8256 /www/nrich/html/content/id/8256/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>Here are some little problems.<br></br> Show us how you could answer the questions using<br></br> - words?<br></br> - pictures?<br></br> - numbers?<br></br> - objects?<br></br> - other ways?</p> <div class="col_layout"> <div class="grid_2" style="border:0;"> <p><mdo:image src="Zoe%20Sweets%20Pic.jpg"></mdo:image></p> </div> <div class="grid_2"> <p style="text-align: left;">Zoe had these three sweets.  Her friend Rajneet gave her</p> <p style="text-align: left;">two more.</p> <p style="text-align: left;"> </p> <p style="text-align: left;">How many has Zoe got now?</p> </div> <div class="grid_2"> <p style="text-align: left;">Karala had 8 dolls.</p> <p style="text-align: left;"> </p> <p style="text-align: left;"> </p> <p style="text-align: left;">She gave 3 of them to her little sister.</p> <p style="text-align: left;">How many dolls has Karala got now? </p> </div> <div class="grid_2" style="border:0;"><mdo:image src="PIc%20of%208%20Dolls.jpg"></mdo:image></div> <p> </p> <p> </p> <div class="grid_2" style="border:0;"><mdo:image src="all%20cards%20medium.jpg"></mdo:image></div> <div class="grid_2"> <p style="text-align: left;">It was Toby&#39;s birthday he had 6 birthday cards.</p> <p style="text-align: left;">The postman brought some more cards for him</p> <p style="text-align: left;">and Toby now has 9 cards.</p> <p style="text-align: left;">How many cards did the postman bring to Toby?</p> <p style="text-align: left;"> </p> </div> <p> </p> <p> </p> <p> </p> </div> <div class="grid_2"> <p style="text-align: left;">Si had 8 balloons looking bright and bouncy.</p> <p> </p> <p style="text-align: left;">Some then popped and he only had 5 left</p> <p style="text-align: left;">that were bright and bouncy.</p> <p style="text-align: left;"> </p> <p style="text-align: left;">How many had popped?</p> </div> <div> <div class="grid_2" style="border: 0pt none;"><mdo:image src="balloons%20in%20space.jpg"></mdo:image></div> <div> <div class="grid_2"> <p style="text-align: left;">Some children were walking to school together.</p> <p style="text-align: left;">Three more joined them.</p> <p style="text-align: left;">Now there were 9 children altogether.</p> <p style="text-align: left;">How many were walking together first of all?</p> <p> </p> </div> <div class="grid_2"> <p style="text-align: left;">Marcus had some coins in his pocket.</p> <p style="text-align: left;">Sadly he lost 7 of them, now he only</p> <p style="text-align: left;">has three coins. How many coins</p> <p style="text-align: left;">were there before he lost them?</p> <p> </p> </div> <p> </p> </div> </div> <p> </p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This <a href="http://www.nrich.maths.org.uk/8256">activity</a> is one in which the pupils can easily become engaged while showing very different ways of viewing the calculation. It is an activity that enables the teacher to have opportunities to observe just how their pupils are considering a problem, this may be somehwhat different to what the teacher expects. Pupils may have been taught one approach but actually have their own ways of working.</div> <br></br> <h3>Possible approach</h3> <div>It is important in this activity to ensure that there is no presumption on the child&#39;s part that there is one way and one way only to see the calculation that may be required. So working with a group and tackling one problem at a time would seem to be appropriate in this instance. It will be then easier for pupils to discuss how they have approached each problem. They may decide to transfer the problem to a calculation which they would record horizontally. More examples can be found here (<a class="doclink" href="/content/id/8256/Pupils%20Represents.doc">doc</a> <a class="pdflink" href="/content/id/8256/Pupils%20Representation.pdf">.,pdf</a> ) the first six increase in difficulty for pupils based on some research evidence, (Children&#39;s Symbolic Representation of Addition and Subtraction Word Problems,  Author(s): Harriett C. Bebout, Source: Journal for Research in Mathematics Education, Vol. 21, No. 2 (Mar., 1990), pp. 123- 131, Published by: National Council of Teachers of Mathematics).</div> <div>In participating in this activity with pupils you may observe things that give rise to some reflection on how pupils deal with these kinds of problems.</div> <h3> </h3> <h3>Key questions</h3> <div>Tell me about how you are working this out.</div> <div>What do you think of _____&#39;s way of doing this?</div> <div>Is the way you&#39;ve done this different from the way you do other additions/subtractions?</div> <br></br> <h3>Possible extension</h3> <div>Ask the pupils to create stories that involve calculations for their partners to do.</div> <div>Give the pupils a written form of an addition/subtraction eg [] - 5 = 12 and challenge them to create a story around  it.</div> <br></br> <h3>Possible support</h3> <div>Some pupils may need to have some small toys/dolls that allow them to enact the situation before being able to think about the calculation. For instance the final balloom problem might be modelled using Lego figures and counters as the balloons.</div> <p><br></br> <br></br> <br></br>  </p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>Find some Lego figures and toys or objects such as counters to make sense of the problem.</p></mdoxml> 2 3 1 1 0 0 0 Here are some short problems for you to try. Talk to your friends about how you work them out. Using, Applying and Reasoning about Mathematics Recording mathematics Calculations and Numerical Methods Addition & subtraction Numbers and the Number System Representing numbers