How are angles measured?

Like any aspect of measurement, the concept of angle enables us to make comparisons and to order. This can be dynamically, by physically doing the rotations involved (for example, with a pencil) and judging which is the greater rotation, which the smaller. It can also be experienced more statically, by cutting out one angle and placing it over another to determine which is the more pointed.

Teaching Point: Include the important stages of developing any measurement concept when teaching angle: comparison, ordering and the use of non-standard units (turns and fractions of turns). Get pupils to compare and order angles by cutting them out and placing them on top of each other.

When explaining about angles, do not always draw diagrams or give examples in which one of the lines is horizontal.

The next stage of development is to introduce a standard unit for measuring angles. For primary-school use this unit is the degree, where 360 degrees (360º) is equal to a complete turn. Hence a right angle (quarter-turn) is 90º and a straight angle (half-turn) is 180º. There is evidence that this system of measuring angles in degrees based on 360 was used as far back as 20000 BC by the Babylonians, and it is thought that it may be related to the Babylonian year being 360 days.

Use 360º protractors for measuring angles in degrees. Emphasize the idea of rotation from zero when explaining to pupils how to use a protractor. Use a transparent protractor on an overhead projector to demonstrate to pupils how to use this device for measuring angles.

The device used to measure angles in degrees is the protractor: we would recommend the use of a 360º protractor, preferably marked with only one scale and with a pointer which can be rotated from one line of the angle being measured to the other, thus emphasizing the dynamic view of angle. Even if there is not an actual pointer, pupils can still be encouraged to imagine the rotation always starting at zero on one line and rotating through 10º, 20º, 30º … to reach the other.