Stringy Quads

Stringy Quads

You will need a loop of string for this activity and three other friends.

 

 

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?

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).

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.