168 /www/nrich/html/content/00/03/letme1/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>Which comes next in each pattern of dominoes?</p> <mdo:image width="377" height="334" alt="Dominoes" src="fig1.gif"></mdo:image> <br></br> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><strong style="font-weight: 400;">Marienka from</strong> Kosice, Slovakia sent in the answers for the dominoes to finish the patterns. <blockquote><strong>0 0 0 0 :</strong> 0 0<br></br> <strong>1 2 3 4 :</strong> 5 6 <p><strong>6 5 4 3 :</strong> 2 1<br></br> <strong>6 5 4 3 :</strong> 2 1</p> <p><strong>6 5 4 3 :</strong> 2 1<br></br> <strong>5 4 3 2 :</strong> 1 0</p> </blockquote> <p><strong style="font-weight: 400;">Bora from</strong> Irmak Primary School, Turkey used some excellent words to describe the patterns.</p> <blockquote>1st row: 5 and 6, because they are in decreasing order.<br></br> 2nd row: 2-2 and 1-1, again in decreasing order, this time in doubles.<br></br> 3rd row: 2-1 and 1-0, again in decreasing order, but both parts are full, upper part goes from 6 to 1, lower from 5 to 0.</blockquote> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Next Domino</h2> <p>Which comes next in each pattern of dominoes?</p> <mdo:image alt="Dominoes" height="334" src="fig1.gif" width="377"></mdo:image></div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/public/viewer.php?obj_id=168&amp;part=index">This problem</a> is an appealing way for children to recognise, interpret, describe and extend number sequences.Developing their own patterns, as in the later part of the activity, provides an opportunity for them to justify their own thinking, and evaluate others&#39; patterns.</div> <br></br> <h3>Possible approach</h3> <div>The children should be familiar with dominoes through free-play and domino games before attempting more formal tasks such as pattern building.</div> <br></br> <div>It would be good to gather the group on the carpet using large floor dominoes for this activity, or alternatively use virtual dominoes on the interactive whiteboard which you can drag around the screen (you might find our <a href="http://nrich.maths.org/public/viewer.php?obj_id=6361&amp;part=index">Dominoes Environment</a> useful). Begin with single patterns as in the first example in the problem, keeping one end of the dominoes constant (as in all sixes, all blanks, all ones etc.). You may want to deliberately get the sequence wrong to challenge pupils to correct your mistake. Encourage them to explain why it is wrong and also why their correction is right.</div> <br></br> <div>Having two patterns running at the same time is quite a challenge for the very young, but you could pair them up and give a set of dominoes to each pair, asking them to find those which complete the sequence. Having a partner will enable them to talk about what they are doing, and will force them to justify their thinking to each other.</div> <br></br> <div>Another way to challenge the children is to locate the missing elements within the sequence, rather than just at the end. This could form the basis of a plenary activity.</div> <br></br> <h3>Key questions</h3> <div>Let&#39;s look at the top of the dominoes first. Can you say the numbers outloud?</div> <div>What comes next?</div> <div>Can you say the numbers at the bottom of the domino?</div> <div>What comes next?</div> <br></br> <h3>Possible extension</h3> <div>Encourage children to build and explain their own patterns. You may just be surprised by the complexity of their thinking! The examples given in the problem are clearly designed for quite young children who have basic counting skills, but more complex patterns can be devised to challenge more advanced children. For example, include addition or subtraction, odds and evens, patterns that build row-by-row, or grid patterns like this one:</div> <br></br> <div><mdo:image alt="" height="332" src="fig2.gif" width="354"></mdo:image></div> <br></br> <h3>Possible support</h3> <div>Many children will benefit from saying the numbers in the sequence out loud to reinforce the familiar counting patterns.</div> <div> </div> <div>Handouts for teachers are available here (<a href="/content/00/03/letme1/Next%20Domino.doc">word document</a>, <a href="/content/00/03/letme1/Next%20Domino.pdf">pdf document</a>), with the problem on one side and the notes on the other.  </div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Try looking at the top of the dominoes first, then the bottom.<br></br></mdoxml> 2 3 1 0 0 0 0 Which comes next in each pattern of dominoes? Mathematics Tools Dominoes Sequences, Functions and Graphs Arithmetic sequence Numbers and the Number System Counting Admin Lower primary mapping document