7552 /www/nrich/html/content/id/7552/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> The countries of the world will take their national flags to the Olympics. Many countries have flags which are three stripes of three different colours.<br></br> <br></br> <div style="text-align: center;"> <mdo:image width="292" height="153" src="7552B.png" alt="4 flags"></mdo:image></div> <br></br>  <br></br> Some have vertical stripes which go up and down and some have horizontal stripes which go across from side to side. These stripes are coloured in different orders for different countries which use them.<br></br> <br></br> Choose three colours and see how many different ways you can colour the vertical and the horizontal stripes. You can download a sheet to help you <a href="/content/id/7552/Flags7552.pdf">here</a>.<br></br> <br></br>  <mdo:image width="238" height="45" alt="3 flags" src="7552C.png"></mdo:image><br></br>  <br></br> You must use just those three colours all the time - so choose colours you like!<br></br></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> <p><a href="http://nrich.maths.org/7552&amp;part=">This problem</a> is about arrangement and combinations. How many ways can the colours be arranged and can children find all the ways themselves?</p> <br></br> <h3>Possible approach</h3> <div>You could start with the flags and look at the ones with vertical stripes, and then the ones with horizontal stripes. Show the children how to begin by choosing one colour to start with. <a href="/content/id/7552/Flags7552.pdf">This sheet</a> can be downloaded, copied and used or the flags could drawn on squared paper.</div> <div> </div> <div>If possible, the children should work in pairs so that they are able to talk through their ideas with a partner.</div> <div> </div> <div>At the end of the lesson everyone can show the flags they have coloured and discuss how many different ones have been found.</div> <br></br> <h3>Key questions</h3> <div>What three colours have you chosen to use?</div> <div>Which will you do first - the horizontal or the vertical stripes?</div> <div>Which colour are you going to start with?</div> <div>How many ways can you arrange the other colours?</div> <div>How can you be sure you have found them all?</div> <br></br> <h3>Possible extension</h3> <p>Learners could also design some flags which have three blocks of colour but which are different from the ones above. More adventurous children may like to try with four stripes - but beware, there are a lot of possibilities!</p> <p> </p> <h3>Possible support</h3> <p>Suggest using <a href="/content/id/7552/Flags7552.pdf">this sheet</a> (enlarged if necessary) with two of each flag crossed out.<br></br>  </p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Use just three colours, and start with one of them. How many different flags can you make now?<br></br></mdoxml> 2 4 1 0 0 0 0 Many countries have flags which are stripes of three different colours. Choose three colours and see how many different ways you can colour the stripes. Decision Mathematics and Combinatorics Combinations Using, Applying and Reasoning about Mathematics Practical Activity Using, Applying and Reasoning about Mathematics Working systematically