8058 /www/nrich/html/content/id/8058/ 1 2012-07-01T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Look at these cards.<br></br>  <br></br>  <mdo:image src="new%20numbers.jpg"></mdo:image><br></br>  <br></br> Can you sort them so that they follow round in a loop?<br></br>  <br></br>  Here is a card from a different set.<br></br>  <br></br>  <mdo:image alt="card" height="126" src="OrdCards2.png" width="115"></mdo:image><br></br> What number would follow it?<br></br>  <br></br> What about this one? What would follow it?<br></br> <br></br>  <mdo:image alt="card" height="126" src="OrdCards3.png" width="116"></mdo:image><br></br>  <br></br> You can download all the above set of cards here <a class="pdflink" href="/content/id/8058/The%2012.pdf">.pdf</a><br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><span class="editorial">This challenge obviously led to some interesting explorations! Here&#39;s a solution sent in by</span> <span class="editorial">Maicy, Caitlan and Taryn
 from Saxmundham Primary School in England</span><br></br> <div><br></br> <br></br> <table style="border-spacing: 1px;" border="1"> <tbody> <tr> <td>Calculation</td> <td style="text-align: center;padding:1px;">Method</td> <td>Answer</td> </tr> <tr> <td>3 x 6</td> <td style="text-align: center;padding:1px;">mental</td> <td>18</td> </tr> <tr> <td>18 - 3</td> <td style="text-align: center;padding:1px;">mental</td> <td>15</td> </tr> <tr> <td>15 ÷ 3</td> <td style="text-align: center;padding:1px;">mental</td> <td>5</td> </tr> <tr> <td>5 x 2</td> <td style="text-align: center;padding:1px;">mental</td> <td>10</td> </tr> <tr> <td>10 x 2</td> <td style="text-align: center;padding:1px;">mental</td> <td>20</td> </tr> <tr> <td>20 + 1</td> <td style="text-align: center;padding:1px;">mental</td> <td>21</td> </tr> <tr> <td>21 ÷ 3</td> <td style="text-align: center;padding:1px;">mental</td> <td>7</td> </tr> <tr> <td>7 x 2</td> <td style="text-align: center;padding:1px;">mental</td> <td>14</td> </tr> <tr> <td>14 - 2</td> <td style="text-align: center;padding:1px;">mental</td> <td>12</td> </tr> <tr> <td>12 ÷ 3</td> <td style="text-align: center;padding:1px;">mental</td> <td>4</td> </tr> <tr> <td>4 x 2</td> <td style="text-align: center;padding:1px;">mental</td> <td>8</td> </tr> <tr> <td>8 - 5</td> <td style="text-align: center;padding:1px;">mental</td> <td>3</td> </tr> </tbody> </table> <br></br> if you use this card from another set $10 \times 3$ the card that follows is $30$.<br></br> <br></br> if you use this card from another set $12 \div 2$ the card what follows is $6$<br></br> <br></br> <span class="editorial">Myles, Joshua and William
 also from  Saxmundham Primary
 School from England
 also sent in;</span><br></br>  </div> <table style="border-spacing: 1px;" border="1"> <tbody> <tr> <td>Sum</td> <td>Method</td> <td>Answer</td> </tr> <tr> <td>7 x 2</td> <td>mental</td> <td>14</td> </tr> <tr> <td>14 - 2</td> <td>mental</td> <td>12</td> </tr> <tr> <td>12 ÷ 3</td> <td>mental</td> <td>4</td> </tr> <tr> <td>4 x 2</td> <td>mental</td> <td>8</td> </tr> <tr> <td>8 - 5</td> <td>mental</td> <td>3</td> </tr> <tr> <td>3 x 6</td> <td>mental</td> <td>18</td> </tr> <tr> <td>18 - 3</td> <td>mental</td> <td>15</td> </tr> <tr> <td>15 ÷ 3</td> <td>mental</td> <td>5</td> </tr> <tr> <td>5 x 2</td> <td>mental</td> <td>10</td> </tr> <tr> <td>10 x 2</td> <td>mental</td> <td>20</td> </tr> <tr> <td>20 + 1</td> <td>mental</td> <td>21</td> </tr> <tr> <td>21 ÷ 3</td> <td>mental</td> <td>7</td> </tr> </tbody> </table> <br></br> If we used the card from a different set $10 \times 3$ it would make $30$.<br></br> If we used $12 ÷ 2$ it would make $6$.