5930 /www/nrich/html/content/id/5930/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <div style="text-align: center;"><mdo:image width="128" height="120" src="PictBogOfMarbles.jpg" alt="bagofMarbles"></mdo:image></div> <br></br> <div style="text-align: left;">Suppose that in a bag of marbles, all the ones that -</div> <br></br> <div style="margin-left: 40px; text-align: left;">are rough to feel, have a blue colour on them;</div> <br></br> <div style="margin-left: 40px; text-align: left;">sparkle when rolling, have a red colour on them;</div> <br></br> <div style="margin-left: 40px; text-align: left;">are cold to touch, have a white colour on them;</div> <br></br> <div style="margin-left: 40px; text-align: left;">are dark inside, have a green colour on them.</div> <br></br> <br></br> <div style="text-align: left;"><span style="font-weight: bold;">What can you say about each of the marbles A - J?</span></div> <br></br> <mdo:image width="553" height="215" src="10Marbles.jpg" alt="10 marbles"></mdo:image><br></br> <br></br> <p><span style="font-weight: bold;">Imagine you are making marbles. What colours must be put on marbles that</span> -</p> <br></br> <div style="margin-left: 40px;"></div> <div style="margin-left: 40px;">sparkle when rolling but are dark inside?</div> <br></br> <div style="margin-left: 40px;">are cold to touch and feel rough?</div> <br></br> <div style="margin-left: 40px;">are cold, but sparkle when rolling?</div> <br></br> <br></br> <span style="font-weight: bold;">What colour(s) could be on a marble that</span> - <br></br> <br></br> <div style="margin-left: 40px;">is cold?</div> <br></br> <div style="margin-left: 40px;">sparkles when rolling?</div> <br></br> <br></br> <span style="font-weight: bold;">What colours would you find on a cold, sparkly, dark and rough marble?</span> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">We were particularly pleased with the kinds of answers and explanations that came with these solutions.We had many sent in and here are just two as a sample. First from Daniel at Englefield Green Infants School:</p> <br></br> <br></br> A. rough to feel and sparkley when rolling<br></br> B. rough to feel and dark inside<br></br> C. dark inside and sparkle when rolling<br></br> D dark inside and cold<br></br> E. cold, dark and rough<br></br> F. cold, sparkle when rolling, rough<br></br> G. rough, sparkle when rolling, dark inside<br></br> H. cold, rough<br></br> I. sparkle when rolling<br></br> J. sparkle when rolling, cold, dark inside.<br></br> <br></br> On marbles that<br></br> sparkle when rolling but are dark inside - red and green<br></br> are cold to touch and feel rough - white and blue<br></br> are cold, but sparkle when rolling - white, red.<br></br> <br></br> What colour(s) could be on a marble that<br></br> is cold - white<br></br> sparkles when rolling - red<br></br> <br></br> The colour you would find on a cold, sparkly, dark and rough marble - <br></br> blue, green, red and white.<br></br> <br></br> <p class="editorial">The second one is from Rebecca at Montsaye Community College:</p> <br></br> <br></br> Marbles -<br></br> A- would be rough to feel and Sparkles when it rolls<br></br> B- would be rough to feel and Dark inside<br></br> C- would Sparkle when it rolls and Dark on the inside<br></br> D- would be Dark on the inside and cold to touch<br></br> E- would be Cold to touch, Rough to feel and and Dark on the inside<br></br> F- would be Cold to touch, Rough to feeland Sparkle when it rolls<br></br> G- would Sparkle when it rolls, be Rough to feel and Dark on the inside<br></br> H- would be cold to touch and Rough to feel<br></br> I- would Sparkle when it rolls and be cold to touch<br></br> J- would Sparkle when it rolls, be cold to touch and dark on the inside<br></br> <br></br> If I was making the Marbles-<br></br> If the Marble would Sparkle when it rolls and be dark on the inside I <br></br> would put Red and Green on it.<br></br> If the Marble would be cold to touch and Rough to feel I would put White<br></br> and Blue on it.<br></br> If the marble would be cold to touch and Sparkle when it rolls I would put<br></br> White and red on it.<br></br> <br></br> If a Marble was cold it could be-<br></br> Just white,<br></br> White and Blue,<br></br> White and Green,<br></br> White and Red,<br></br> White and Blue and Red,<br></br> White and Blue and Green,<br></br> White and Red and Blue and Green.<br></br> <br></br> If a Marble Sparkled when it rolled it could be-<br></br> Red.<br></br> Red and Blue,<br></br> Red and Green,<br></br> Red and White,<br></br> Red and Blue and White,<br></br> Red and Blue and Green,<br></br> Red and White and Green,<br></br> Red and White and Green and Blue.<br></br> <br></br> If a Marble was cold, sparkly, dark and rough it would be-<br></br> White and Red and Green and Blue.<br></br> <br></br> <p class="editorial">Other solutions came from;</p> <span class="editorial">Kristy at Singapore International School</span> <div style="clear: both;"><span class="editorial">Various un-named pupils from Buckingham College Preparatory School</span><br></br> <div style="clear: both;"><span class="editorial">Talia and Alex at Red Hill Field School</span><br></br> <div style="clear: both;"><span class="editorial">Saskia and Amrita at Jebal School</span><br></br> <div style="clear: both;"><span class="editorial">Rhea at Mason Middle School</span><br></br> <div style="clear: both;"><span class="editorial">Alaa at Gateway School</span><br></br> <div style="clear: both;"><span class="editorial">Lauren at Danesfield School</span><br></br> <div style="clear: both;"><span class="editorial">A girl called Charlie at Culford Preparatory School</span><br></br> <div style="clear: both;"><span class="editorial">Sarah at Seabrook High School</span><br></br> <div style="clear: both;"><span class="editorial">Sofia at Glenarm College</span><br></br> <div style="clear: both;"><span class="editorial">Samantha at Kaleen School</span><br></br> <div style="clear: both;"><span class="editorial">Libby, Patrick, Peter and Olivia at Danes Hill School</span><br></br> <div style="clear: both;"><span class="editorial">Marianne and Aramide at Clapham Manor School</span><br></br> <span class="editorial">Samantha at Driftwood Middle</span><br></br> <span class="editorial">and last but not least, Meghan and Kia</span></div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> <br></br> <p class="editorial">Well done everyone!