2913
/www/nrich/html/content/id/2913/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div style="text-align: center;">You will need a loop of string for this activity and three other friends.</div>
<br></br>
<div style="text-align: center;"><mdo:image alt="loop of string" height="146" src="string.gif" width="227"></mdo:image><br></br>
</div>
<div style="text-align: center;">Stretch the string out so that each of you is holding a corner to make a quadrilateral.<br></br>
</div>
Try to make one which has exactly one line of symmetry.<br></br>
Is it possible?<br></br>
How could you convince someone else that your shape has just one line of symmetry?<br></br>
Can you make any other quadrilaterals with just one line of symmetry?<br></br>
<br></br>
Try again, but this time answer the same questions for a quadrilateral with exactly two lines of symmetry.<br></br>
<br></br>
Try again, but this time answer the same questions for a quadrilateral with exactly three lines of symmetry.<br></br>
<br></br>
Try again, but this time answer the the same questions for a quadrilateral with exactly four lines of symmetry.</mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<span class="editorial">Robert, Anezka, Billy, Liam and Zoe from
Coldean Primary experimented with lots of different quadrilaterals.
They found some shapes with one line of symmetry, some with two and
some with no symmetry at all. They also found that there are no
quadrilaterals with three lines of symmetry, and that only squares
have four lines of symmetry. They tested a hypothesis about the
relationship between symmetry and pairs of equal edges which didn't
quite work out, but it was a very thorough investigation and
excellent work all round! You can see their results</span> <a href="/content/id/2913/VgdfNB-Stringy%20Quads%20solution-1.doc" class="editorial">here</a> <span class="editorial">.</span><br></br>
<br></br>
<span class="editorial">In answer to how you could prove to someone
watching that you have identified all the lines of symmetry, they
suggested making the shapes out of paper and folding them in half
so that the edges and vertices match up. You could also prove it
with a mirror. If you get the person to place a mirror halfway
across your shape and gradually rotate it, they will see that the
only positions where the reflection allows you to 'see' the whole
of the original shape are the lines of symmetry that you have
identified.</span><br></br>
<br></br>
<span class="editorial">Thanks for sending in your solution. Keep
up the good work!</span><br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Stringy Quads</h2>
<div style="text-align: center;">You will need a loop of string for this activity and three other friends.</div>
<br></br>
<div style="text-align: center;"><mdo:image alt="loop of string" height="146" src="string.gif" width="227"></mdo:image><br></br>
</div>
<div style="text-align: center;">Stretch the string out so that each of you is holding a corner to make a quadrilateral.<br></br>
</div>
Try to make one which has one line of symmetry.<br></br>
Is it possible?<br></br>
How could you convince someone else watching that your shape has just one line of symmetry?<br></br>
Can you make any other quadrilaterals with just one line of symmetry?<br></br>
<br></br>
Try again, but this time answer the questions after making one with $2$ lines of symmetry.<br></br>
<br></br>
Try again, but this time answer the questions after making one with $3$ lines of symmetry.<br></br>
<br></br>
Try again, but this time answer the questions after making one with $4$ lines of symmetry.<br></br>
<br></br>
<p style="font-style: italic;"> </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=2913&part=index">This problem</a> brings shape alive in a practical context and is a good way to reinforce properties of quadrilaterals. By working in a group, children will have the opportunity to solve the problem collaboratively and valuable discussions may take place.</div>
<br></br>
<h3>Possible approach</h3>
<div>Ideally, this activity is best done where there is space for pupils to stand up and move, for example in a hall, or a classroom with the furniture pushed to one side. If this isn't possible, then you could ask children to simply stand near their tables or lay the string on their tables. Wherever you are, learners will need to be in groups of four (or three).</div>
<br></br>
<div>Give each group a loop of string and invite each pupil to take the string using just one hand (if there are three pupils in a group, one will need to use both hands). Ask them to make a quadrilateral from the string which has just one line of symmetry. Leave them to have a go, circulating round the room to see how they approach the task. When a group has made one shape, ask them whether
there are any others.</div>
<br></br>
<div>After a suitable length of time, bring everyone together and ask one group to show one of the shapes they made and give its name. Encourage them to prove to you that it does indeed have only one line of symmetry (for example, by folding). Continue like this for different numbers of lines of symmetry and conclude the lesson with a plenary which brings out the different ways each group
approached the task. For example, they might have "played around" with the string to make new shapes which fitted the criteria; they might have sketched ideas before using the string; or they might have gone through a "list" of quadrilaterals aloud to come up with other possibilities to test. Make a point of mentioning those that worked well as a group. The results would make a great classroom
display, perhaps using smaller loops of string to make each quadrilateral.</div>
<br></br>
<br></br>
<h3>Key questions</h3>
<div>Where are the lines of symmetry?</div>
<div>How could you convince me?</div>
<div>Are there any other quadrilaterals with exactly one/two/three/four line/s of symmetry?</div>
<br></br>
<h3>Possible extension</h3>
Ask children to try and convince you why the result for three lines of symmetry is true. This is by no means easy but listen for explanations which use sound logic and apply relevant properties of quadrilaterals.<br></br>
<br></br>
<h3>Possible support</h3>
<div>Some children may find it useful to research different quadrilaterals to start with and then analyse their characteristics, using the string to test the lines of symmetry. Some might find mini-whiteboards or paper useful for sketching.</div>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
Can you each move your hands in some way to show where the line(s)
of symmetry are?<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">Robert, Anezka, Billy, Liam and Zoe from Coldean Primary experimented with lots of different quadrilaterals. They found some shapes with one line of symmetry, some with two and some with no symmetry at all. They also found that there are no quadrilaterals with three lines of symmetry, and that only squares have four lines of symmetry. They tested a hypothesis about the relationship between
symmetry and pairs of equal edges which didn't quite work out, but it was a very thorough investigation and excellent work all round! You can see their results here .<br></br>
<br></br>
In answer to how you could prove to someone watching that you have identified all the lines of symmetry, they suggested making the shapes out of paper and folding them in half so that the edges and vertices match up. You could also prove it with a mirror. If you get the person to place a mirror halfway across your shape and gradually rotate it, they will see that the only positions where the
reflection allows you to 'see' the whole of the original shape are the lines of symmetry that you have identified.<br></br>
<br></br>
Thanks for sending in your solution. Keep up the good work!<br></br>
<br></br></mdoxml>
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Stringy Quads
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
2D Geometry, Shape and Space
Quadrilaterals
Transformations and their Properties
Symmetry
Using, Applying and Reasoning about Mathematics
Practical Activity
Using, Applying and Reasoning about Mathematics
Visualising
Admin
Upper primary mapping document