<br></br> <br></br> <span class="editorial">Ashton from Raynsford Voluntary Controlled First School in England sent in this solution;</span><br></br> <br></br> I started with $8 - 5$ at that $3$ then I found the problem starts with $3$<br></br> and that was $3 \times 6$ then I work it out and then I did what you have just done<br></br> again so it will be $18 - 3$ then $15 ÷ 3$ then $5 \times 2$ then $10 \times 2$ then $20 + 1$ then $21 ÷ 3$<br></br> then $7 \times 2$ then $14 - 2$ then $12 ÷ 3$ then $4 \times 2$ then $8 - 5$ and that is what we started<br></br> with at the beginning so we have finish the loop game.<br></br> <br></br> <span class="editorial">Thank you for these well thought out solutions. Thank you also to those who pointed out that we had slipped up on day $1$ with an incorrect card. </span></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Ordering Cards</h2> <br></br> Look at these cards.<br></br>  <br></br>  <mdo:image src="new%20numbers.jpg"></mdo:image><br></br>  <br></br> Can you sort them so that they follow round in a loop?<br></br>  <br></br>  Here is a card from a different set.<br></br>  <br></br>  <mdo:image alt="card" height="126" src="OrdCards2.png" width="115"></mdo:image><br></br> What number would follow it?<br></br>  <br></br> What about this one? What would follow it?<br></br> <br></br>  <mdo:image alt="card" height="126" src="OrdCards3.png" width="116"></mdo:image><br></br>  <br></br> You can download all the above set of cards here <a class="pdflink" href="/content/id/8058/The%2012.pdf">.pdf</a></div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <a href="http://nrich.maths.org/8058&amp;part=">This problem</a> is designed to help children to learn, and to use, the two and three times tables.<br></br> <h3>Possible approach</h3> <div>You could print out this sheet  <a class="pdflink" href="/content/id/8058/The%2012.pdf">.pdf</a> and cut it into the twelve separate cards and give these to the group to work on in pairs, so that they are able to talk through their ideas with a partner.</div> <div> </div> <div>The cards should form a loop so it does not matter which card is used to start. If you want to make the loop longer, or make your own loop, you could download these similar but <a href="/content/id/8058/OrdCardsSheet2.pdf">blank cards</a>.</div> <div> </div> <div>If you lengthen the loop you will need to take out one card and replace it with your new ones. Avoid repeating a number which has been used already and multiplying and then immediately dividing by the same number.</div> <h3>Key questions</h3> <div>Which card did you start with?</div> <div>How does your sequence of numbers go?</div> <div>Look carefully at the loop here and check your answers.</div> <h3>Possible extension</h3> Learners could make their own set of looping cards using these <a href="/content/id/8058/OrdCardsSheet2.pdf">blank cards</a>.<br></br> <h3>Possible support</h3> Suggest working with another child who can do the calculations, consulting the two and three times tables or using a calculator.<br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">You will find this problem much easier if you <a href="/content/id/8058/OrdCardsSheet1.pdf">download</a> the cards.<br></br>  <br></br> If you would like some blank cards to make your own set you can get them <a href="/content/id/8058/OrdCardsSheet2.pdf">here</a>.<br></br></mdoxml> 2 3 1 1 0 0 0 Ordering cards This problem is designed to help children to learn, and to use, the two and three times tables. Using, Applying and Reasoning about Mathematics Selecting and using information Calculations and Numerical Methods Multiplication & division Admin Upper primary mapping document Admin Lower primary mapping document