You will learn
- Classify by sides.
- Classify by angles.
- Use the angle sum 180°.
- Find a missing angle.
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
- The angles of a triangle add to 180°.
- Classify by sides: equilateral, isosceles, scalene.
- Classify by angles: acute, right, obtuse.
- Find a missing angle by subtracting.
Words to know
3 equal sides.
2 equal sides.
No equal sides.
Has a 90° angle.
1. Discover: triangle families
Two triangles have sides 5, 5, 5 and 3, 4, 5. How are they different? What do their angles add up to?
2. Understand: classifying triangles
- By sides: equilateral (3 equal), isosceles (2 equal), scalene (none equal).
- By angles: acute (all < 90°), right (one 90°), obtuse (one > 90°).
- The three angles of any triangle add to 180°.
- Missing angle: 180° − 50° − 60° = 70°.
Idea 1: Angle sum
Missing angle with 90° and 40°: 90 + 40 = 130 and 180 − 130 = 50°. With 60° and 60°: 60°.
Idea 2: By sides
7, 7, 3 has two equal sides, so it is isosceles. 3, 4, 5 has no equal sides, so it is scalene.
Idea 3: By angles
100°, 40°, 40° has one angle over 90°, so it is obtuse.
Why 180°? Tearing off the corners of a triangle makes a straight line.
3. Worked examples
Example 1 (I show you): Missing
90° and 40°
- 180 − 130.
Answer: 50°
Example 2 (We do it together): Sides
7, 7, 3
- Two equal.
Answer: isosceles
Example 3 (You try): Angles
100°, 40°, 40°
Show the steps and answer
- One angle over 90°.
Answer: obtuse triangle
Did you know?
An equilateral triangle has three 60° angles.
Why this matters
Triangles are the strongest shape in bridges and roofs.
4. Explore: angle sum
You need paper.
- Draw a triangle.
- Measure its angles.
- Add them.
- Compare with 180°.
Think about it: what did you notice?
Close to 180°.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The angles add to ___.
- The missing angle is ___.
- It has ___ equal sides, so it is ___.
- It has an angle of ___, so it is ___.
Guided practice
Question 1. Angles in a triangle add to?
180°.
Question 2. Missing angle when others are 50° and 60°?
70°.
Question 3. Triangle with a 90° angle?
Right triangle.
Independent practice
Level 1: Start
- Missing angle: 90° and 40°
- Missing angle: 60° and 60°
- Sides 7, 7, 3: type
- Sides 3, 4, 5: type
- Angles 100°, 40°, 40°: type by angles
Level 2: Grow
- Missing angle: 70° and 60°
- Sides 6, 6, 6
- Angles 90°, 45°, 45°
Level 3: Stretch
- Missing angle: 35° and 85°
- An isosceles triangle has top angle 80°. Each base angle is…
- Ben says 80°, 70° and 40° make a triangle. Check it.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Two angles of a roof triangle are 70° and 50°. What is the third?
Show a sample answer
60°.
Another one. A triangle has angles 55° and 65°. Find the third angle and name the triangle by angles.
Show a sample answer
180 − 120 = 60°. All angles are less than 90°, so it is acute.
7. Common mistakes
Fix: Subtract the known angles.
Fix: Add the two known angles, then subtract.
Fix: Isosceles has two equal sides; scalene has none.
8. Lesson summary and revision card
- I can classify by sides.
- I can classify by angles.
- I can use the angle sum 180°.
- I can find a missing angle.
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
- Classify by sides and angles.
- Angle sum 180°.
- Subtract to find missing.
11. Next lesson
Next lesson: Symmetry. 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.
- Find the missing angle when two angles are 90° and 40°. [2 marks]
- Find the missing angle when two angles are 60° and 60°. [2 marks]
- Name the triangle with sides 7, 7, 3. [1 mark]
- Name the triangle with sides 3, 4, 5. [1 mark]
- Kofi says angles 100°, 40°, 40° make an acute triangle. Is he right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 90 + 40 = 130 [1]; 50° [1]
- 60 + 60 = 120 [1]; 60° [1]
- Isosceles [1]
- Scalene [1]
- No [1]. 100° is greater than 90° [1]. It is obtuse [1].
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Missing: 90° and 40°
- Missing: 60° and 60°
- Sides 7, 7, 3
- Sides 3, 4, 5
- Angles 100°, 40°, 40°
- The angles of a triangle add to
- Missing angle: 50° and 60°
- Missing angle: 90° and 40°
- Sides 7, 7, 3 make an
- Angles 100°, 40°, 40° make an
Homework
Draw one triangle of each kind and measure its angles.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Missing: 90° and 40° | 50° | 2 |
| Missing: 60° and 60° | 60° | 2 |
| Sides 7, 7, 3 | isosceles | 2 |
| Sides 3, 4, 5 | scalene | 2 |
| Angles 100°, 40°, 40° | obtuse | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 50°; 2 60°; 3 isosceles; 4 scalene; 5 obtuse.
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): 6 180°; 7 70°; 8 50°; 9 isosceles triangle; 10 obtuse triangle.
Independent practice answers. Level 1: 1 50°; 2 60°; 3 isosceles; 4 scalene; 5 obtuse triangle. Level 2: 1 50°; 2 equilateral; 3 right-angled triangle. Level 3: 1 60°; 2 50°; 3 80 + 70 + 40 = 190, not 180, so it cannot be a triangle..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Classify by sides | 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 Classify by angles | 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 Use the angle sum 180° | 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 a missing 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 |
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: Forgetting that angles add to 180°. Subtract the known angles.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Cut and tear angles to see 180°.
- 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 classifies triangles and finds missing angles. You do not need to be good at mathematics to help.
- Draw triangles and measure the angles.
- Ask: how many sides are equal?
- Tear the corners of a paper triangle to see 180°.
- 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: classify by sides; classify by angles; use the angle sum 180°; find a missing angle.
Prerequisite knowledge. Lessons 7 and 8.
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. How many sides are equal? What do the angles add up 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. Forgetting that angles add to 180°. Subtract the known angles.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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. Cut and tear angles to see 180°. 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.G.A.2 and 8.G.A.5; Cambridge Primary Mathematics Stage 5 (triangles and angle sum). These sources informed the lesson.