One Good Turn

Students need to recognise that each of the shapes in question 1 is made to a pattern. When students have made the various shapes, give them the opportunity to discuss the patterns they see. Encourage them to look for mirror lines in each shape and to recognise that some parts of the shape are mirror images or rotations of another part of the shape. This will help with visualisation.

Once students have made their shapes, have them either trace or draw these onto graph paper so that they can physically rotate the shapes and see how many times each shape maps onto itself. (The use of graph paper will help students be accurate in their drawing.)

The centre of rotation is the point that does not move when the shape is rotated. It is normally shown with a dot.

Rotational symmetry is the number of times a shape matches itself exactly during one complete turn.

This has rotational symmetry of order 3. The triangle matches itself exactly three times during one complete turn.

See also pages 4, 19, and 20 of the students’ booklet.

Answers to Activity

1. a. Practical activity
   b. i.
   The figure fits onto itself every 1 / 4 turn about the centre (90°). It has rotational symmetry of order 4.
   ii.
   The figure fits onto itself every 1 / 3 turn about the centre (120°). It has rotational symmetry of order 3.
   iii.
   The figure fits onto itself every 1 / 4 turn about the centre (90°). It has rotational symmetry of order 4.
   iv.
   The figure fits onto itself every 1 / 3 turn about the centre (120°). It has rotational symmetry of order 3.
   v.
   The figure fits onto itself every 1 / 2 turn about the centre (180°). It has rotational symmetry of order 2.
   vi.
   The figure fits onto itself every 1 / 2 turn about the centre (180°). It has rotational symmetry of order 2.
   vii.
   The figure fits onto itself every 1 / 2 turn about the centre (180°). It has rotational symmetry of order 2.
2. Practical activity