You will learn
- Classify triangles by sides.
- Classify by angles.
- Find a missing angle.
- Explain why a triangle cannot have two right angles.
Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.
Student lesson
Words to know
3 equal sides.
2 equal sides.
No equal sides.
One 90° angle.
1. Discover: triangle families
Two triangles each have a 75° angle and a 45° angle. What is the third angle?
2. Understand: triangles
- By sides: equilateral, isosceles, scalene.
- By angles: acute (all < 90°), right (one 90°), obtuse (one > 90°).
- Angles add to 180°: 180 − 75 − 45 = 60°.
- An equilateral triangle has three 60° angles.
3. Explore: classify
You need a ruler and protractor.
- Draw a triangle.
- Measure sides.
- Measure angles.
- Name it two ways.
Think about it: what did you notice?
e.g. scalene acute.
4. Practise
Guided practice
Question 1. Third angle: 75° and 45°?
60°.
Question 2. Angles of an equilateral triangle?
60° each.
Question 3. Triangle with a 100° angle?
Obtuse.
Independent practice
- Third angle: 90°, 35°
- Third angle: 50°, 50°
- Sides 5, 5, 8: type
- Angles 60°, 60°, 60°: type
- Can a triangle have two right angles?
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
Two angles of a roof are 75° and 45°. What is the third?
Show a sample answer
60°.
6. Common mistake
Fix: Subtract from 180°.
7. Check and master
Answer all questions. You will see feedback after each one.
Your result appears here after you answer every question.
8. Key takeaways
- Sides and angles.
- Sum 180°.
- Equilateral: 60°.
9. Next lesson
Next lesson: Quadrilaterals. Keep going with the next idea in this course.
Printable worksheet
- Third angle: 90°, 35°
- Third angle: 50°, 50°
- Sides 5, 5, 8
- Angles 60° each
- Two right angles in a triangle? (yes/no)
Homework
Draw and classify five triangles.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Third angle: 90°, 35° | 55° | 2 |
| Third angle: 50°, 50° | 80° | 2 |
| Sides 5, 5, 8 | isosceles | 2 |
| Angles 60° each | equilateral | 2 |
| Two right angles in a triangle? (yes/no) | no | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 55°; 2 80°; 3 isosceles; 4 equilateral; 5 no.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Classify triangles 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 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 |
| O4 Explain why a triangle cannot have two right 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Forgetting 180°. Subtract from 180°.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Triangle sides and 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.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: classify triangles by sides; classify by angles; find a missing angle; explain why a triangle cannot have two right angles.
Prerequisite knowledge. Lesson 2.
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. 35–45 minutes.
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 ruler and protractor. 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.
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 180°. Subtract from 180°.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Triangle sides and 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
Alignment is pending verification and no external 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. Specific standard codes will be added once checked against the official documents.