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Classifying Shapes: The Family of Quadrilaterals

Fifth graders discover how 2-D shapes fit into a hierarchy — a square is also a rectangle, a rhombus, a parallelogram, and a quadrilateral — learning to classify shapes by their properties.

Grade 5Geometry50 minutes1 class periodGradual ReleaseExplicit 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…

  • ✓Classify quadrilaterals.
  • ✓Understand the shape hierarchy.
  • ✓Explain why a square is a rectangle.
  • ✓Sort shapes by properties.
Essential Question

Is a square also a rectangle? Surprisingly, yes! Shapes belong to families inside families. How do their properties decide where they fit?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Shape Explorer · Interactive

The Shape Explorer

Project this and tap each level. Have students see how shapes fit inside families — all the way down to the special square!

🔺 Explore the family of shapes — tap eachTry 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

Launch — A Square Is a Rectangle?

5 min

Is a square also a rectangle? Believe it or not — yes!

👩‍🏫 Teacher Moves

  • Pose the square-rectangle puzzle.
  • Ask how that’s possible.
  • Set the goal: classifying shapes.

🎒 Student Actions

  • Consider the puzzle.
  • Wonder how.
  • Predict the idea.
2

I Do — Families of Shapes

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Polygons and quadrilaterals.
  • Parallelograms.
  • Rectangle, rhombus, square.

🎒 Student Actions

  • Learn polygons.
  • Learn parallelograms.
  • Learn the special ones.
3

We Do — Explore Together

13 min

Class uses the Shape Explorer.

👩‍🏫 Teacher Moves

  • Tap each level.
  • Explain the properties.
  • Trace the hierarchy.

🎒 Student Actions

  • Tap each level.
  • Explain properties.
  • Trace it.
4

You Do — On Your Own

12 min

Students classify.

👩‍🏫 Teacher Moves

  • Classify quadrilaterals.
  • Explain why a square fits many families.
  • Sort shapes by properties.

🎒 Student Actions

  • Classify them.
  • Explain the square.
  • Sort them.
5

Close — Close

5 min

One shape.

👩‍🏫 Teacher Moves

  • Give a shape to classify.
  • Name all its families.
  • Hand out the exit ticket.

🎒 Student Actions

  • Classify it.
  • Name families.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
5.G.3

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

CCSS
5.G.4

Classify two-dimensional figures in a hierarchy based on properties.

CCSS
5.G.4

Reason about the relationships among quadrilaterals.

SMP
MP.7

Look for and make use of structure (shape hierarchy).

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Shape family diagram.
  • Sentence frame: “A ___ is also a ___.”
  • Sort shape cards.

Support & Access

IEP / 504
  • Start with quadrilateral vs. not.
  • Use a labeled hierarchy.
  • Match shape to name.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Draw a shape hierarchy tree.
  • Explain why a rhombus isn’t always a square.
  • Classify a trapezoid.
Materials

What to gather

  • 📽️Projector / board
  • 📐Shape cards
  • 💻The Shape Explorer
  • 📄A hierarchy diagram
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

polygona closed shape with straight sidesquadrilaterala 4-sided polygonparallelograma quadrilateral with 2 pairs of parallel sidesrectanglea parallelogram with 4 right anglesrhombusa parallelogram with 4 equal sidessquarea rectangle and a rhombushierarchya system of families and subfamiliespropertya feature of a shape
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
Why is a square also a rectangle?
Because a square has 4 right angles (which is what makes a rectangle) — plus 4 equal sides.
QUESTION 2
How many sides does every quadrilateral have?
Four.
QUESTION 3
Is every rectangle a square? Why or why not?
No — a rectangle needs 4 right angles but not 4 equal sides, so only some rectangles (the ones with equal sides) are squares.

Going deeper? Draw the tree.

Have students draw a hierarchy tree showing how quadrilateral, parallelogram, rectangle, rhombus, and square all connect. A printable shape-hierarchy sheet is in the Math 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.

🃏 Classifying 2-D ShapesFlip
Card 1
Term
Tap to flip →
Meaning
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Practice · Quiz

Check your understanding

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

📝 Classifying 2-D ShapesQuiz
Score: 0
1 / 6
Question 1
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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.

🖨️ Classifying 2-D ShapesPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: hierarchy, parallelogram, polygon, property, quadrilateral, rectangle, rhombus, square
  1. a quadrilateral with 2 pairs of parallel sides
  2. a system of families and subfamilies
  3. a feature of a shape
  4. a parallelogram with 4 equal sides
  5. a rectangle and a rhombus
  6. a closed shape with straight sides
  7. a 4-sided polygon
  8. a parallelogram with 4 right angles

Part B · Show what you learned

  1. Why is a square also a rectangle?
  2. How many sides does every quadrilateral have?
  3. Is every rectangle a square? Why or why not?
Answer key — Part A: 1) parallelogram · 2) hierarchy · 3) property · 4) rhombus · 5) square · 6) polygon · 7) quadrilateral · 8) rectangle
Part B: 1) Because a square has 4 right angles (which is what makes a rectangle) — plus 4 equal sides. 2) Four. 3) No — a rectangle needs 4 right angles but not 4 equal sides, so only some rectangles (the ones with equal sides) are squares.