Mathematics
Intermediate
41 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen
Protractor
Measure the Angles practice sheet

Measuring Angles Accurately with a Protractor

Learn to place a protractor correctly on a vertex and baseline, then read angles accurately using the right scale. Measure acute, obtuse and reflex angles to the nearest degree.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedHere is an angle with a protractor laid on top of it. Just by looking, does this look right to you, or does something seem off?

    Key point

    Two things to check with your eyes. The middle dot of the protractor should sit right where the two arms meet, at the corner. The straight bottom edge of the protractor should lie flat along one of the arms. Is each of those in the right place here?

    2 - Watch and Notice ~9 mins

    40 degrees: an acute angle

    Watch the placement: the centre dot (the vertex, where the arms meet) sits right on the corner, and the bottom edge (the baseline) lies along one arm starting at zero. Now look at the two number rings. The baseline arm sits on 0 on the ring that counts up towards the second arm, so we follow that same ring up to the second arm and read 40°. The other ring would say 140° — that is the wrong ring, because it does not start at zero on our baseline arm.

    130 degrees: an obtuse angle

    Same careful placement. We start at the zero on our baseline arm and follow that ring up. The second arm reaches past the right angle, so we read 130°.

    90 degrees: a right angle

    The two arms make a perfect square corner. Both rings meet at the same number here, so the scale reads exactly 90° either way.

    290 degrees: a reflex angle

    This angle bends past halfway round. The protractor only reaches 180°, so look at the two angles together. The small angle is 70°, and the big reflex angle is the rest of the way round. Together they go the whole way round the vertex — and a full turn round a point is 360°. So the reflex angle is whatever is left after the 70°: 360°70° = 290°.

    3 - Try It Together ~11 mins

    We measure on the board together now. One pupil comes up, places the protractor carefully, and reads the angle aloud. Everyone else: keep your own protractor out at your desk, estimate the size silently in your head first, then get ready to agree or to say what you would change.

    Key point

    For this round the angle stays between and 180°, so each one is acute, right or obtuse. Estimate the size first — your estimate tells you which ring to trust.

    Measure the angle together

    4 - Measure the Angles in Your Copy ~3 mins

    COPYBOOK MOMENT

    Take out your 'Measure the Angles' practice sheet. With your own protractor, measure each of the three angles on the sheet and write its size in degrees beside it. Then mark each one as acute, right or obtuse.

    5 - Class Challenge ~8 mins

    Today we work through these angles together: 35°, then 95°, then 145°, and finally a reflex angle of 290°. Each one gets a step harder. We place the protractor, read the size, and check before moving on.

    Measure each angle

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    How does estimating the size of an angle first stop us from reading the wrong scale on the protractor?

    7 - What's Next ~3 mins

    What we learned today

    • Put the protractor's centre on the vertex first, then lay the baseline along one arm.
    • Read from the ring that starts at zero on that arm.
    • Estimate the size first, so you read the correct ring.
    • For a reflex angle, measure the smaller angle and take it from 360°, because the two angles together make one full turn round the vertex.

    Coming up

    Coming up

    Next we turn the skill around: instead of reading an angle, you will construct your own exact angles with the protractor.

    Pupil practice
    Module 7 · 2D Shape, 3D Shape and Angles Data & Chance
    Lesson 72 · Measuring Angles Accurately with a Protractor
    Download Activity Book page (PDF)
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