaire rod environment for the problem below. Here is the environment (just scroll down for the problem itself):<br></br> <br></br> <mdo:flash height="400" id="/content/id/4782/cuisenaire.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/4782/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> Here are three pairs of rods. The ratio of all the pairs is 3 : 2.<br></br> <br></br> <div style="text-align: center;"><mdo:image alt="three pairs of rods in ratio 3:2" height="153" src="Rat1.gif" width="180"></mdo:image></div> <br></br> What is the ratio of the pair below?<br></br> <br></br> <div style="text-align: center;"><mdo:image alt="two rods" height="153" src="Rat2.gif" width="40"></mdo:image></div> <div>Using only single rods what pair can you find with the same ratio as the pair below?</div> <div> </div> <div style="text-align: center;"><mdo:image alt="yellow and pink rods" height="86" src="Rat3.gif" width="42"></mdo:image></div> <div>Using only pairs of single rods what pairs can you find with the same ratio as those below?</div> <div> </div> <div style="text-align: center;"><mdo:image alt="orange+yellow:blue rods" height="256" src="Rat5.gif" width="42"></mdo:image></div> Using only pairs of single rods what pairs can you find with the ratio 9 : 6?</div> <br></br> Cuisenaire rods are a fantastic resource for investigating ratio. The way the problem is written assumes knowledge of the concept of ratio, but Cuisenaire rods could be used to introduce the ideas initially. Children will find it useful to have some "real" rods to use while working on the problem, and the interactivity can be a good medium in which to engage the whole class in initial discussion, perhaps on an interactive whiteboard or using a projector. White rods (which are unit length) can be used to demonstrate what exactly a ratio of 3:2 means and there is a lot to be talked about in terms of why 3:2 is the same as 6:4, 9:6 and so on.<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Can you use the interactivity to help you? You can choose the correct length rods from the interactivity by matching their colours. <br></br> Perhaps you could line up white rods alongside the coloured rods to help work out their lengths and then their relative ratios. <br></br> You could also use the grid lines to find the lengths of the rods.<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">1. 9 : 7 <br></br>2.10 : 8 <br></br>3. 5 : 3, 10 : 6<br></br> 4. 3 : 2, 6 : 4, 9 : 6.<br></br></mdoxml> 2 5 0 1 0 0 0 Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6? Mathematics Tools Cuisenaire rods Admin Learning through exploration Information and Communications Technology Interactivities Fractions, Decimals, Percentages, Ratio and Proportion Ratio