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Stringy Quads

Age 7 to 11
Challenge Level

Stringy Quads

You will need a loop of string for this activity and three other friends.
loop of string
Stretch the string out so that each of you is holding a corner to make a quadrilateral.
Try to make one which has one line of symmetry.
Is it possible?
How could you convince someone else watching that your shape has just one line of symmetry?
Can you make any other quadrilaterals with just one line of symmetry?

Try again, but this time answer the questions after making one with $2$ lines of symmetry.

Try again, but this time answer the questions after making one with $3$ lines of symmetry.

Try again, but this time answer the questions after making one with $4$ lines of symmetry.



Why do this problem?

This problem brings shape alive in a practical context.  It 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. It is a great task in which to develop a flexible approach to geometry.


Possible approach

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, or outside. If this isn't possible, then you could ask children to 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).

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.
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 who worked well as a group. The results would make a great classroom display, perhaps using smaller loops of string to make each quadrilateral.

Key questions

Where are the lines of symmetry?
How could you convince me?
Are there any other quadrilaterals with exactly one/two/three/four line/s of symmetry? How do you know?


Possible extension

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. Learners might pose conjectures which focus on, for example, whether the number of lines of symmetry is linked to the factors of the number of sides of the shape being investigated.


Possible support

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.