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Polygon or Not a Polygon

Third graders learn that a polygon follows clear rules, a closed shape with straight sides and no curves, and test shapes against those rules, then sort them into polygons and non-polygons.

Grade 3Polygon or Not a Polygon30 minutes1 class periodPlay-BasedExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Know the polygon rules.
  • ✓Spot straight sides.
  • ✓See why curves and gaps fail.
  • ✓Sort each shape.
Essential Question

A triangle is a polygon but a circle is not, even though both are shapes. What rules let one in and keep the other out?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Sort the Shapes · Interactive

Sort the Shapes

Project this and sort each shape into polygon or not a polygon — tap a shape, then tap where it belongs.

📐 Sort each shape: polygon or not?Try it
✅ Polygon
❌ Not a polygon
Tap a shape, then tap whether it is a polygon (closed, straight sides) or not.
The Lesson · Play-Based Learning (Gather · Explore · Play · Reflect)

30 minutes, five moves

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

1

Hook — What Makes a Polygon

5 min

A triangle is a polygon, but a circle is not. Both are shapes, so what is the rule that lets one in and keeps the other out?

👩‍🏫 Teacher Moves

  • Show a triangle and a circle.
  • Ask what is different.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Sort the Shapes

12 min

Students sort shapes into polygons and non-polygons.

👩‍🏫 Teacher Moves

  • Send students to Sort the Shapes.
  • Drop each one.
  • Explain each choice.

🎒 Student Actions

  • Sort.
  • Say.
  • Explain.
3

Modify — Test the Rules

13 min

Students check a shape against the rules.

👩‍🏫 Teacher Moves

  • Pick a shape.
  • Check: closed, straight sides, no curves.
  • Say polygon or not.

🎒 Student Actions

  • Pick.
  • Check.
  • Say.
4

Create — My Shape Sort

15 min

Students draw and sort.

👩‍🏫 Teacher Moves

  • Draw two polygons.
  • Draw two non-polygons.
  • Label why each belongs.

🎒 Student Actions

  • Draw.
  • Draw.
  • Label.
5

Reflect — The Rules of a Polygon

5 min

Students reflect on polygons.

👩‍🏫 Teacher Moves

  • What three rules make a shape a polygon?
  • Why is a circle not a polygon?
  • 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 (Grade 3).

CCSS
3.G.A.1

Understand that shapes in different categories may share attributes, such as having straight sides.

CCSS
2.G.A.1

Recognize and draw shapes having specified attributes, such as a given number of sides.

CCSS
5.G.B.3

Understand that attributes of a category of figures belong to all figures in that category.

CCSS
MP.7

Look for and make use of structure.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Shape picture cards.
  • Sentence frame: “This shape is ___ because ___ .”
  • Sort two shapes at a time.

Support & Access

IEP / 504
  • Start with a triangle and a circle.
  • Trace the straight sides together.
  • Sort the polygons first.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Add tricky shapes, like a shape with one curved side.
  • Name each polygon by its sides.
  • Explain why straight sides and closure both matter.
Materials

What to gather

  • 📽️Projector / board
  • 🖼️Shape picture cards
  • 💻Sort the Shapes
  • 📐Shape tiles
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

polygona closed shape made of straight sidessideone of the straight line segments of a polygonvertexa corner where two sides meetclosed shapea shape with no gaps or openingscurvea rounded line, which a polygon cannot havetrianglea polygon with three sidesquadrilaterala polygon with four sidesattributea feature of a shape, like sides or corners
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 three rules make a shape a polygon?
It must be closed, made only of straight sides, and have no curves or gaps.
QUESTION 2
Why is a circle not a polygon?
A circle has a curved side and no straight sides, so it breaks the polygon rules.
QUESTION 3
Is an open shape a polygon? Why or why not?
No; a polygon must be fully closed, with no gaps between its sides.

Create: my shape sort.

Have students draw two polygons and two non-polygons and label why each one belongs, so the rules become their own test. A printable polygon 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.

🃏 Polygon or Not a PolygonFlip
Card 1
Term
Tap to flip →
Meaning
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Nice work!

Practice · Quiz

Check your understanding

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

📝 Polygon or Not a PolygonQuiz
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.

🖨️ Polygon or Not a PolygonPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: attribute, closed shape, curve, polygon, quadrilateral, side, triangle, vertex
  1. a shape with no gaps or openings
  2. a rounded line, which a polygon cannot have
  3. a polygon with four sides
  4. a feature of a shape, like sides or corners
  5. a corner where two sides meet
  6. a polygon with three sides
  7. a closed shape made of straight sides
  8. one of the straight line segments of a polygon

Part B · Show what you learned

  1. What three rules make a shape a polygon?
  2. Why is a circle not a polygon?
  3. Is an open shape a polygon? Why or why not?
Answer key — Part A: 1) closed shape · 2) curve · 3) quadrilateral · 4) attribute · 5) vertex · 6) triangle · 7) polygon · 8) side
Part B: 1) It must be closed, made only of straight sides, and have no curves or gaps. 2) A circle has a curved side and no straight sides, so it breaks the polygon rules. 3) No; a polygon must be fully closed, with no gaps between its sides.