Triangle Edges

2342 /www/nrich/html/content/id/2342/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> How many triangles can you make using sticks that are 3cm, 4cm and 5cm long? Each side can only use one stick but a triangle can use more than one stick of the same length. You could use the interactivity below to investigate the problem and try making some triangles. You need to choose three sticks by clicking on the red, green or blue buttons. You can then rotate each stick (turn it round) by clicking and dragging on its end. If you click and drag near the middle of a stick, you can move it. <mdo:flash height="400" id="/content/id/2342/sticks1.swf" width="400"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param> <param name="movie" value="/content/id/2342/sticks1.swf"></param> <param name="quality" value=""></param> <param name="bgcolor" value=""></param> </mdo:flash> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Lucy from Avoca Beach, Australia wrote to say: <div> I made triangles using red, green and blue sticks. Red was 3cm, green was 4cm and blue was 5cm.These are all my triangles:</div> <div>333 334 335 444 344 445 555 554 355 345</div> There are ten different triangles. <div style="clear: both;">Ruth from Swanbourne House School gave us a little more detail about the triangles: <div style="clear: both;">3 equilateral triangles where all sides are equal (3x3cm, 3x4cm and 3x5cm).</div> <div style="clear: both;">1 right angled triangle, with 1x3cm, 1x4cm and 1x5cm rod.</div> <div style="clear: both;">The other 6 were isoceles triangles, where two of the sides were equal.</div> Thank you to both of you. </div> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Triangle Edges</h2> How many triangles can you make using sticks that are 3cm, 4cm and 5cm long? Each side can only use one stick but a triangle can use more than one stick of the same length. You could use the interactivity below to investigate the problem and try making some triangles. Choose three sticks by clicking on the red, green or blue buttons. You can then rotate each stick (turn it round) by clicking and dragging on its end. If you click and drag near the middle of a stick, you can move it. <mdo:flash height="400" id="/content/id/2342/sticks1.swf" width="400"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param> <param name="movie" value="/content/id/2342/sticks1.swf"></param> <param name="quality" value=""></param> <param name="bgcolor" value=""></param> </mdo:flash> </div> <h3>Why do this problem?</h3> This problem lends itself very well to practical exploration using sticks or cuisenaire rods. Having this "hands-on" experience will help children to realise the need to be systematic and develop their own recording system. The interactivity will enable the whole class to share their findings after the initial practical exploration. The task offers children the chance to explore all the ways in which they can choose three different sticks from sets of sticks. <h3>Possible approach</h3> Ideally allow the children to explore making triangles using strips of paper of lengths $3$, $4$ and $5$ cm (or scaled up if you think these are too fiddly for young children). You could use Cuisenaire rods or construction toy strips instead. Ask the children to make triangles and see how many different ones they can find. Once they have made some, bring the class together to share their results. Present them on the IWB or by creating a display. Encourage the children to use descriptive language that is accurate mathematically to tell you about the triangles they have made. <h3>Key questions</h3> How many have you made? How do you know they are different? Have you found them all? Are there any that are similar in any way? How? <h3>Possible extension</h3> Try introducing an additional length such as $6$ units. This will mean that there may be some triangles that can't be made. Why? How many extra possiblilities would this create? This approach lays the foundations for systematic working that is so important in mathematics. You could also introduce the idea of perimeter - the distance around the edge of the shape - using questions such as: How could you make the triangle with the smallest possible distance around the outside (smallest perimeter)? How about the triangle with the next smallest perimeter? <h3>Possible support</h3> For children who are finding this difficult start by focusing on making specific triangles such as one with three sides of length three. Then change one side. Stay with using practical apparatus for longer and help to scaffold their thinking systmatically. Encourage them to use descriptive language and to look for similarities and differences between triangles. Ask them what is the same and what is different about two triangles.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Can you make a triangle which has all sides the same length? Are there any other triangles with equal length sides?</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Old Notes This problem lends itself very well to practical exploration using sticks or cuisenaire rods. Having this "hands-on" experience will help children to realise the need to be systematic and develop their own recording system. Possible triangles: 3, 3, 3 4, 4, 4 5, 5, 5 3, 3, 4 3, 3, 5 4, 4, 3 4, 4, 5 5, 5, 3 5, 5, 4 3, 4, 5 Total = 10 <mdo:image width="117" height="280" alt="tris" src="tris.jpg"></mdo:image> </mdoxml> 2 5 1 0 0 0 0 Triangle Edges How many triangles can you make using sticks that are 3cm, 4cm and 5cm long? Using, Applying and Reasoning about Mathematics Working systematically 2D Geometry, Shape and Space Mixed triangles Decision Mathematics and Combinatorics Combinations Mathematics Tools Construction kits Information and Communications Technology Interactivities