2358 /www/nrich/html/content/id/2358/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Yasmin and Zach have some bears to share. Which numbers of bears can they share equally so that there are none left over?</p> <p>You might like to use the interactivity below to help you decide.</p> <p>Use the up and down arrow keys on your keyboard to choose the number of bears you would like to share. You can choose any number from $1$ up to $10$.</p> <p>Press the enter key to start sharing.</p> <p>What do you notice about the numbers they can share fairly?</p> <p><mdo:flash height="400" width="550"><param value="/content/id/2358/mentalBears.swf" name="movie" ></param><param value="6" name="flashplayerversion" ></param><param value="400" name="height" ></param><param value="550" name="width" ></param></mdo:flash></p> <br></br> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">Thank you for all your correct solutions to Share Bears. Natah from Claremont Fan Court School, Marcus from St Philip's School and Halo from Arden Primary School, Australia were able to find a general pattern. Here is what Halo wrote:</p> <br></br> Yasmin and Zach can share a number 2, 4, 6, 8 or 10 bears between themselves. I noticed that all these numbers were even. I think this is because the bears are shared between 2 people, so only multiples of 2 can be shared between them. <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Share Bears</h2> <br></br> <p>Yasmin and Zach have some bears to share. Which numbers of bears can they share equally so that there are none left over?</p> <p>You might like to use the interactivity below to help you decide.</p> <p>Use the up and down arrow keys on your keyboard to choose the number of bears you would like to share. You can choose any number from $1$ up to $10$.</p> <p>Press the enter key to start sharing.</p> <p>What do you notice about the numbers they can share fairly?</p> <p><mdo:flash height="400" id="/content/id/2358/mentalBears.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/2358/mentalBears.swf"></param> <param name="flashplayerversion" value="6"></param> <param name="height" value="400"></param> <param name="width" value="550"></param> </mdo:flash></p> <br></br> <br></br>  </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=2358&amp;part=index">This problem</a> is an appealing way to help children understand the process of division as sharing. In particular, they will have the opportunity to investigate patterns when dividing by two and thus identify even numbers and hence multiples of two.</div> <br></br> <h3>Possible approach</h3> <div>It would be great to have some plastic bears for the children to physically share if they are not using the interactivity. Of course, cubes or counters would do just as well.</div> <br></br> <div>You could ask pairs of children to have a go at the problem, noting down on their mini-whiteboards (or shading a <a href="/content/id/2358/100square.doc">hundred square</a> ) which numbers of bears do share equally. Bring the class back to talk about their findings. You could shade the numbers they have managed to share on a hundred square and then use this as a basis for discussing these special even numbers. Can the class predict what the next even number will be? How do they know? What is the largest even number on the hundred square? How do they know?</div> <br></br> <h3>Key questions</h3> <div>How about starting with just one bear? Can you share this one bear fairly between both Yasmin and Zach?</div> <div>What is the smallest number of bears that you can share equally?</div> <div>How will you record which numbers do share fairly?</div> <div>What about using a hundred square?</div> <br></br> <h3>Possible extension</h3> <div>Children could investigate sharing the bears between more children and recording their findings on a hundred square in a similar way.</div> <br></br> <h3>Possible support</h3> <div>Pairs of children could physically share the bears/counters between themselves - this makes the problem more accessible.</div> <div> </div> <div>Handouts for teachers are available here (<a href="/content/id/2358/Share%20Bears.doc">word document</a>, <a href="/content/id/2358/Share%20Bears.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"><br></br> <p>How about starting with just one bear? Can you share this one bear fairly between both Yasmin and Zach?</p> <p>What is the smallest number of bears that you can share equally?</p> <p>It might help to look at a number line and mark the numbers that do share fairly onto it. Do you notice a pattern?</p> <p>How about using a <a href="/content/id/2358/100square.doc">100 square</a>?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p> The numbers they can share equally are 2, 4, 6, 8, 10. </p> <p> These are even numbers. </p> </mdoxml> 2 3 1 0 0 0 0 Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over? Mathematics Tools Compare bears Numbers and the Number System Divisibility Numbers and the Number System Odd and even numbers Numbers and the Number System Factors and multiples Information and Communications Technology Interactivities Admin Lower primary mapping document