Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.2

Lesson 5.5Determine the Volume of Rectangular Prisms

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the volume of a rectangular prism with whole-number edges using length × width × height.

Why This Matters Your team is building time capsule containers to store class memories. Each container is a rectangular prism, and you need to figure out how much each one can hold. That means calculating the volume using whole number dimensions! Container A is 5 inches long, 3 inches wide, and 4 inches tall. How much can it hold?

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
VolumeSpanish: Volumen How much space is inside a solid shape. V = l × w × h
Rectangular prismSpanish: Prisma rectangular A solid box shape with six flat rectangle sides. a cereal box
Cubic unitsSpanish: Unidades cúbicas The units used to measure space inside, like cubic inches. cm³, in³, ft³
Length, width, heightSpanish: Largo, ancho, altura How long, how wide, and how tall a box is. V = l × w × h: for a box 5 × 3 × 2, volume = 30 cubic units
NetSpanish: Plantilla (desarrollo plano) A flat shape that folds up into a solid. A cross-shaped pattern of 6 rectangles folds into a rectangular box
EdgeSpanish: Arista The line where two flat sides of a solid meet. A cube has 12 edges — 4 along the top, 4 along the bottom, 4 vertical

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A box is 6 cm long, 3 cm wide, and 4 cm tall.

  1. One layer: 6 × 3 = 18 cubes.
  2. 4 layers stack up.
  3. 18 × 4 = 72.

Answer: V = 72 cm³

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Now a smaller box: 5 long, 2 wide, 2 tall. What formula do we use?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The length is , the width is , and the height is .
  • The base area is × = square units.
  • The volume is cubic units.
  • I used cubic units instead of square units because .

Word bank volumerectangular prismlengthwidthheightbase arealayerunit cubecubic unitsmultiplysolidface

Watch out!A common mistake

A common mistake in Volume with Whole Number Edges is multiplying only two of the three edges and stopping there

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.2

Lesson 5.5Determine the Volume of Rectangular Prisms

Level 0Most support · every hint printed

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the volume of a rectangular prism with whole-number edges using length × width × height.

Why This Matters Your team is building time capsule containers to store class memories. Each container is a rectangular prism, and you need to figure out how much each one can hold. That means calculating the volume using whole number dimensions! Container A is 5 inches long, 3 inches wide, and 4 inches tall. How much can it hold?

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A box is 6 cm long, 3 cm wide, and 4 cm tall.

  1. One layer: 6 × 3 = 18 cubes.
  2. 4 layers stack up.
  3. 18 × 4 = 72.

Answer: V = 72 cm³

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Find the volume of each rectangular prism.

    LengthWidthHeightVolume
    5 in3 in4 in
    6 cm6 cm2 cm
    9 ft2 ft5 ft
    Steps to try
    1. Each row gives a length, width, and height. The empty Volume cell wants one number with cubic units.
    2. For each row use V = l × w × h: multiply the first two numbers, then multiply by the third.
    3. Row 1: multiply 5 × 3 = 15 first, then multiply by the height, 4. Don't forget in³ in your answer.
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    What is the volume of a rectangular prism with l = 7 in, w = 3 in, h = 4 in?

    1. A14 in³
    2. B42 in³
    3. C84 in³
    4. D84 in²
    Steps to try
    1. Notice the three edge lengths: l = 7 in, w = 3 in, h = 4 in. Volume asks how much space fills the whole box.
    2. Use the volume formula V = l × w × h, and remember volume is measured in cubic units (in³).
    3. Start with 7 × 3 = 21 for the base, then multiply that result by the height, 4 inches.
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  2. 3Circle the letter of the best answer. Show how you know.

    A time capsule box has a volume of 120 cm³. Its length is 10 cm and width is 4 cm. What is its height?

    1. A3 cm
    2. B4 cm
    3. C6 cm
    4. D12 cm
    Steps to try
    1. You already know the volume (120 cm³) and two edges (10 cm and 4 cm). The height is the missing piece.
    2. Work backward: since V = l × w × h, divide the volume by the base area (length × width) to find the height.
    3. First find the base area: 10 × 4 = 40 cm². Then figure out what number times 40 gives 120.
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  3. 4Circle the letter of the best answer. Show how you know.

    Which unit is used for volume?

    1. ASquare inches (in²)
    2. BCubic inches (in³)
    3. CInches (in)
    4. DDegrees (°)
    Steps to try
    1. Re-read each unit and think dimensions: volume fills 3D space — length, width, AND height.
    2. Match the exponent to the dimensions: 2D area uses square units (²), so 3D volume needs one more dimension.
    3. Picture stacking little cubes inside a box. Each cube is 1 in × 1 in × 1 in — which unit describes a cube like that?
    Show your work

Explain your thinkingContainer C holds the most (96 in³) and Container B holds the least (50 in³). What do you notice about the dimensions that make one volume larger than another?

Sentence starter Container C has the largest volume because ___ × ___ × ___ = ___. Compared to Container B, the dimensions ___ produce a ___ volume because ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help