241 /www/nrich/html/content/03/03/letme1/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <table width="100%" cellpadding="5" border="0"> <tbody> <tr> <td>Find the next two terms in each case:</td> </tr> <tr> <td style="text-align: center;"><mdo:image width="390" height="410" src="Dom241.gif" alt=""></mdo:image></td> </tr> <tr> <td></td> </tr> <tr> <td></td> </tr> <tr> <td></td> </tr> <tr> <td></td> </tr> </tbody> </table> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <table width="100%" cellpadding="5" border="0"> <tbody> <tr> <td colspan="2">David from Tithe Barn Primary School sent us some drawings of the dominoes which complete these sequences. Abigail and Rachel from Histon and Impington Infants School have explained the patterns for the last two:</td> </tr> <tr> <td colspan="2"><mdo:image width="139" height="98" alt="1/4, 1/5" src="sol1.gif"></mdo:image></td> </tr> <tr> <td colspan="2"><mdo:image width="137" height="98" alt="3/1, 2/0" src="sol2.gif"></mdo:image></td> </tr> <tr> <td colspan="2"><mdo:image width="135" height="97" alt="4/3, 3/3" src="sol3.gif"></mdo:image></td> </tr> <tr> <td><mdo:image width="139" height="97" alt="4/3, 5/2" src="sol4.gif"></mdo:image></td> <td>You are counting backwards on the bottom and forwards on the top. You would need an extra domino set, because the same dominos are used twice.</td> </tr> <tr> <td><mdo:image width="216" height="60" alt="3/0, 3/5" src="sol5.gif"></mdo:image></td> <td>There are two patterns that bounce over each other:<br></br> 0/5 1/5 2/5 3/5 and 1/0 2/0 3/0</td> </tr> <tr> <td colspan="2">Jeff from Kelly Elementary School in Carlsbad, California and Charlie and Jake from Moorfield Junior School also sent us correct solutions.</td> </tr> </tbody> </table> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Domino Sequences</h2> <br></br> <table style="" border=""> <tbody> <tr> <td>Find the next two terms in each case:</td> </tr> <tr> <td style="text-align: center;padding:5px;"><mdo:image alt="" height="410" src="Dom241.gif" width="390"></mdo:image></td> </tr> <tr> <td> </td> </tr> <tr> <td> </td> </tr> <tr> <td> </td> </tr> <tr> <td> </td> </tr> </tbody> </table> </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=241">This problem</a> introduces sequences in a simple way using a familiar resource. The sequences become increasingly complex so that there is also a challenge for learners.<br></br> <h3>Possible approach</h3> <div>You might need to spend some time exploring dominoes in general before tackling this problem, depending on how familiar the children are with dominoes.</div> <br></br> <div>Look at the first sequence together, perhaps using giant dominoes on the floor, or some on the interactive whiteboard (you might find our <a href="http://nrich.maths.org/public/viewer.php?obj_id=6361&amp;part=index">Dominoes Environment</a> useful). Ask children to talk in pairs about what they notice and then share ideas with the whole group. Then invite them to suggest how the pattern could be continued, focusing on their explanations and justifications.</div> <br></br> <div>Once the learners have tried this first one together, they should be able to work in their pairs on the rest of the problem. They might find <a href="/content/03/03/letme1/241.pdf">this sheet</a> of the problem useful.</div> <br></br> <h3>Key questions</h3> <div>What do you notice about the numbers at the top of the dominoes? What will the next one be?</div> <br></br> <div>What do you notice about the numbers at the bottom of the dominoes? What will the next one be?</div> <br></br> <div>Can you explain the pattern?</div> <br></br> <h3>Possible extension</h3> <div>Learners could use dominoes to make their own sequences for a friend to continue. They could make some sequences with a nine-spot set of dominoes, using <a href="/content/03/03/letme1/9SpotDoms.pdf">this sheet</a> of them.</div> <br></br> <h3>Possible support</h3> Having a number line or number square available to mark off numbers might help children identify a pattern.<br></br> <br></br>  <br></br> Handouts for teachers are available here (<a href="/content/03/03/letme1/Domino%20Sequences.doc">word document</a>, <a href="/content/03/03/letme1/Domino%20Sequences.pdf">pdf document</a>), with the problem on one side and the notes on the other. <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Look at the tops and the bottoms of the dominoes separately.<br></br></mdoxml> 2 3 1 0 0 0 0 Find the next two dominoes in these sequences. Mathematics Tools Dominoes Sequences, Functions and Graphs Arithmetic sequence Admin Lower primary mapping document