Look at the drawing on the left. Do you see: a. a set of irregular polygons?

b. a kangaroo?

c. a slug with a crown?

If you answered a, award yourself with a gold star and super-teacher status. If you answered b or c, console yourself that you are not alone. Many adults and children prefer their shapes regular and do not see these as polygons. When given this picture in the 1997 national tests, many 11-year-olds had difficulty in finding the octagons and hexagons asked for.

Clearly children will be helped in coping with questions such as this if they are used to dealing with both irregular and regular shapes. Using a wide range of shapes in your teaching is also a way of reducing or challenging some common misconceptions.

Many children have formed their own informal rules about what counts as an example of a certain shape. Often these ignore or exclude irregular shapes or those with curved sides or reflex angles. They should be helped by seeing a wide variety of forms, something not always provided by books or schemes. Books also have a tendency to show shapes with one side horizontal, leading children to regard other examples as incorrect.

Whatever level the children are working on, and whichever shapes are being considered, discussion and use of language are vital. Children can be asked to sort shapes and to justify their sorting or to draw shapes given a description. These activities sound simple but they can be challenging if a variety of shapes are used. Other possible activities include forming irregular shapes or looking for them in the environment.

With practice and appropriate activities, children will become competent at using the correct mathematical terms. Thus the shapes below will be instantly recognised as a trapezium, hexagon and heptagon. Did someone say roof-top, bow-tie and Christmas tree? How irregular!