5729 /www/nrich/html/content/id/5729/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Can you put the numbers in the correct place in this Carroll diagram?<br></br> <br></br> You can try out your ideas using the interactivity, or you could print off this <a href="/content/id/5729/Carroll2A.pdf">sheet</a> for the first diagram and <a href="/content/id/5729/Carroll2B.pdf">this</a> for the second.<br></br> <br></br> <a href="/content/id/5729/Carroll2A.swf">Full Screen Version</a> <br></br> <mdo:flash height="400" width="550"><param value="/content/id/5729/Carroll2A.swf" name="movie" ></param><param value="7" name="flashplayerversion" ></param></mdo:flash><br></br> <div>Now have a look at this Carroll diagram. This time, the idea is to fill in the labels for the rows and columns.</div> <br></br> <div>You could use the interactivity, or print off <a href="/content/id/5729/Carroll2B.pdf">this sheet</a> to complete.</div> <br></br> <a href="/content/id/5729/Carroll2B.swf">Full Screen Version</a> <br></br> <mdo:flash height="400" width="550"><param value="/content/id/5729/Carroll2B.swf" name="movie" ></param><param value="7" name="flashplayerversion" ></param></mdo:flash><br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p><span class="editorial">Rowena from Christ Church Primary Schoolexplained how she filled in the first diagram:</span></p> I first looked at the two columns. Between $5$ and $15$ you don't use $5$ and $15$. So I started at $6$ for the right hand column, it went in the top row, $7$ in the bottom etc. When you count up it goes from bottom to top and back again until you reach a multiple of $10$, then it stays in the box you just put a number in. After I did this for $6$ up to $14$, I moved to the left hand column and repeated the same process for $1-5$ and $15-30$.<br></br> <br></br> <p class="editorial">Well explained, Rowena, thank you. Here is the picture Rowena sent of her completed diagram:</p> <br></br> <br></br> <mdo:image width="487" height="300" alt="first diagram completed" src="sol2.gif"></mdo:image><br></br> <p><span class="editorial">Thank you also to Cong from St Peter's Roman Catholic Primary School and Callum and Katie from Eynesbury CE(C) School for their solutions. Callum and Katie, you were so close in the second Carroll diagram, there was just one heading which you had slipped up on. Perhaps you can see why Cong's works? Here is Cong's completed diagram for the second challenge:</span></p> <br></br> <br></br> <mdo:image width="400" height="291" alt="second solution" src="sol1.gif"></mdo:image><br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>More Carroll Diagrams</h2> <br></br> Can you put the numbers in the correct place in this Carroll diagram?<br></br> <br></br> You can try out your ideas using the interactivity, or you could print off this <a href="/content/id/5729/Carroll2A.pdf">sheet</a> for the first diagram and <a href="/content/id/5729/Carroll2B.pdf">this</a> for the second.<br></br> <br></br> <a href="/content/id/5729/Carroll2A.swf">Full Screen Version</a><br></br> <mdo:flash height="400" id="/content/id/5729/Carroll2A.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/5729/Carroll2A.swf"></param> <param name="flashplayerversion" value="7"></param> </mdo:flash><br></br> <div>Now have a look at this Carroll diagram. This time, the idea is to fill in the labels for the rows and columns.</div> <br></br> <div>You could use the interactivity, or print off <a href="/content/id/5729/Carroll2B.pdf">this sheet</a> to complete.</div> <br></br> <a href="/content/id/5729/Carroll2B.swf">Full Screen Version</a><br></br> <mdo:flash height="400" id="/content/id/5729/Carroll2B.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/5729/Carroll2B.swf"></param> <param name="flashplayerversion" value="7"></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=5729&amp;part=index">This problem</a> gives children a way of sorting numbers according to different properties and also forces them consider more than one aspect 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. If your class has not had much experience of Carroll diagrams, it might be useful to look at the problem <a href="http://nrich.maths.org/public/viewer.php?obj_id=5728&amp;part=index">Carroll Diagrams</a> which also has suggestions in the notes of how you could go about introducing the relevant ideas.</div> <br></br> <div>This problem offers more of a challenge in that children are asked to identify the criteria by which the numbers have been sorted. Encourage them to talk to each other about how they might work out the labels for each row and column. There are many different approaches and sharing some of their ideas with the whole group would be beneficial. Try to focus on the clarity of their arguments, thereby encouraging well-reasoned solutions.</div> <br></br> <div>Alan Parr, who has contributed many great ideas to NRICH, has sent in this <a href="/content/id/5729/CarrollDiagramsFurtherIdeas.DOC">Word document</a> of further Carroll diagram sorting activities which you may like to use as follow-up to this problem.</div> <br></br> <h3>Key questions</h3> <div>Do you think that the number "5" is between 5 and 15 or not?</div> What can you say about the numbers is this box that is different from the numbers in that box?<br></br> <h3>Possible extension</h3> Learners could go on to using <a href="/content/id/5729/CarrollDiagramsFurtherIdeas.DOC">these sheets</a> given above as a follow-up, especially that last four questions.<br></br> <h3>Possible support</h3> Children could start with the simpler <a href="http://nrich.maths.org/public/viewer.php?obj_id=5728&amp;part=index">Carroll Diagrams</a> problem.<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 $1$, for example? So where would you put it in the diagram?<br></br> You could look at each number in turn in this way.<br></br> <br></br> In the second Carroll diagram, what do all the numbers in the top left box have in common? <br></br> How are they different to the numbers in the bottom left box, for example?<br></br></mdoxml> 2 3 0 1 0 0 0 How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column? Information and Communications Technology Interactivities Calculations and Numerical Methods Addition & subtraction Numbers and the Number System Comparing and Ordering numbers Numbers and the Number System Odd and even numbers Handling, Processing and Representing Data Carroll diagrams/Two way tables Admin Upper primary mapping document