You will learn
- Place a protractor correctly.
- Read the correct scale.
- Measure an angle.
- Draw an angle of given size.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Put the centre of the protractor on the vertex.
- Line the baseline up with one arm.
- Read the scale that starts at 0.
- Check against acute or obtuse.
Words to know
Tool for measuring angles.
Unit of angle size.
The 0° line.
The numbers on the protractor.
1. Discover: measuring turns
How can we say exactly how wide an angle is? What tool has a curved edge with numbers from 0 to 180?
2. Understand: protractor
- Put the protractor centre on the vertex.
- Line one arm up with the 0° baseline.
- Read where the other arm crosses the scale that starts at 0.
- An acute angle reads less than 90°, e.g. 60°.
- An obtuse angle reads more than 90°, e.g. 120°.
To draw 70°: draw an arm, place the protractor, mark 70° and join to the vertex.
Idea 1: Place
Put the protractor’s centre on the vertex and its baseline along one arm.
Idea 2: Read
Read the scale that starts at 0 on the arm. A 60° angle is acute and a 120° angle is obtuse. A straight line is 180°.
Idea 3: Draw
To draw 70°: draw one arm, place the protractor, mark 70° from the 0, and join to the vertex.
Why check the type? A reading of 110° for a small angle shows we used the wrong scale.
3. Worked examples
Example 1 (I show you): Tool
Measuring angles
- A half-circle tool.
Answer: protractor
Example 2 (We do it together): Type
120°
- More than 90°.
Answer: obtuse
Example 3 (You try): Max
Protractor
Show the steps and answer
- A half circle.
Answer: 180°
Did you know?
A semicircle protractor goes from 0° to 180°.
Why this matters
Measuring angles lets us build and design accurately.
4. Explore: measure
You need a protractor and paper.
- Draw an angle.
- Centre the protractor.
- Read the scale from 0.
- Draw a 70° angle.
Think about it: what did you notice?
70°.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The vertex is at the ___.
- I read the scale that starts at ___.
- The angle is ___ degrees.
- So it is ___.
Guided practice
Question 1. Where do we place the centre?
On the vertex.
Question 2. Which scale do we read?
The one starting at 0°.
Question 3. Is 60° acute or obtuse?
Acute.
Independent practice
Level 1: Start
- Tool for measuring angles
- Is 120° acute or obtuse?
- Maximum reading on a protractor
- Draw 70°: where do you mark?
- Angle of a straight line
Level 2: Grow
- Type of a 70° angle
- Type of a 90° angle
- Type of a 150° angle
Level 3: Stretch
- Two angles on a straight line: one is 115°. The other is…
- Say how to draw a 125° angle
- Ben says a protractor goes to 360°. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A ramp makes an angle of 30° with the ground. Is it acute or obtuse?
Show a sample answer
Acute.
Another one. Describe how to measure an angle with a protractor.
Show a sample answer
Centre on the vertex, baseline on one arm, read the scale from 0 where the other arm crosses.
7. Common mistakes
Fix: Start at 0°.
Fix: Start from the 0 on the arm.
Fix: The centre must sit on the vertex.
8. Lesson summary and revision card
- I can place a protractor correctly.
- I can read the correct scale.
- I can measure an angle.
- I can draw an angle of a given size.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Centre on the vertex.
- Baseline on 0°.
- Read the correct scale.
11. Next lesson
Next lesson: Classifying triangles. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Name the tool used to measure angles. [1 mark]
- Is 120° acute or obtuse? Explain. [2 marks]
- What is the largest reading on a protractor? [1 mark]
- Describe how to draw an angle of 70°. [3 marks]
- Ana measures an acute angle as 110°. What is her mistake? [3 marks]
Total: 10 marks.
Marking guide and model answers
- Protractor [1]
- Greater than 90° [1]; obtuse [1]
- 180° [1]
- Draw one arm along the baseline [1]; mark 70° from 0 [1]; join to the vertex [1]
- An acute angle is less than 90° [1]; she read the wrong scale [1]; the reading should be 70° [1]
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Tool for angles
- 120° is acute or obtuse
- Max on a protractor
- 60° is acute or obtuse
- Straight angle
- A protractor measures
- The centre goes on the
- A 60° angle is
- A 120° angle is
- A straight line has an angle of
Homework
Measure five angles in your notebook.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Tool for angles | protractor | 2 |
| 120° is acute or obtuse | obtuse | 2 |
| Max on a protractor | 180° | 2 |
| 60° is acute or obtuse | acute | 2 |
| Straight angle | 180° | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 protractor; 2 obtuse; 3 180°; 4 acute; 5 180°.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 angles; 7 vertex; 8 acute; 9 obtuse; 10 180°.
Independent practice answers. Level 1: 1 a protractor; 2 obtuse; 3 180°; 4 mark 70° on the scale starting from 0; 5 180°. Level 2: 1 acute; 2 right; 3 obtuse. Level 3: 1 65°; 2 Draw one arm, put the protractor on the vertex, mark 125° from 0, join the vertex to the mark.; 3 A half-circle protractor goes from 0° to 180°..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Place a protractor correctly | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Read the correct scale | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Measure an angle | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Draw an angle of given size | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Reading the wrong scale. Start at 0°.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Measure angles of cut-out shapes.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child measures and draws angles with a protractor. You do not need to be good at mathematics to help.
- Use a protractor with household objects.
- Ask: acute or obtuse?
- Estimate before measuring.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: place a protractor correctly; read the correct scale; measure an angle; draw an angle of given size.
Prerequisite knowledge. Lesson 7.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need a protractor and paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. Is the centre on the vertex? Which scale starts at 0?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Reading the wrong scale. Start at 0°.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Measure angles of cut-out shapes. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 4 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 4.MD.C.6 (measure angles with a protractor); Cambridge Primary Mathematics Stage 5 (measuring angles). These sources informed the lesson.