Estimating/classifying angles | Year 5

01 / LEARN

Understand the idea.

An angle measures a turn

An angle measures the turn from one ray to another around their shared vertex. Compare the opening between the rays. Extending either ray makes the drawing longer but does not change that turn.

Use familiar turns as benchmarks: a quarter turn is $90^{\circ}$ , a half turn is $180^{\circ}$ and a full turn is $360^{\circ}$ . The degree symbol records the unit of angle.

Use benchmarks

An acute angle is between $0^{\circ}$ and $90^{\circ}$ ; an obtuse angle is between $90^{\circ}$ and $180^{\circ}$ . Exactly $90^{\circ}$ is right, and exactly $180^{\circ}$ is straight.

A reflex angle is greater than $180^{\circ}$ but less than $360^{\circ}$ . Look at the marked arc: the same two rays can show a small turn or the larger turn going the other way.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

A small turn

Classify 35 degrees.

Worked solution

1
Compare with the right-angle benchmark.
$0^{\circ} < 35^{\circ} < 90^{\circ}$
The angle is positive and smaller than a quarter turn.
2
Name the angle class.
An angle strictly between zero and a right angle is acute.

Answer

Acute

EXAMPLE 02

Past a half turn

Classify 225 degrees.

Worked solution

1
Compare with a half turn.
$225^{\circ} > 180^{\circ}$
The turn has passed the straight-angle benchmark.
2
Check it is smaller than a full turn.
$180^{\circ} < 225^{\circ} < 360^{\circ}$
The angle lies in the reflex range, so it is reflex.

Answer

Reflex

03 / YOUR TURN

Try it yourself.

Check your understanding

Is exactly 90 degrees acute or right?

Show answer & reasoning

Right

Exactly $90^{\circ}$ is a right angle. The acute range stops before $90^{\circ}$ , so the endpoint is not acute.

Keep practising

6 worksheet questions · 7 marks

Open worksheet Worked solutions

Read the questions online

Classify 48 degrees.
1 mark
Classify 90 degrees.
1 mark
Classify 135 degrees.
1 mark
Classify 180 degrees.
1 mark
Classify 290 degrees.
1 mark
Two angles both measure 55 degrees. One has longer rays. Which is larger? Explain.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Classify 48 degrees.
1 mark
$0 < 48 < 90$ .
Acute
Classify 90 degrees.
1 mark
A quarter turn is exactly 90 degrees.
Right
Classify 135 degrees.
1 mark
$90 < 135 < 180$ .
Obtuse
Classify 180 degrees.
1 mark
A half turn is 180 degrees.
Straight
Classify 290 degrees.
1 mark
$180 < 290 < 360$ .
Reflex
Two angles both measure 55 degrees. One has longer rays. Which is larger? Explain.
2 marks
Both have the same 55-degree turn. Ray length does not change the angle.
Neither; they are equal.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Year 5 angle estimation and measurement using a protractor.

Official curriculum source ↗

In this lesson

Understand the idea.

An angle measures a turn

Use benchmarks

See the method in action.

A small turn

Compare with the right-angle benchmark.

Name the angle class.

Past a half turn

Compare with a half turn.

Check it is smaller than a full turn.

Try it yourself.

Check your understanding

Keep practising