5728 /www/nrich/html/content/id/5728/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Use the interactivities below to fill in the Carroll diagrams.<br></br> <br></br> If you prefer, you could print off these sheets: <a href="/content/id/5728/Carroll1A.pdf">First</a> and <a href="/content/id/5728/Carroll1B.pdf">Second</a> .<br></br> <br></br> Can you explain how you know where to place the numbers?<br></br> <br></br> <a href="/content/id/5728/CaN1A.swf">Full Screen Version</a><br></br> <mdo:flash height="400" width="550"><param name="movie" value="/content/id/5728/CaN1A.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> <a href="/content/id/5728/CaNos1B.swf">Full Screen Version</a><br></br> <mdo:flash height="400" width="550"><param name="movie" value="/content/id/5728/CaNos1B.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">Robert from Matthew Pearce Public School sent a solution to the first part of this problem. Robert says:</p> put $3, 9, 5, 7, 1$ in odd numbers and less than ten<br></br> put $2, 4, 6, 8$ in even numbers and less than ten<br></br> put $17, 11, 13, 15, 19$ in odd numbers and not less than ten<br></br> put $10, 12, 14, 16, 18$ in even numbers and not less then ten<br></br> <br></br> <p class="editorial">So, the completed Carroll diagram would look like this:</p> <br></br> <mdo:image width="350" height="259" alt="first solution" src="sol1.gif"></mdo:image><br></br> <br></br> <p class="editorial">Well done also to Eliza from Danebank School who also completed this diagram.</p> <p class="editorial">Rowena from Christ Church Primary told us how she went about filling in the second Carroll diagram:</p> <div>I decided the numbers that were between $10$ and $20$ did not include $10$ or $20$, this left $11-19$, all these numbers have an odd tens digit so they went in the bottom left corner. All the remaining numbers must be in the 'Not between $10$ and $20$' column, $10$ and $30$ have odd tens digit so they went at the bottom of that column, all the $20$'s went in the top. I decided that $0$ is an even number, so $1-9$ have even tens digit.</div> <br></br> <p class="editorial">Here is a picture of Rowena's completed diagram:</p> <br></br> <div><mdo:image width="407" height="296" alt="second diagram" src="sol3.gif"></mdo:image></div> <br></br> <p class="editorial">You've explained this very well, Rowena. It's interesting that you've decided that the numbers $1-9$ have zero as their tens digit and that zero is even. Perhaps some of you have comments about this?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Carroll Diagrams</h2> <br></br> Use the interactivities below to fill in the Carroll diagrams.<br></br> <br></br> If you prefer, you could print off these sheets: <a href="/content/id/5728/Carroll1A.pdf">First</a> and <a href="/content/id/5728/Carroll1B.pdf">Second</a> .<br></br> <br></br> Can you explain how you know where to place the numbers?<br></br> <br></br> <a href="/content/id/5728/CaN1A.swf">Full Screen Version</a><br></br> <mdo:flash height="400" id="/content/id/5728/CaN1A.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/5728/CaN1A.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> <a href="/content/id/5728/CaNos1B.swf">Full Screen Version</a><br></br> <mdo:flash height="400" id="/content/id/5728/CaNos1B.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/5728/CaNos1B.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> <a href="http://nrich.maths.org/public/viewer.php?obj_id=5728&amp;part=index">This problem</a> gives children a way of sorting numbers according to different properties and also forces them to consider more than one attribute at once. It also provides opportunities for children to explain their placing of the numbers, using appropriate language.<br></br> <h3>Possible approach</h3> <div>There are two aspects to this problem: Firstly, it focuses on sorting numbers according to certain properties and secondly, it requires a knowledge of how a Carroll diagram works. At first children may find Carroll diagrams challenging to complete because of the need to think about two characteristics simultaneously.</div> <br></br> <div>One way to introduce this idea would be simply to ask the children to list the numbers under each of the four headings, written separately and not in the form of a table.</div> <br></br> <div>You could then ask questions such as:</div> <ul> <li>What can you tell me about the number $3$?</li> <li>Why does the number $10$ appear in two lists?</li> <li>Do all the numbers appear in two lists? Why or why not?</li> </ul> This could then lead on to the Carroll diagram itself. This could either be done with the whole class using the interactivity on an interactive whiteboard, in pairs at individual computers or using these sheets - <a href="/content/id/5728/Carroll1A.pdf">First</a> and <a href="/content/id/5728/Carroll1B.pdf">Second</a> . Children should be given time for discussion both between themselves and as a larger group.<br></br> <h3>Key questions</h3> <div>What do you know about the number $1$? Where would it go?</div> <div>What can you tell me about the number ...? Where would it go?</div> <div>Do you think that the number "$10$" is less than ten?</div> <div>Where will odd numbers go?</div> <h3>Possible extension</h3> <div>For more of a challenge, you could give children a Carroll diagram with the numbers in place, but with no labels for the cells and ask them to decide what the categories could be. See <a href="http://nrich.maths.org/public/viewer.php?obj_id=5729&amp;part=index">More Carroll Diagrams</a> for an example.</div> <br></br> <h3>Possible support</h3> Suggest looking at all the odd numbers first and deciding whether they are less than $10$ or not.<br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> What do you know about the number $1$? Where would it go?<br></br> How about the number $2$? And $3$?<br></br> You could look at all the odd numbers first, for example, and decide where they go in the diagram. <br></br></mdoxml> 2 3 1 0 0 0 0 Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers? Information and Communications Technology Interactivities Handling, Processing and Representing Data Carroll diagrams/Two way tables Calculations and Numerical Methods Addition & subtraction Numbers and the Number System Odd and even numbers Numbers and the Number System Comparing and Ordering numbers Admin Lower primary mapping document