</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>A Bag of Marbles</h2> <br></br> <div style="text-align: center;"><mdo:image alt="bagofMarbles" height="120" src="PictBogOfMarbles.jpg" width="128"></mdo:image></div> <br></br> <div style="text-align: left;">Suppose that in a bag of marbles, all the ones that -</div> <br></br> <div style="text-align: left; margin-left: 40px;">are rough to feel, have a blue colour on them;</div> <br></br> <div style="text-align: left; margin-left: 40px;">sparkle when rolling, have a red colour on them;</div> <br></br> <div style="text-align: left; margin-left: 40px;">are cold to touch, have a white colour on them;</div> <br></br> <div style="text-align: left; margin-left: 40px;">are dark inside, have a green colour on them.</div> <br></br> <br></br> <div style="text-align: left;"><span style="font-weight: bold;">What can you say about each of the marbles A - J?</span></div> <br></br> <mdo:image alt="10 marbles" height="215" src="10Marbles.jpg" width="553"></mdo:image><br></br> <br></br> <p><span style="font-weight: bold;">Imagine you are making marbles. What colours must be put on marbles that</span> -</p> <br></br> <div style="margin-left: 40px;"> </div> <div style="margin-left: 40px;">sparkle when rolling but are dark inside?</div> <br></br> <div style="margin-left: 40px;">are cold to touch and feel rough?</div> <br></br> <div style="margin-left: 40px;">are cold, but sparkle when rolling?</div> <br></br> <br></br> <span style="font-weight: bold;">What colour(s) could be on a marble that</span> -<br></br> <br></br> <div style="margin-left: 40px;">is cold?</div> <br></br> <div style="margin-left: 40px;">sparkles when rolling?</div> <br></br> <br></br> <span style="font-weight: bold;">What colours would you find on a cold, sparkly, dark and rough marble?</span></div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This <a href="http://nrich.maths.org/public/viewer.php?obj_id=5930&amp;part=index">problem</a> builds on simple sorting skills and gives children the experience of using logical reasoning.</div> <br></br> <h3>Possible approach</h3> <div>It would be helpful if pupils had a sheet of marbles to cut out so that they could physically move or group them. (You might find it useful to print off this <a href="/content/id/5930/marbles.pdf">sheet</a> which depicts four sets of the marbles.) In addition, some children might benefit from having coloured pens to use so that they can record different marbles easily.</div> <br></br> <div>The first part of the problem, describing each marble, could be done as a whole group so that everyone become more familiar with the different attributes. You could then ask pairs of pupils to work on the second and third parts of the problem, emphasising that you will be interested in how they arrived at their solutions. You may like to draw attention to efficient ways of approaching the problem that you see, or to clear ways of recording their solutions. It might be appropriate to stop them briefly after five minutes or so, once they have had a chance to look at the first question in the third part "What colour(s) could be on a marble that is cold?". The idea here is for the children to appreciate that there is not just one right answer - there are in fact several possibilities. You could challenge the class to find all the possible marbles which fit the criteria, perhaps by having a section of a display board devoted to collecting examples over the week to come.</div> <br></br> <h3>Key questions</h3> <div>How do you know that the marbles you&#39;ve chosen are correct?</div> What other colours could be on a marble which is cold/sparkles when rolling?<br></br> <h3>Possible extension</h3> <div>Children could be challenged to look at how marbles could be coloured if they have exactly two attributes, or three attributes or all attributes, and to record the number of possibilties each time. Do they have a system for making sure they don&#39;t leave out any possibilities each time?</div> <br></br> <h3>Possible support</h3> <div>Having circles of paper cut out to represent marbles, and coloured pens to mark each with, may help children access this problem.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> You could print off <a href="/content/id/5930/marbles.pdf">this sheet</a> which has pictures of the marbles on. If you cut them out, you could move them around and group them as you work on the problem.<br></br> Is there only one marble that sparkles when rolling and is dark inside?<br></br> How do you know?<br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> A sparkle and rough<br></br> B dark and rough<br></br> C sparkle and dark<br></br> D cold and dark<br></br> E cold, dark and rough<br></br> F cold, rough and sparkle<br></br> G rough, sparkle and dark<br></br> H cold and rough<br></br> I sparkle and cold<br></br> J sparkle, cold and dark<br></br> <br></br> sparkle, when rolling but are dark inside - red and green<br></br> are cold to touch and feel rough - white and blue<br></br> are cold, but sparkle when rolling - white and red<br></br> <br></br> a cold marble could be:<br></br> W<br></br> WR<br></br> WB<br></br> WG<br></br> WRB<br></br> WRG<br></br> WBG<br></br> <br></br> one that sparkles could be:<br></br> R<br></br> RW<br></br> RB<br></br> RG<br></br> RWB<br></br> RWG<br></br> RBG<br></br> <br></br> cold, sparkly, cloudy and rough marble would be all four colours<br></br></mdoxml> 2 4 1 0 0 0 0 Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside? Using, Applying and Reasoning about Mathematics Mathematical reasoning & proof Using, Applying and Reasoning about Mathematics Working systematically