Home›Lesson Plans›Mathematics›Geometry · Grade 4

Types of Triangles

Fourth graders discover that every triangle can be named two ways, by its sides and by its angles, and explore the six categories so they can describe any triangle they meet.

Grade 4Types of Triangles50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Assign or share this lesson

Copy link works with Canvas, Schoology, Moodle and any other LMS — paste it in as a resource or assignment.

Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Classify triangles by sides.
  • ✓Classify triangles by angles.
  • ✓Use the right names.
  • ✓Describe any triangle.
Essential Question

Every triangle has three sides and three angles, yet they come in many shapes. What are the two ways mathematicians sort triangles into groups?

0
Lesson Phases
0
Vocabulary Terms
0
Standards Aligned
0
Interactive Task
Explore the Triangles · Interactive

Explore the Triangles

Project this and open each card to explore a type of triangle, sorted by its sides or by its angles.

📐 Explore the types of trianglesTry it

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Hook — Not All Triangles Are Alike

5 min

Every triangle has three sides and three angles, yet a tall thin one and a wide flat one look nothing alike. How can we sort them into groups?

👩‍🏫 Teacher Moves

  • Show three different triangles.
  • Ask how they differ.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Explore the Triangles

12 min

Students explore the types of triangles.

👩‍🏫 Teacher Moves

  • Send students to Explore the Triangles.
  • Open each card.
  • Name the type.

🎒 Student Actions

  • Explore.
  • Read.
  • Say it.
3

Modify — Name It Two Ways

13 min

Students give each triangle two names.

👩‍🏫 Teacher Moves

  • Pick a triangle.
  • Name it by its sides.
  • Name it by its angles.

🎒 Student Actions

  • Pick.
  • Name.
  • Name.
4

Create — Triangle Sort

15 min

Students build a sorting chart.

👩‍🏫 Teacher Moves

  • Draw or cut out six triangles.
  • Sort them by sides.
  • Sort the same ones by angles.

🎒 Student Actions

  • Draw.
  • Sort.
  • Sort.
5

Reflect — Two Ways to Sort

5 min

Students reflect on classifying triangles.

👩‍🏫 Teacher Moves

  • What makes a triangle equilateral?
  • What is a right triangle?
  • Complete the exit ticket.

🎒 Student Actions

  • Say it.
  • Say it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
4.G.A.2

Classify two-dimensional figures based on the presence or absence of angles of a specified size; recognize right triangles as a category.

CCSS
4.G.A.1

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and identify these in two-dimensional figures.

CCSS
3.G.A.1

Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category.

CCSS
MP.7

Look for and make use of structure.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Triangle picture cards.
  • Sentence frame: “This triangle is ___ because ___ .”
  • Explore one type at a time.

Support & Access

IEP / 504
  • Start with sorting by sides only.
  • Measure sides with a ruler to check.
  • Learn one type fully before the next.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Name each triangle by sides AND angles.
  • Prove why a triangle cannot have two right angles.
  • Sort a mixed pile of real triangles.
Materials

What to gather

  • 📽️Projector / board
  • 📐Triangle cutouts
  • 💻Explore the Triangles
  • 📏Rulers and protractors
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

trianglea closed shape with three straight sides and three anglesequilateral trianglea triangle with all three sides equalisosceles trianglea triangle with exactly two sides equalscalene trianglea triangle with no sides equalright trianglea triangle with one 90-degree angleacute trianglea triangle with all angles less than 90 degreesobtuse trianglea triangle with one angle greater than 90 degreesanglethe amount of turn between two sides that meet at a point
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What makes a triangle equilateral?
All three of its sides are equal in length (and all three angles are equal too).
QUESTION 2
What is a right triangle?
A triangle that has one angle of exactly 90 degrees, a square corner.
QUESTION 3
Why can one triangle have two names, like isosceles and right?
Because triangles are sorted two ways at once, by their sides and by their angles.

Create: a triangle sort.

Have students draw or cut out six triangles, sort them once by sides and again by angles, and label each group, so the two ways of classifying become clear. A printable triangles worksheet is in the Mathematics library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Types of TrianglesFlip
Card 1
Term
Tap to flip →
Meaning
0

Nice work!

Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Types of TrianglesQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Types of TrianglesPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: acute triangle, angle, equilateral triangle, isosceles triangle, obtuse triangle, right triangle, scalene triangle, triangle
  1. a triangle with no sides equal
  2. a triangle with one 90-degree angle
  3. a triangle with one angle greater than 90 degrees
  4. the amount of turn between two sides that meet at a point
  5. a triangle with exactly two sides equal
  6. a triangle with all angles less than 90 degrees
  7. a closed shape with three straight sides and three angles
  8. a triangle with all three sides equal

Part B · Show what you learned

  1. What makes a triangle equilateral?
  2. What is a right triangle?
  3. Why can one triangle have two names, like isosceles and right?
Answer key — Part A: 1) scalene triangle · 2) right triangle · 3) obtuse triangle · 4) angle · 5) isosceles triangle · 6) acute triangle · 7) triangle · 8) equilateral triangle
Part B: 1) All three of its sides are equal in length (and all three angles are equal too). 2) A triangle that has one angle of exactly 90 degrees, a square corner. 3) Because triangles are sorted two ways at once, by their sides and by their angles.