5944 /www/nrich/html/content/id/5944/ 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 alt="equilateral and isosceles triangles" height="70" src="Feb9.gif" width="455"></mdo:image></div> <br></br> If you have some triangles like these can you make the repeating patterns below?<br></br> <br></br> <mdo:image alt="repeating patterns from the triangles" height="236" src="Feb11.gif" width="300"></mdo:image><br></br> <br></br> What other repeating patterns can you make with these triangles?<br></br> <br></br> Please send us some pictures of your creations.<br></br> <br></br> You could print off <a href="/content/id/5944/NRICHGrids1.pdf">these sheets</a> of triangles on coloured paper, or you could use the interactivity below to try out your ideas.<br></br> <br></br> <br></br> <a href="/content/id/5944/Triangles.swf">Full screen version</a><br></br> <mdo:flash height="400" id="/content/id/5944/Triangles.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/5944/Triangles.swf"></param> <param name="flashplayerversion" value="8"></param> </mdo:flash><br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">Daniel from Englefield Green Infant School sent us this picture of his own repeating pattern:</p> <br></br> <br></br> <mdo:image width="375" height="390" src="danielsol.gif" alt=""></mdo:image><br></br> <br></br> <p class="editorial">Thank you, Daniel. I wonder whether anyone can describe what the repeating part is?</p> <p class="editorial">If anyone makes other repeating patterns, we'd love to see them!</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Repeating Patterns</h2> <br></br> <div style="text-align: center;"><mdo:image alt="equilateral and isosceles triangles" height="70" src="Feb9.gif" width="455"></mdo:image></div> <br></br> If you have some triangles like these can you make the repeating patterns below?<br></br> <br></br> <mdo:image alt="repeating patterns from the triangles" height="236" src="Feb11.gif" width="300"></mdo:image><br></br> <br></br> What other repeating patterns can you make with these triangles?<br></br> <br></br> Please send us some pictures of your creations.<br></br> <br></br> You could print off <a href="/content/id/5944/Triangles.pdf">these sheets</a> of triangles on coloured paper, or you could use the interactivity below to try out your ideas.<br></br> <br></br> <br></br> <a href="/content/id/5944/Triangles.swf">Full screen version</a><br></br> <mdo:flash height="400" id="/content/id/5944/Triangles.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param> <param name="movie" value="/content/id/5944/Triangles.swf"></param> <param name="flashplayerversion" value="8"></param> </mdo:flash></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=5944">This problem</a> offers children the opportunity to recognise, make and describe repeating patterns of triangles, and then challenges them to create repeating patterns of their own.<br></br> <br></br> <h3>Possible approach</h3> <div>You could use the interactivity on an interactive whiteboard and begin to make the first pattern for the group to see. Ask children to work in pairs to make the same pattern and continue it, using cut out coloured triangles. (You may like to print off <a href="/content/id/5944/NRICHGrids1.pdf">these sheets</a> of the triangles onto coloured paper or card.) Invite one pair to come to the board to continue the pattern and discuss with the whole class how they knew what to do. Encourage children to articulate the repetition of the two yellow and two green triangles making a rectangle. (Referring to the colours of the shapes rather than their names may be more appropriate for some.) Listen out for different ways of describing the repetition - there is not just one "right" way.</div> <br></br> <div>Children could then try to continue the second pattern. (Some might notice that both patterns have two yellow and two green triangles as the repeating part, joined in the same way but turned round.) Follow on by asking pairs to make their own pattern/s. Pairs could then swap over so that they try to carry on the pattern created by a neighbouring pair.</div> <br></br> <div>A plenary could consist of sharing a few of the class&#39; patterns, again focusing on how we know how to continue them. You could do this by starting the pattern on the interactive whiteboard and then continuing it wrongly, to see whether the children can correct you.</div> <br></br> <h3>Key questions</h3> <div>Can you tell me about the pattern?</div> <div>How would you carry on this pattern?</div> <div>How do you know?</div> <br></br> <h3>Possible extension</h3> Children could be offered other shapes to use in creating patterns in addition to the two triangles here. For example, a triangle which is half the size of each could be used as well.<br></br> <br></br> <h3>Possible support</h3> Some children might find it helpful to have more examples of patterns to continue before creating their own.<br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Talking to someone else about what you see in the pattern will help.<br></br> Which triangle will you use next?<br></br> Where will it go?<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image src="Tri%20Pattern%20By%20BB.jpg"></mdo:image> by BB</mdoxml> 2 3 1 0 0 0 0 Try continuing these patterns made from triangles. Can you create your own repeating pattern? 2D Geometry, Shape and Space Mixed triangles Using, Applying and Reasoning about Mathematics Practical Activity Using, Applying and Reasoning about Mathematics Investigations Admin Lower primary mapping document