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Volume of Rectangular Prisms

Fifth graders learn to measure the space inside a box-shaped solid, first by counting unit cubes and then by multiplying length, width, and height.

Grade 5Volume of Rectangular Prisms50 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…

  • ✓Define volume.
  • ✓Use cubic units.
  • ✓Apply V = l × w × h.
  • ✓Find a prism's volume.
Essential Question

A moving box, a fish tank, a shipping container: all hold a certain amount. How do we measure the space inside a three-dimensional shape?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

Volume Check

Project this and answer each question about finding the volume of rectangular prisms — read the explanation after each one.

📦 Check what you know about volumeTry it
Answer each question about the volume of rectangular prisms.
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 — How Many Boxes Fit?

5 min

How many small cubes would it take to completely fill this box?

👩‍🏫 Teacher Moves

  • Show a cube-filled box.
  • Ask how to count them.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Volume Check

12 min

Students answer questions about finding volume.

👩‍🏫 Teacher Moves

  • Send students to the Volume Check.
  • Answer each question.
  • Read the why.

🎒 Student Actions

  • Answer.
  • Check.
  • Read it.
3

Modify — Count and Multiply

13 min

Students find volume two ways.

👩‍🏫 Teacher Moves

  • Count the unit cubes.
  • Multiply l × w × h.
  • See they match.

🎒 Student Actions

  • Count.
  • Multiply.
  • Check.
4

Create — Design a Box

15 min

Students build a box to a target volume.

👩‍🏫 Teacher Moves

  • Pick a volume, like 24 cubic cm.
  • Choose l, w, h that fit.
  • Show the multiplication.

🎒 Student Actions

  • Pick.
  • Choose.
  • Show.
5

Reflect — Space Inside

5 min

Students reflect on volume vs area.

👩‍🏫 Teacher Moves

  • Why cubic units?
  • How is volume different from area?
  • 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
5.MD.C.3

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

CCSS
5.MD.C.4

Measure volumes by counting unit cubes.

CCSS
5.MD.C.5

Relate volume to multiplication and apply V = l × w × h and V = b × h.

CCSS
MP.5

Use appropriate tools strategically.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Unit-cube picture cards.
  • Sentence frame: “Volume is ___ × ___ × ___ .”
  • Count one layer at a time.

Support & Access

IEP / 504
  • Start by counting cubes.
  • Build prisms with linking cubes.
  • Multiply only after counting matches.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Find a missing dimension from the volume.
  • Add volumes of two joined prisms.
  • Compare prisms with equal volume, different shape.
Materials

What to gather

  • 📽️Projector / board
  • 🧊Unit / linking cubes
  • 💻Volume Check
  • 📦Empty boxes
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

volumethe amount of space inside a solid figurerectangular prisma box-shaped solid with six rectangular facescubic unita cube one unit long on each edge, used to measure volumelengthhow long a solid iswidthhow wide a solid isheighthow tall a solid isunit cubea cube measuring one unit on every sidefaceone flat surface of a solid figure
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 does volume measure, and what units is it in?
The space inside a solid, measured in cubic units (like cubic cm).
QUESTION 2
What is the formula for the volume of a rectangular prism?
Volume = length × width × height (V = l × w × h).
QUESTION 3
A prism is 5 by 2 by 3 units. What is its volume?
30 cubic units, because 5 × 2 × 3 = 30.

Create: design a box.

Have students choose a target volume (like 24 cubic cm), pick length, width, and height that multiply to it, and show the calculation. A printable volume 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.

🃏 Volume of Rectangular PrismsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

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

📝 Volume of Rectangular PrismsQuiz
Score: 0
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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.

🖨️ Volume of Rectangular PrismsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: cubic unit, face, height, length, rectangular prism, unit cube, volume, width
  1. how long a solid is
  2. how wide a solid is
  3. a cube measuring one unit on every side
  4. one flat surface of a solid figure
  5. a cube one unit long on each edge, used to measure volume
  6. how tall a solid is
  7. the amount of space inside a solid figure
  8. a box-shaped solid with six rectangular faces

Part B · Show what you learned

  1. What does volume measure, and what units is it in?
  2. What is the formula for the volume of a rectangular prism?
  3. A prism is 5 by 2 by 3 units. What is its volume?
Answer key — Part A: 1) length · 2) width · 3) unit cube · 4) face · 5) cubic unit · 6) height · 7) volume · 8) rectangular prism
Part B: 1) The space inside a solid, measured in cubic units (like cubic cm). 2) Volume = length × width × height (V = l × w × h). 3) 30 cubic units, because 5 × 2 × 3 = 30.