You will learn
- Name the parts of a triangle.
- Tell equilateral, isosceles and scalene triangles apart.
- Measure and compare sides.
- Find the perimeter of a triangle.
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
- A triangle has 3 sides and 3 vertices.
- Equilateral: 3 equal sides.
- Isosceles: 2 equal sides.
- Scalene: no equal sides.
Words to know
All three sides equal.
Two sides equal.
No sides equal.
The distance around.
1. Discover: roof frames
Three roof frames are triangles. One has sides 5, 5, 5. One has 4, 4, 6. One has 3, 4, 5. How are they different?
2. Understand: triangles
A triangle has 3 sides and 3 vertices. We classify it by its sides:
- Equilateral: all 3 sides equal (5, 5, 5).
- Isosceles: 2 sides equal (4, 4, 6).
- Scalene: no sides equal (3, 4, 5).
The perimeter of a triangle is the sum of its sides: 4 + 4 + 6 = 14.
Idea 1: Three kinds
Equilateral: all 3 sides equal, like 6, 6, 6. Isosceles: 2 sides equal, like 7, 7, 3. Scalene: no equal sides, like 2, 3, 4.
Idea 2: Perimeter
A triangle with sides 4, 4, 6 has perimeter 4 + 4 + 6 = 14.
Idea 3: Vertices
A triangle has 3 vertices and 3 sides.
Why classify? The names tell us how the sides compare.
3. Worked examples
Example 1 (I show you): Name
Sides 6, 6, 6.
- All equal.
Answer: equilateral
Example 2 (We do it together): Name
Sides 7, 7, 3.
- Two equal.
Answer: isosceles
Example 3 (You try): Perimeter
Sides 4, 4, 6.
Show the steps and answer
- 4 + 4 + 6.
Answer: 14
Did you know?
Equilateral means equal sides. Isosceles comes from a Greek word meaning equal legs.
Why this matters
Triangles are the strongest shape in bridges and roofs.
4. Explore: measure triangles
You need a ruler and paper.
- Draw a triangle with sides 5, 5, 5 cm.
- Draw one with sides 4, 4, 6 cm.
- Draw one with sides 3, 4, 5 cm.
- Name each and find the perimeter.
Think about it: what did you notice?
Equilateral 15 cm; isosceles 14 cm; scalene 12 cm.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The sides are ___, ___ and ___.
- It is ___ because ___.
- The perimeter is ___.
- A triangle has ___ vertices.
Guided practice
Question 1. Sides 5, 5, 5?
Equilateral.
Question 2. Sides 4, 4, 6?
Isosceles.
Question 3. Sides 3, 4, 5?
Scalene.
Independent practice
Level 1: Start
- Name a triangle with sides 6, 6, 6
- Name a triangle with sides 7, 7, 3
- Name a triangle with sides 2, 3, 4
- Perimeter of 4, 4, 6
- How many vertices has a triangle?
Level 2: Grow
- Name a triangle with sides 9, 9, 9
- Name a triangle with sides 5, 6, 7
- Perimeter of a triangle with sides 3, 4, 5
Level 3: Stretch
- Perimeter of an equilateral triangle with side 12
- Name a triangle with sides 10, 10, 4
- Ana says a triangle with sides 4, 4, 6 is scalene. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A frame has sides 6 m, 6 m and 8 m. What type is it and what is its perimeter?
Show a sample answer
Isosceles; 20 m.
Another one. Draw an isosceles triangle with sides 5 cm, 5 cm and 3 cm. Find its perimeter.
Show a sample answer
13 cm
7. Common mistakes
Fix: Isosceles has exactly 2 equal sides.
Fix: Isosceles has two equal sides. Scalene has none.
Fix: Write cm or m.
8. Lesson summary and revision card
- I can name the parts of a triangle.
- I can tell the three triangles apart.
- I can compare sides.
- I can find the perimeter.
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
- Triangles have 3 sides.
- Equilateral, isosceles, scalene.
- Perimeter = sum of sides.
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.
- Name a triangle with sides 6, 6, 6. [1 mark]
- Name a triangle with sides 7, 7, 3. [1 mark]
- Name a triangle with sides 2, 3, 4. [1 mark]
- Find the perimeter of a triangle with sides 4, 4, 6. [2 marks]
- Ali says a triangle with sides 5, 5, 5 is isosceles only. Is he right? Explain. [3 marks]
Total: 8 marks.
Marking guide and model answers
- Equilateral [1]
- Isosceles [1]
- Scalene [1]
- 4 + 4 + 6 [1] = 14 [1]
- No [1]. All 3 sides are equal [1]. It is equilateral [1].
Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- Sides 6, 6, 6
- Sides 7, 7, 3
- Sides 2, 3, 4
- Perimeter of 4, 4, 6
- Vertices of a triangle
- Sides 5, 5, 5 make an ___ triangle.
- Sides 4, 4, 6 make an ___ triangle.
- Sides 3, 4, 5 make a ___ triangle.
- Perimeter of 4, 4, 6 =
- A triangle has ___ vertices.
Homework
Find three triangles at home and classify them by measuring their sides.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Sides 6, 6, 6 | equilateral | 2 |
| Sides 7, 7, 3 | isosceles | 2 |
| Sides 2, 3, 4 | scalene | 2 |
| Perimeter of 4, 4, 6 | 14 | 2 |
| Vertices of a triangle | 3 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 equilateral; 2 isosceles; 3 scalene; 4 14; 5 3.
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 equilateral; 7 isosceles; 8 scalene; 9 14; 10 3.
Independent practice answers. Level 1: 1 equilateral; 2 isosceles; 3 scalene; 4 14; 5 3. Level 2: 1 equilateral; 2 scalene; 3 12. Level 3: 1 36; 2 isosceles; 3 Two sides are equal, so it is isosceles..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name the parts of a triangle | 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 Tell equilateral, isosceles and scalene triangles apart | 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 and compare 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 |
| O4 Find the perimeter of a triangle | 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: Thinking isosceles means 3 equal sides. Isosceles has exactly 2 equal sides.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Cut straws to make triangles with different sides.
- 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 by their sides. You do not need to be good at mathematics to help.
- Measure the sides of a triangle on paper.
- Ask: how many sides are equal?
- Make triangles with straws.
- 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 the parts of a triangle; tell equilateral, isosceles and scalene triangles apart; measure and compare sides; find the perimeter of a triangle.
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 a ruler 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. How many sides are equal? What is the perimeter?
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. Thinking isosceles means 3 equal sides. Isosceles has exactly 2 equal sides.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 8-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 straws to make triangles with different sides. 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 3 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 3.G.A.1 and 4.G.A.2 (classify triangles); Cambridge Primary Mathematics Stage 3 (2D shapes). These sources informed the lesson.