4964 /www/nrich/html/content/id/4964/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Arrange these pieces of wallpaper in order of size. Put the smallest first.<br></br> <br></br> <div style="text-align: center;"><mdo:image width="515" height="588" alt="pieces of wallpaper" src="wallpaper.gif"></mdo:image></div> <p style="text-align: left;">Can you explain how you did it?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">This problem was well answered - thank you to all who sent us solutions. Most of you explained that you worked out the size of each piece of wallpaper by counting the number of stars and spots. Jamie from Great Sankey High School decided to show this in a table. He said:</p> First, I found out how many stars and circles there were in each irregular shape. I then wrote it in a graph <span class="editorial">(I think Jamie means a table here)</span> to show my results clearly. I then added up each of the totals to make a grand total of shapes for each irregular shape. Finally, I ranked them smallest first to end up with a solution.<br></br> <br></br> <table border="1"> <tbody> <tr> <td style="text-align: center;">Shape</td> <td style="text-align: center;">Stars</td> <td style="text-align: center;">Circles</td> <td style="text-align: center;">Total</td> <td style="text-align: center;">Place</td> </tr> <tr> <td style="text-align: center;">A</td> <td style="text-align: center;">13</td> <td style="text-align: center;">12</td> <td style="text-align: center;">25</td> <td style="text-align: center;">5</td> </tr> <tr> <td style="text-align: center;">B</td> <td style="text-align: center;">10</td> <td style="text-align: center;">9</td> <td style="text-align: center;">19</td> <td style="text-align: center;">4</td> </tr> <tr> <td style="text-align: center;">C</td> <td style="text-align: center;">18</td> <td style="text-align: center;">17</td> <td style="text-align: center;">35</td> <td style="text-align: center;">6</td> </tr> <tr> <td style="text-align: center;">D</td> <td style="text-align: center;">19</td> <td style="text-align: center;">19</td> <td style="text-align: center;">38</td> <td style="text-align: center;">7</td> </tr> <tr> <td style="text-align: center;">E</td> <td style="text-align: center;">4</td> <td style="text-align: center;">5</td> <td style="text-align: center;">9</td> <td style="text-align: center;">1</td> </tr> <tr> <td style="text-align: center;">F</td> <td style="text-align: center;">9</td> <td style="text-align: center;">7</td> <td style="text-align: center;">17</td> <td style="text-align: center;">2</td> </tr> <tr> <td style="text-align: center;">G</td> <td style="text-align: center;">9</td> <td style="text-align: center;">9</td> <td style="text-align: center;">18</td> <td style="text-align: center;">3</td> </tr> </tbody> </table> <br></br> <p class="editorial">(In fact, Jamie ordered them from largest to smallest in his solution, but I've changed them intosmallest to largest in the table so that it matches the question.) So, Jamie concluded, that from smallest to largest the shapes were: E, F, G, B, A, C, D.</p> <p class="editorial">Rowena from Christ Church Infants also recorded her results in a table - a good idea. Some of you didn't agree exactly with Jamie's final order, but it depended on how you counted the stars and spots. Jack from Hitchin Boys' School said:</p> <div>I found the solution by counting the amount of circles and stars in each shape, two halves making one.</div> <br></br> <p class="editorial">It wasn't always easy to decide when a shape was half and when it was less or more than half was it?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Wallpaper</h2> <br></br> Arrange these pieces of wallpaper in order of size. Put the smallest first.<br></br> <br></br> <div style="text-align: center;"><mdo:image alt="pieces of wallpaper" height="588" src="wallpaper.gif" width="515"></mdo:image></div> <p style="text-align: left;">Can you explain how you did it?</p> </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=4964&amp;part=index">This activity</a> is designed to help children begin to understand the meaning of area. It is a follow-up to <a href="http://nrich.maths.org/public/viewer.php?obj_id=4962&amp;part=index">Sizing Them Up</a> as it makes an explicit link to the concept of area. In this challenge, learners can use the pattern on the wallpaper to count the number of stars and spots inside each piece so that they should end up with the same ordering.<br></br> <h3>Possible approach</h3> <div>You could start the activity off by showing the children two of the shapes which are obviously very different "sizes" so that they will agree on an order. Invite them to explain why they ordered them in that way.</div> <br></br> <div>After this you could show the children the shapes from <a href="/content/id/4964/wallpaper.doc">this sheet.</a> Then they could to work in pairs with the shapes. It is important to allow plenty of time for children to share their ordering and explanations with their partners and the rest of the group. In this challenge, pupils can use the pattern on the wallpaper to count the number of stars and spots inside each piece so that they should end up with the same ordering. It is likely that they will spend some time discussing how best to approach this problem before reaching that conclusion. If they do not suggest counting the stars and spots you could say something like, "I wonder how many stars there are on this shape?". This could lead into a discussion, in simple terms, about why it might be useful for everyone to have the same way of working out how much space is covered by an object - perhaps relating it to a sports pitch or a tablecloth. Some children might suggest making a table for their results, others might find <a href="/content/id/4964/4964.pdf">this sheet</a> helpful.</div> <br></br> <div>There is no reason why you should not make your own irregular shapes from wallpaper or wrapping paper using the activity as an idea rather than a problem to be solved.</div> <br></br> <h3>Key questions</h3> <div>How are you going to decide which is smallest?</div> How might the pattern on the wallpaper help?<br></br> <h3>Possible extension</h3> You could extend the challenge by adding in a piece of wallpaper or wrapping paper of your own which has a different pattern and ask the children to cut different shapes of the "same size".<br></br> <h3>Possible support</h3> Suggest counting the stars and spots on each shape and making a list or using the table on <a href="/content/id/4964/4964.pdf">this sheet.</a><br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Perhaps you will need to think or talk about what you mean by biggest and smallest first.<br></br> How might the pattern on the wallpaper help?<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">[Stars + spots counted] <br></br> E (9), G (15.5), F (16), B (18), A (20), C (34.5), D (37.5).<br></br></mdoxml> 2 4 1 0 0 0 0 These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it? Measures and Mensuration Area Admin Lower primary mapping document