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Benchmarks for angle

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Last updated 26 October 2012 15:30 by NZTecAdmin
Benchmarks for angle (PDF, 253 KB)

Measurement progression, 4th step

The purpose of the activity

In this activity, the learners develop an understanding of what angles are and how to measure them. The learners also develop their skill at measuring and estimating angles using degrees.

The teaching points

  • Angles are composed of two rays that are infinite in length and meet at a common point (vertex).

Image of angle.

  • The attribute of angle size can be thought of as the amount of turn to move from one ray to the other or the spread of the angle’s rays.
  • The standard measure for measuring angles is degrees.
  • Measuring using protractors. The protractor is generally poorly understood as a measuring instrument. Part of the difficulty occurs because the units (degrees) are very small; for example a single degree is physically impossible to cut out and use in much the same way that a single millimetre is too small to use. Another problem with protractors is that there are no visible angles showing on the protractor and only a series of marks around the outside. Finally, the numbering on most protractors is confusing with the numbers running both clockwise and anticlockwise. Ensure the learners understand the conventions for using protractors.
  • Discuss with the learners relevant or authentic situations where the use of benchmarks for estimating angle is applicable.


  • Paper circles of two different colours both cut along a radius and slid together along the cut to form an angle estimator. Turn one of the circles to create angles of different sizes with the contrast in the two colours creating the angle.

Image of paper circles cut along a radius.

  • Protractors.

The guided teaching and learning sequence

1. Begin by discussing rotations or turns in real situations. In these examples, focus the learners on the various ways of measuring the amount of turn about a particular point, starting at one position and finishing in another.

Open a door and ask:

“When you open a door to walk through it, how could you describe the amount that the door has turned?” (almost a 1/4 turn)
“Where is the point of the turn?” (hinge)
“How could you draw this?”

Image of near-quarter rotation.

2. Ask the learners to draw a half-turn and a full-turn.

Image of half-turn rotation.

3. Introduce the learners to the unit for measuring an amount of turn called the degree. Start by referring to a full turn as representing a turn of 360 units (or small amounts of turn) called degrees and denoted by “°”.

4. Ask the learners to relate turns of one-quarter, one-half and three-quarters to a full turn of 360°. In particular, a one-half turn becomes 180°, a one-quarter turn becomes 90°, and a three-quarter turn becomes 270°.

“What was the size of the angle when we opened the door?” (Almost a right angle or almost 90 degrees.)

5. Ask the learners to use the angle estimator to create the following angles:

  • 45 degrees
  • 200 degrees
  • 270 degrees.

For each angle, ask the learners to check their estimates with other learners and explain how they made the estimate.

“How did you estimate 45 degrees?”
(half of a quarter turn or right angle)
“How did you estimate 200 degrees?”
(slightly more than half a turn)
“How did you estimate 270 degrees?”
(a three-quarter turn)

6. The angle estimator shows two amounts of turn. Ask:

“How do you think they are related?”

The two angles together make up a full turn. If appropriate, you could introduce conjugate angles, which is the name given to two angles that combine to make a full-turn or 360 degrees. Supplementary angles is the name given to two angles that combine to make a half turn or 180 degrees.

7. Discuss with the learners the usefulness of using ‘benchmark turns’ for estimating angles (for example, using a quarter turn (right angle or 90 degrees) as a benchmark). Relate the need for angle measurements to the workplace or course as appropriate.

8. Give the learners protractors, explaining that they are the measuring tool used to measure angles. With the learners working in pairs, ask them to discuss how the protractor works. Encourage them to reflect on the angle estimators.

9. Ask the learners to use protractors to measure accurately one-quarter, one-half and three-quarter turns. Let them also measure accurately 30°, 60° and 120°.

10. Ask the learners to describe how they would help someone who had incorrectly measured the following angle as 110°.

Image of protractor.

Follow-up activity

Ask pairs of learners to take turns drawing angles. They give the angle to their partner who first draws a rough estimation of the angle and then, using the scale on the protractor, draws the accurate value.

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