What is rotational symmetry?

A parallelogram is perhaps a surprise, because this too does not have reflective symmetry. If you think, for example, that one of the diagonals is a line of symmetry, copy the shape onto paper and use the colouring, cutting out and turning face-down procedure, or try folding it in half along the diagonal. But it does have a different kind of symmetry. To see this, trace the shape on to tracing paper and then rotate it around the centre point through a half-turn. The shape matches the original shape exactly. A shape that can be rotated on to itself like this is said to have rotational symmetry. The point about which we rotate it is called the centre of rotational symmetry.

Teaching Point

Use the tracing paper approach to explore the ideas of rotation and rotational symmetry.

Another practical way of exploring rotational symmetry is to cut out a shape carefully and see how many ways it can be fitted into the hole left in the paper, by rotation. The ideas of reflective and rotational symmetry are fundamental to the creation of attractive designs and patterns, and are employed effectively in a number of cultural traditions, particularly the Islamic. Pupils can learn first to recognize these kinds of symmetry in the world around them, and gradually to learn to analyse them and to employ them in creating designs of their own.

Teaching Point

Use geometrical designs from different cultural traditions, such as Islamic patterns, to provide a rich experience of transformations and symmetry.

Think about your own school environment and think about the possibilities for a mathematical trail using the occurrence of various shapes?