171 /www/nrich/html/content/00/04/letme2/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Explore ways of colouring this set of triangles.</p> <p><mdo:image height="185" width="212" src="fig2.gif" alt="triangles"></mdo:image></p> <p><br></br> Can you make symmetrical patterns? With two colours? Three colours? More than three colours?<br></br> <br></br> Can you colour the small triangles, using four colours, with no two triangles of the same colour side-by-side?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">Children from Dennington Primary School have worked very hard on this problem. Julia and Ryan have each found a different way of making a symmetrical pattern with two colours:</p> <table width="100%" cellpadding="5" border="0"> <tbody> <tr> <td> <div align="center"><mdo:image height="126" width="150" src="julia1.gif" alt="triangle coloured with red and blue in symmetrical design"></mdo:image></div> </td> <td> <div align="center"><mdo:image height="102" width="125" src="ryan.gif" alt="triangle coloured with blue and black symmetrically"></mdo:image></div> </td> </tr> </tbody> </table> <p class="editorial">Julia also used three colours to create this symmetrical pattern and has drawn in the line of symmetry too:</p> <p align="center"><mdo:image height="117" width="142" src="julia2.gif" alt="yellow, red and blue coloured triangle"></mdo:image></p> <p align="left" class="editorial">Ben has used the white background with two other colours to make these designs:</p> <p align="center"><mdo:image height="97" width="400" src="ben.gif" alt="three more symmetrical triangles, each using three colours"></mdo:image></p> <p align="left" class="editorial">Kesavan from Latymer All Saints C of E Primary sent the following designs, which all have a vertical line of symmetry:</p> <p align="left"><mdo:image height="315" width="580" alt="" src="KesavanSol.gif"></mdo:image></p> <p align="left"></p> <p align="left" class="editorial">Rebecca looked at ways of colouring the small triangles with four colours so that no two triangles of the same colour are side by side:</p> <table width="100%" cellpadding="5" border="0"> <tbody> <tr> <td> <div align="center"><mdo:image height="116" width="136" src="rebecca1.gif" alt="one way to colour little triangles using four different colours"></mdo:image> </div> </td> <td> <div align="center"><mdo:image height="134" width="150" src="rebecca2.gif" alt="a second way to colour little triangles using four different colours"></mdo:image> </div> </td> <td> <div align="center"><mdo:image height="133" width="150" src="rebecca3.gif" alt="a third way to colour little triangles using four different colours"></mdo:image> </div> </td> </tr> </tbody> </table> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Colouring Triangles</h2> <br></br> <p>Explore ways of colouring this set of triangles.</p> <p><mdo:image alt="triangles" height="185" src="fig2.gif" width="212"></mdo:image></p> <p><br></br> Can you make symmetrical patterns? With two colours? Three colours? More than three colours?<br></br> <br></br> Can you colour the small triangles, using four colours, with no two triangles of the same colour side-by-side?</p> </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=171&amp;part=index">This problem</a> will help children recognise reflective symmetry, but it offers more than that. By giving children the freedom to create their own symmetrical patterns, they will push their own understanding of symmetry further and may well suprise you! It also provides an opportunity for children to discuss what makes one symmetrical pattern different, or the same as, another.</div> <br></br> <h3>Possible approach</h3> <div>You could begin by displaying two sets of the triangles, each one coloured but only one of them coloured to create a symmetrical design. (You may want to recreate the two pictures on <a href="/content/00/04/letme2/TwoTrianglesnewicons.doc">this sheet</a> , or display these images directly on the interactive whiteboard.) Invite the children to look carefully at the images on their own for a moment, then talk to a partner about what they see.</div> <br></br> <div>Take suggestions from the class about what they notice. They may talk about the shapes they see, the colours, the number of colours, the number of triangles of each colour etc etc. Welcome all suggestions and if the idea of symmetry doesn&#39;t come up naturally, you may like to ask the group to look for differences between the two pictures. You can then set them off on the activity, perhaps by giving out copies of <a href="/content/00/04/letme2/ColouringTrianglesWorksheetnewicons.doc">this sheet</a> of the triangles. After a little while, give them time to share their designs with a partner so that the two children together confirm that each way of colouring does indeed have line symmetry.</div> <br></br> <div>Let them work further on their designs and then encourage each child to select just one to share with everyone at the end. (You could of course make an engaging display of these for the classroom wall.) The plenary can also be a time to bring up some points for discussion that might have arisen as the children worked. For example, did anyone create a design which had more than one line of symmetry? If we turn the design round, does that make a new design or is it the same?</div> <br></br> <h3>Key questions</h3> <div>Where is the line of symmetry in this design?</div> <div>How do you know it is a line of symmetry?</div> <div>Have you tried with fewer/more colours?</div> <div>Tell me about this design.</div> <br></br> <h3>Possible extension</h3> <div>Encourage children to ask their own &#39;what if ...?&#39; questions. For example, what would happen if there were more triangles? What would happen if I was only allowed to colour in triangles on the bottom &#39;row&#39;? What would happen if I joined two of the triangle designs together?</div> <br></br> <h3>Possible support</h3> <div>Many children will be happier if they draw in the line of symmetry. You could also have mirrors available for those that want them. Some learners may want to cut out their triangles and try to fold them to check the mirror lines.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> You might find it useful to print off <a href="/content/00/04/letme2/ColouringTrianglesWorksheet.doc">this sheet</a> of lots of the triangles.<br></br> How do you know your design has a line of symmetry?<br></br> Have you tried using more/fewer colours?<br></br></mdoxml> 2 4 1 0 0 0 0 Explore ways of colouring this set of triangles. Can you make symmetrical patterns? Transformations and their Properties Symmetry 2D Geometry, Shape and Space Equilateral triangles Using, Applying and Reasoning about Mathematics Investigations Admin Lower primary mapping document