Mathematics

Intermediate

50 mins

Teacher/Student led

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Classifying Triangles: Equilateral, Isosceles and Scalene

Learn to sort triangles into three families by their side lengths: equilateral (all equal), isosceles (two equal) and scalene (none equal). Explore why a triangle's position never changes its family.

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Draw One of Each in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Here are three triangles. One has all its sides the same length, one has two sides the same, and one has no two sides the same.

What is the same about all three of them? And what is different?

Teacher Notes

Hold up (or display) three real triangle cut-outs — one all-equal, one with two equal sides, one with none equal. Take two or three hands-up answers, not open call-outs. Steer the class toward noticing that all three have three straight sides and three corners (same) but the side lengths differ (different) — this is the idea the whole lesson hangs on.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Three triangles are shown sorted into their families by the length of their sides. Notice how many sides match each time, and that the last one is still the same family when turned on its side.

Teacher Notes

Equilateral (5, 5, 5): all three sides match. A strip laid along one side reaches exactly along the other two. Like a yield sign.

Isosceles (6, 6, 4): exactly two match. Find the pair, then the odd one out. Say it slowly, eye-SOSS-uh-leez, and have the class echo it once.

Scalene (3, 5, 6): no two line up, all three different. Say SKAY-leen.

Tilted scalene: same triangle turned. Ask whether anything about the sides changed just because you turned it. It hasn't, so still scalene. Turning never changes the family.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~8 mins

Today we sort triangles into their three families. One pupil comes to the board to drag a triangle. Before they drag, everyone watching says which sides they think match — then the pupil drags it to the right family: equilateral, isosceles or scalene.

Sort the triangles into families

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Before each pupil drags, have the class say which sides they think match. Use the paper-strip check on screen if a triangle is hard to judge by eye. Rotate enough pupils to work through the practice set briskly. Watch for the common slip of counting an equilateral as isosceles (all-equal triangles also have 'two equal sides', but we name them by the strongest match — all three equal).

+15 XP

4 - Draw One of Each in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, draw one triangle of each kind. Label one equilateral, one isosceles and one scalene.

Teacher Notes

Walk the room and glance for three clearly different triangles and the right labels — no marking, this is whole-class copybook practice. Look for the equilateral being drawn too lopsided and the scalene being drawn with two sides that look equal.

+10 XP

5 - Class Challenge ~11 mins

Now we make triangles with strips of paper or lollipop sticks. Work through these in order:

Make a triangle with all three sides equal.
Make a triangle with exactly two sides equal.
Make a triangle with no two sides equal.
Try to make a triangle with sides of 3 cm, 3 cm and 7 cm.

Hands-on Task

Teacher Notes

These are the practice questions — pupils work the four builds at their desks with strips or sticks, and the class confirms each result aloud before moving on. Keep it brisk rather than over-explaining.

All equal = equilateral; two equal = isosceles; none equal = scalene — name the family each time.
The 3-3-7 build is the stretch: the two short sides cannot reach across the long one, so the triangle cannot close. Have pupils lay the 3 cm and 3 cm strips end to end against the 7 cm strip so they see the gap, then ask 'why won't it close?' before telling them.
Fast finishers: name the family of a triangle they can spot somewhere in the room.

Differentiation: pair a pupil who is less secure with a peer who can model laying the strips end to end carefully (teacher's grouping choice).

+15 XP

6 - What Did We Notice? ~3 mins

MATHS TALK

Can a triangle ever belong to two families at once? Think about a triangle with all three sides equal — does it also have two sides equal?

Teacher Notes

Listen for the insight that an equilateral triangle does have two equal sides (it has three) — but we give it the strongest name, equilateral, not isosceles. Revoice a good answer: 'so all-equal beats two-equal — we name it by the most that matches.' Head off the idea that turning a triangle could move it between families.

+10 XP

7 - What's Next ~2 mins

What we learned today

Every triangle has three sides — the side lengths sort it into a family.
All three equal is equilateral, exactly two equal is isosceles, none equal is scalene.
An equilateral triangle does have two equal sides too — but because all three match, we give it the strongest name, equilateral.
Turning a triangle never changes its family.

Coming up

Next we look at four-sided shapes — squares, rectangles, rhombuses and more — and sort them by their sides and corners too.

Teacher Notes

Close briskly. A quick whole-class recall of the three family names by their side rule is enough.

+5 XP

Pupil practice

Module 7 · 2D and 3D Shapes and Angles Data & Chance

Lesson 78 · Classifying Triangles: Equilateral, Isosceles and Scalene

Download Activity Book page (PDF)

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This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Classifying Triangles: Equilateral, Isosceles and Scalene

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

3 - Try It Together ~8 mins

Sort the triangles into families

4 - Draw One of Each in Your Copy ~3 mins

5 - Class Challenge ~11 mins

Hands-on Task

6 - What Did We Notice? ~3 mins

7 - What's Next ~2 mins

What we learned today

Coming up

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