You will learn
- Classify by sides.
- Classify by angles.
- Use the angle sum.
- Find an unknown 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
- Equilateral: all sides equal. Isosceles: two. Scalene: none.
- Angles in a triangle add to 180°.
- Equilateral triangles have three 60° angles.
- Subtract two angles from 180° to find the third.
Words to know
All sides equal.
Two sides equal.
No sides equal.
180° in a triangle.
1. Discover: triangle sorting
A triangle has angles 50° and 60°. What is the third angle?
2. Understand: triangles
- The angles of a triangle add to 180°, so 180 − 50 − 60 = 70°.
- Equilateral: three equal sides, each angle 60°.
- Isosceles: two equal sides and two equal angles.
- Right triangle: one 90° angle.
Idea 1: Third angle
90° and 40°: 180 − 130 = 50°. 50° and 60°: 180 − 110 = 70°.
Idea 2: Equilateral
Each angle is 180 ÷ 3 = 60°.
Idea 3: Sides
5, 5, 8 cm has two equal sides: isosceles. 3, 4, 5 cm has none equal: scalene.
Why 180°? The three corners of any triangle fit on a straight line.
3. Worked examples
Example 1 (I show you): Third angle
90° and 40°
- 90 + 40 = 130.
- 180 − 130.
Answer: 50°
Example 2 (We do it together): Equilateral
Each angle
- 180 ÷ 3.
Answer: 60°
Example 3 (You try): Type
Sides 5, 5, 8 cm
Show the steps and answer
- Two sides equal.
Answer: isosceles
Did you know?
Isosceles triangles also have two equal angles.
Why this matters
Triangles are used in bridges, roofs and maps.
4. Explore: find
You need paper.
- Add known angles.
- Subtract from 180.
- Name the triangle.
- Check.
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 angles add to ___.
- The third angle is ___.
- Two sides are equal, so ___.
- No sides are equal, so ___.
Guided practice
Question 1. 180 − 50 − 60?
70.
Question 2. Angle of an equilateral triangle?
60°.
Question 3. Sides equal in isosceles?
two.
Independent practice
Level 1: Start
- Third angle: 90° and 40°
- Third angle: 50° and 60°
- Each angle of an equilateral triangle
- Type: 5, 5, 8 cm
- Type: 3, 4, 5 cm
Level 2: Grow
- Third angle: 30° and 70°
- Sides 6, 6, 6 cm
- Angles of a triangle add to
Level 3: Stretch
- Isosceles triangle, apex angle 40°. Each base angle
- Third angle: 90° and 25°
- Ben says sides 3, 4, 5 is isosceles. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Two angles of a triangle are 50° and 60°. The third?
Show a sample answer
70°.
Another one. A triangle has angles 50° and 60°. Find the third and name the type by angles.
Show a sample answer
70°; acute-angled
7. Common mistakes
Fix: It is 180°.
Fix: Triangle angles add to 180°.
Fix: Isosceles has two equal sides.
8. Lesson summary and revision card
- I can classify by sides.
- I can classify by angles.
- I can use the angle sum.
- I can find an unknown 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
- Angles total 180°.
- Name by sides.
- Name by angles.
11. Next lesson
Next lesson: Quadrilaterals. 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 third angle of a triangle with angles 90° and 40°. [2 marks]
- Find the third angle of a triangle with angles 50° and 60°. [2 marks]
- Find each angle of an equilateral triangle. [2 marks]
- A triangle has sides 5 cm, 5 cm and 8 cm. Name its type. [2 marks]
- Ali says a triangle with sides 3, 4 and 5 cm is isosceles. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 90 + 40 = 130 [1]; 180 − 130 = 50° [1]
- 50 + 60 = 110 [1]; 70° [1]
- 180 ÷ 3 [1]; 60° [1]
- Two sides equal [1]; isosceles [1]
- No [1]. Isosceles needs two equal sides [1]. All sides differ, so it is scalene [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- Third angle: 90° and 40°
- Third angle: 50° and 60°
- Each angle of an equilateral triangle
- Type: 5, 5, 8 cm
- Type: 3, 4, 5 cm
- Third angle of 90° and 40°
- Third angle of 50° and 60°
- Each angle in an equilateral triangle
- Sides 5, 5, 8 cm
- Sides 3, 4, 5 cm
Homework
Draw one of each triangle type.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Third angle: 90° and 40° | 50 | 2 |
| Third angle: 50° and 60° | 70 | 2 |
| Each angle of an equilateral triangle | 60 | 2 |
| Type: 5, 5, 8 cm | isosceles | 2 |
| Type: 3, 4, 5 cm | scalene | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 50; 2 70; 3 60; 4 isosceles; 5 scalene.
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 50°; 7 70°; 8 60°; 9 isosceles; 10 scalene.
Independent practice answers. Level 1: 1 50°; 2 70°; 3 60°; 4 isosceles; 5 scalene. Level 2: 1 80°; 2 equilateral; 3 180°. Level 3: 1 70°; 2 65°; 3 No two sides are equal: it is scalene..
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 | 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 an unknown 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: Using 360° for a triangle. It is 180°.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Shape names.
- 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.
- Cut out a triangle and tear off the corners.
- Ask: how many sides are equal?
- Add the angles together.
- 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; find an unknown angle.
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. 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 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 360° for a triangle. It is 180°.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. Shape names. 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.G.A.2 and 7.G.A.2; Cambridge Primary Mathematics Stage 6 (triangles). These sources informed the lesson.