You will learn
- Name angle types.
- Measure an angle.
- Find angles on a straight line.
- Find angles around a point.
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
- Acute is less than 90°; obtuse is between 90° and 180°.
- Angles on a straight line add to 180°.
- Angles around a point add to 360°.
- Vertically opposite angles are equal.
Words to know
Less than 90°.
Between 90° and 180°.
180°.
Equal angles across a crossing.
1. Discover: opening a door
As a door opens, its angle grows. When is it a right angle?
2. Understand: angles
- Acute < 90°; right = 90°; obtuse between 90° and 180°; straight = 180°; reflex > 180°.
- Angles on a straight line total 180°: 180 − 65 = 115°.
- Angles around a point total 360°.
- Vertically opposite angles are equal.
Idea 1: Types
45° is acute. 120° is obtuse. 90° is a right angle and 180° is a straight angle.
Idea 2: Line
Angles on a line: 180 − 65 = 115°.
Idea 3: Point and crossing
Around a point: 360 − 100 − 120 = 140°. Vertically opposite to 70° is 70°.
Why equal? Crossing lines make matching pairs.
3. Worked examples
Example 1 (I show you): Type
45°
- Less than 90°.
Answer: acute
Example 2 (We do it together): Line
180° − 65°
- Angles on a line add to 180°.
Answer: 115°
Example 3 (You try): Point
100°, 120°, ?
Show the steps and answer
- Total 360°.
Answer: 140°
Did you know?
A full turn is 360° and a half turn is 180°.
Why this matters
Angles describe turns, corners and directions.
4. Explore: find
You need paper.
- Name the total.
- Subtract known angles.
- Write the answer.
- Check the sum.
Think about it: what did you notice?
115°.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The angle is ___, so it is ___.
- Angles on a line add to ___.
- Angles around a point add to ___.
- Vertically opposite angles are ___.
Guided practice
Question 1. Angle with 65° on a straight line?
115°.
Question 2. Total around a point?
360°.
Question 3. An angle of 120° is?
obtuse.
Independent practice
Level 1: Start
- Type of 45°
- Type of 120°
- 180 − 65
- Angles around a point: 100°, 120°, ?
- Vertically opposite to 70°
Level 2: Grow
- Type of 30°
- Type of 150°
- Angles on a line: 80° and ?
Level 3: Stretch
- Two lines cross with a 40° angle. The angle next to it
- Around a point: 90°, 90°, 90°, ?
- Ben says the angle vertically opposite 70° is 110°. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
On a straight line one angle is 65°. Find the other.
Show a sample answer
115°.
Another one. A door opens by 35°. What angle is left to a straight line?
Show a sample answer
145°
7. Common mistakes
Fix: Straight line is 180°.
Fix: A straight line is 180°.
Fix: Acute is small; obtuse is wide.
8. Lesson summary and revision card
- I can name angle types.
- I can measure an angle.
- I can find angles on a line.
- I can find angles around a point.
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
- Straight 180°.
- Full turn 360°.
- Vertically opposite equal.
11. Next lesson
Next lesson: 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.
- State the type of a 45° angle. [2 marks]
- State the type of a 120° angle. [2 marks]
- Two angles on a line: one is 65°. Find the other. [2 marks]
- Angles around a point are 100°, 120° and one more. Find it. [3 marks]
- Ali says the angle vertically opposite 70° is 110°. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- Less than 90° [1]; acute [1]
- Between 90° and 180° [1]; obtuse [1]
- Angles on a line sum to 180° [1]; 115° [1]
- Angles around a point sum to 360° [1]; 360 − 100 − 120 [1]; 140° [1]
- No [1]. Vertically opposite angles are equal [1]. It is 70° [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 45° type
- 120° type
- 180 − 65
- 100 + 120 + ? = 360
- Opposite to 70°
- Type of 45°
- Type of 120°
- 180 − 65
- Around a point: 100°, 120°, ?
- Vertically opposite to 70°
Homework
Find five angles at home and classify them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 45° type | acute | 2 |
| 120° type | obtuse | 2 |
| 180 − 65 | 115 | 2 |
| 100 + 120 + ? = 360 | 140 | 2 |
| Opposite to 70° | 70 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 acute; 2 obtuse; 3 115; 4 140; 5 70.
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 acute; 7 obtuse; 8 115°; 9 140°; 10 70°.
Independent practice answers. Level 1: 1 acute; 2 obtuse; 3 115°; 4 140°; 5 70°. Level 2: 1 acute; 2 obtuse; 3 100°. Level 3: 1 140°; 2 90°; 3 Vertically opposite angles are equal: 70°..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name angle types | 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 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 |
| O3 Find angles on a straight line | 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 Find angles around a point | 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: Using 90° for a straight line. Straight line is 180°.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Right angles.
- 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 names and calculates angles. You do not need to be good at mathematics to help.
- Open a door to show different angles.
- Ask: is it less than a right angle?
- Use a clock for turns.
- 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: name angle types; measure an angle; find angles on a straight line; find angles around a point.
Prerequisite knowledge. Lesson 1.
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 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. What type is it? What do the angles add to?
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. Using 90° for a straight line. Straight line is 180°.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. Right angles. 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 6 » 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.5 to 4.MD.C.7 and 7.G.B.5; Cambridge Primary Mathematics Stage 6 (angles). These sources informed the lesson.