5638
/www/nrich/html/content/id/5638/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
These triangles belong to three different families.<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="triangles" height="154" src="12triangles.gif" width="513"></mdo:image></div>
<br></br>
<div>All the triangles in the same family are the same shape.</div>
<div>But they may not be the same size or the same way up.<br></br>
</div>
Can you sort them out and explain how you did it?<br></br>
<br></br>
You may want to use this interactivity to sort the triangles:<br></br>
<br></br>
<div style="text-align: center;"><mdo:flash height="400" id="/content/id/5638/Triangles1.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param>
<param name="movie" value="/content/id/5638/Triangles1.swf"></param>
<param name="flashplayerversion" value="7"></param>
</mdo:flash></div>
<br></br>
Or you could print off pictures of the triangles (<a href="/content/id/5638/MatchingTriangles.doc">here as a Word document</a> or <a href="/content/id/5638/MatchingTriangles.pdf">here as a pdf</a> ), then cut them out and sort them practically.<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p class="editorial">This problem was a little more difficult that it looked, I think.</p>
<p class="editorial">We had some suggestions that the three groups should be right-angled triangles, equilateral triangles and isosceles triangles. I'm not sure that any of the triangles are equilateral. How do I know?</p>
<p class="editorial">Emily from said St James School told us:</p>
<div>I think that these triangles are sorted into right-angled scalene, right-angled isosceles and non-right-angled isosceles.</div>
<div>There are no equilateral triangles because they do not ever have any right angles and none of those triangles had the same sides and angles.</div>
<br></br>
<p class="editorial">You're right, Emily, thank you. Beatrice from Raffles Girls' School in Singapore sent in a picture of the completed groups:</p>
<br></br>
<mdo:image alt="beatrice's solution" height="420" src="sol1.gif" width="575"></mdo:image><br></br>
<br></br>
<p><span class="editorial">Cong, from St Peter's RC Primary also sent us an image of his solution:</span></p>
<br></br>
<br></br>
<mdo:image alt="cong's solution" height="279" src="sol2.gif" width="536"></mdo:image><br></br>
<br></br>
<p class="editorial">I think that each one of you has put just one triangle in the wrong place. I wonder whether you can spot which one it is in each picture?</p>
<p class="editorial">Well done all of you!</p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Matching Triangles</h2>
<br></br>
These triangles belong to three different families.<br></br>
<br></br>
<div style="text-align: center;"><mdo:image alt="triangles" height="154" src="12triangles.gif" width="513"></mdo:image></div>
<br></br>
<div style="text-align: center;">All the triangles in a family are the same shape.</div>
<div style="text-align: center;">But they may not be the same size or the same way up.</div>
Can you sort them out and explain how you did it?<br></br>
<br></br>
You may want to use this interactivity to sort the triangles:<br></br>
<div style="text-align: center;"><mdo:flash height="400" id="/content/id/5638/Triangles1.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param>
<param name="movie" value="/content/id/5638/Triangles1.swf"></param>
<param name="flashplayerversion" value="7"></param>
</mdo:flash></div>
<br></br>
Or you could print off <a href="/content/id/5638/sortTri.pdf">this sheet</a> of the triangles, then cut them out and sort them practically.</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=5638&part=index">This activity</a> is a good one to try with young children once they are familiar with the properties of a triangle. Often, they associate the name "triangle" with a shape in a particular orientation and this problem is an excellent way to challenge this assumption. Other children may dismiss all three-sided shapes as
triangles without looking at their other attributes. The activity will require pupils to look carefully at each shape and scrutinise its properties.<br></br>
<br></br>
<h3>Possible approach</h3>
<div>You could start by asking the group to tell you what they know about triangles. You could then ask one child to draw a triangle on the board and ask someone else to draw a different triangle. Invite the group to talk about what is the same and what is different about them. In this way, the discussion will include shape, size and orientation, but you could draw some triangles yourself to
bring out certain aspects.</div>
<br></br>
<div>Next you could show the group the interactivity on an interactive whiteboard or show them the triangles on <a href="/content/id/5638/MatchingTriangles.pdf">these sheets</a>. (The first page has the triangles in colour, the second in black and white so that it can be photocopied.)</div>
<br></br>
<div>After this you could encourage the group to work in pairs so that they are able to talk through their ideas with a partner. This could be done at a computer or using the sheets of triangles to cut out and sort. Listening to their justifications can reveal a lot about their understanding of similar triangles, even though this terminology is not used.</div>
<h3>Key questions</h3>
<div>What do you see if you turn this triangle round? Do the two look the same shape now?</div>
What is the difference between these two triangles and what is the same?<br></br>
<h3>Possible extension</h3>
Children could draw their own families of triangles and label the differences and similarities.<br></br>
<h3>Possible support</h3>
Use one of these sheets <a href="/content/id/5638/MatchingTriangles.pdf">one of these sheets</a> so that the triangles can be cut out, then rotated and placed on top of one another. (The first page has the triangles in colour, the second in black and white.)<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">Try concentrating on one triangle at a time. Perhaps you can imagine moving it around in your head so that it is a different way up?<br></br>
You could print off <a href="/content/id/5638/MatchingTriangles.pdf">this sheet</a> of the triangles, then cut them out to sort them. (The first page is in colour, the second in black and white.)<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">Solutions prior to Dec 2012<br></br>
This problem was a little more difficult that it looked, I think.<br></br>
We had some suggestions that the three groups should be right-angled triangles, equilateral triangles and isosceles triangles. I'm not sure that any of the triangles are equilateral. How do I know?<br></br>
Emily from said St James School told us:<br></br>
I think that these triangles are sorted into right angled scalene, right angled isosceles and non-right angled isosceles.<br></br>
There are no equilateral triangles because they do not ever have any right angles and none of those triangles had the same sides and angles.<br></br>
<br></br>
You're right, Emily, thank you. Beatrice from Raffles Girls' School in Singapore sent in a picture of the completed groups:<br></br>
<br></br>
<br></br>
<br></br>
Cong, from St Peter's RC Primary also sent us an image of his solution:<br></br>
<br></br>
<br></br>
<br></br>
<br></br>
I think that each one of you has put just one triangle in the wrong place. I wonder whether you can spot which one it is in each picture?<br></br>
Well done all of you!</mdoxml>
2
3
1
0
0
0
0
Matching Triangles
Can you sort these triangles into three different families and explain how you did it?
2D Geometry, Shape and Space
Similar triangles
2D Geometry, Shape and Space
Mixed triangles
Information and Communications Technology
Interactivities
Admin
Lower primary mapping document