4725 /www/nrich/html/content/id/4725/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br><a href="/content/id/4725/balancer.swf">Full Screen Version</a> <br></br> <mdo:flash height="400" width="550"><param name="movie" value="/content/id/4725/balancer.swf" ></param><param name="flashplayerversion" value="7" ></param><param name="height" value="400" ></param><param name="width" value="550" ></param></mdo:flash> <br></br> This is a number balance. <br></br> <br></br> <div style="text-align: center;"><mdo:image width="370" height="143" src="NosBal1.gif" alt="number balance"></mdo:image></div> <div></div> <div>It is also called a 'balance bar' or an 'equaliser'. It has weights: </div> <div style="text-align: center;"><mdo:image width="40" height="34" src="NosBal3.gif" alt="weights"></mdo:image> </div> <div> These are hung below the numbers. It balances equal numbers, for example like this:</div> <div></div> <div style="text-align: center;"><mdo:image width="296" height="115" src="NosBal2.gif" alt="balancing 10 on one side with 2 and 8 on the other"></mdo:image></div> <div style="text-align: center;"></div> <div style="text-align: left;">Where would you need to hang the weight to make the one below balance?</div> <div style="text-align: left;"></div> <div style="text-align: center;"><mdo:image width="329" height="177" src="NosBal5.gif" alt="9=3+4+?"></mdo:image></div> <div style="text-align: center;"></div> <div style="text-align: left;">What about this one?</div> <div style="text-align: left;"></div> <div style="text-align: center;"> <mdo:image width="336" height="204" alt="9+4=6+?" src="NosBal6.gif"></mdo:image></div> <div>If you had to use two weights and make the one below balance, where could you put them? </div> <div></div> <div style="text-align: center;"><mdo:image width="352" height="146" alt="9 and 6 on one side, 10 and 4 on the other" src="NosBal7.gif"></mdo:image></div> <div> How many different ways can you make it balance with two weights?</div><div>You may like to use the interactivity above to explore the problem.</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <span class="editorial">Amy from Stoke by Nayland Middle School sent us her work on this problem.</span><br></br> <br></br> On the first question you would need to put a weight on number $2$ on the right side.<br></br> <br></br> On the second question you would need to put a weight on number $7$ on the left side.<br></br> <br></br> On the third question you could put one weight on 1 on the left side and the other on $2$ on the right side.<br></br> <br></br> <span class="editorial">Good work, Amy!</span><br></br> <br></br> <span class="editorial">Sam from Shepherd School noticed that there were several answers for the third question.</span><br></br> <br></br> You could put them on point $6$ on the right and point $5$ on the left, for example. There are $9$ solutions to this, they could go anywhere where the weight on the right is 1 more than the weight on the left.<br></br> <br></br> <span class="editorial">Well done Sam!</span><br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Number Balance</h2> <br></br> <a href="/content/id/4725/balancer.swf">Full Screen Version</a><br></br> <mdo:flash height="400" id="/content/id/4725/balancer.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/4725/balancer.swf"></param> <param name="flashplayerversion" value="7"></param> <param name="height" value="400"></param> <param name="width" value="550"></param> </mdo:flash><br></br> This is a number balance.<br></br> <br></br> <div style="text-align: center;"><mdo:image alt="number balance" height="143" src="NosBal1.gif" width="370"></mdo:image></div> <div> </div> <div>It is also called a &#39;balance bar&#39; or an &#39;equaliser&#39;. It has weights:</div> <div style="text-align: center;"><mdo:image alt="weights" height="34" src="NosBal3.gif" width="40"></mdo:image></div> <div>These are hung below the numbers. It balances equal numbers, for example like this:</div> <div> </div> <div style="text-align: center;"><mdo:image alt="balancing 10 on one side with 2 and 8 on the other" height="115" src="NosBal2.gif" width="296"></mdo:image></div> <div style="text-align: center;"> </div> <div style="text-align: left;">Where would you need to hang the weight to make the one below balance?</div> <div style="text-align: left;"> </div> <div style="text-align: center;"><mdo:image alt="9=3+4+?" height="177" src="NosBal5.gif" width="329"></mdo:image></div> <div style="text-align: center;"> </div> <div style="text-align: left;">What about this one?</div> <div style="text-align: left;"> </div> <div style="text-align: center;"><mdo:image alt="9+4=6+?" height="204" src="NosBal6.gif" width="336"></mdo:image></div> <div>If you had to use two weights and make the one below balance, where could you put them?</div> <div> </div> <div style="text-align: center;"><mdo:image alt="9 and 6 on one side, 10 and 4 on the other" height="146" src="NosBal7.gif" width="352"></mdo:image></div> <div>How many different ways can you make it balance with two weights?</div> <div>You may like to use the interactivity above to explore the problem.</div> </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=4725&amp;part=index">This problem</a> requires children to utilise their knowledge of number bonds in an unusual context and requires them to explain and reason through their solutions.</div> <br></br> <h3>Possible approach</h3> <div>Before tackling Number Balance, pupils will need practical experience of working with balances, if possible.</div> <br></br> <div>To introduce the problem, show the class the balance on the interactive whiteboard and, without saying anything, hang weights to make it balance (two on each side). Take the weights off and put on a different combination of two weights on each side to balance the equaliser. Repeat this a few times and invite learners to talk to each other in pairs about what they think is happening. You could then try the first two examples in the problem as a whole group, asking the children to talk to each other about what to do before sharing ideas amongst the whole group.</div> <br></br> <div>In the main challenge, you may want the children to be at a computer in pairs or you may prefer them to work on mini-whiteboards/paper to begin with. After leaving time for them to work on this, bring them together and discuss their solutions. You may want to ask pairs to write up some solutions on individual strips of paper which can be stuck on the board. You could follow on by looking for patterns in the solutions, which may lead to the children suggesting other possibilities. Alternatively (or in addition) you could focus on the number sentences that can be written from the pupils&#39; solutions.</div> <br></br> <div>By inviting learners to talk through what is happening at each stage of this problem, you will be able to assess how well they have grasped addition and subtraction, and whether they can apply their understanding.</div> <br></br> <h3>Key questions</h3> <div>Can you tell me how the balance works?</div> <div>How can you tell from the pictures or interactivity which side we need to add a weight to?</div> <div>What is the total of the weights on this side?</div> <div>What is the total of the weights on the other side?</div> <br></br> <h3>Possible extension</h3> <div>You could encourage children to work systematically to find all the possible solutions to the final part of the problem.</div> <br></br> <h3>Possible support</h3> <div>Having access to the interactivity, either on the whiteboard, or on individual computers, will help some children gain in confidence as they will be able to try out their ideas without the anxiety of getting things wrong.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> If a weight on the $10$ hook balances with a weight on the $2$ hook together with a weight on the $8$ hook, can you see how the balance works?<br></br> How can you tell from the pictures or interactivity which side is lighter?<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> hang on the 2 hook on the right <br></br> hang on the 7 on the left<br></br> <br></br>9+6=15, 4+10=14 therefore could put on:<br></br>1 on left and 2 on right<br></br>2 on left and 3 on right<br></br>3 on left and 4 on right etc...<br></br></mdoxml> 2 4 1 0 0 0 0 Can you hang weights in the right place to make the equaliser balance? Numbers and the Number System Comparing and Ordering numbers Calculations and Numerical Methods Addition & subtraction Information and Communications Technology Interactivities Admin Lower primary mapping document