Diagrams not drawn accurately

When doing past examination questions, students occasionally complain about the ‘Diagram not accurately drawn’ statement that sometimes appears next to geometrical figures: “Why not? Couldn’t they be bothered? Why didn’t they make some effort and do it properly?” The answer to this is usually that the examiner didn’t want to make the question answerable by measurement. The question is attempting to test something like calculation of angles, and so, if the angle can be measured with a protractor, this would provide an alternative method that the examiner wishes to block. Of course, any method relying on measurement could only ever be approximate, but a student might use it to confirm or refute a calculation that they have done, or they might assume that an angle that seems to be near, say 30°, is 30°, and so it could provide help that the examiner doesn’t wish to offer. But what about in the classroom? Practices used in high-stakes assessments are often poor guides to what is likely to be most helpful during teaching. When should mathematical diagrams be drawn accurately and when should they, perhaps deliberately, be ‘not to scale’ (see Note)?