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.

Start hereWords for this lesson

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

Word	What it means	Example
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 examplefinding the volume of a rectangular prism

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

A storage box is 8 cm long, 6 cm wide, and 9 cm tall. Find its volume.

Name the three dimensions. l = 8 cm w = 6 cm h = 9 cm
Find the base area first — that is one layer of cubes. 8 × 6 = 48
Stack the layers by multiplying by the height. 48 × 9 = 432

Answer: The volume of the box is 432 cubic centimeters (432 cm³).

Now you trySame steps, your turn

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

A crate is 12 ft long, 7 ft wide, and 10 ft tall. Find its volume.

Name the three dimensions. l = ft w = ft h = ft
Find the base area. × = ft²
Multiply by the height. × = ft³

Answer:volume of the crate

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 outA common mistake

A common mistake in Volume with Whole Number Edges is multiplying only two of the three edges and stopping there — for example, seeing a box that is 6 in long, 4 in wide, and 3 in tall, multiplying just 6 × 4 = 24, and calling that the volume, when 24 is only the area of the bottom face (in square inches), not the volume of the whole box. The height must also be multiplied in: V = 6 × 4 × 3 = 72 cubic inches. A second common mistake is adding the three edges instead of multiplying them (6 + 4 + 3 = 13 instead of 6 × 4 × 3 = 72 cubic inches). Volume always MULTIPLIES all three edges, and the answer is always labeled in cubic units (in³), never square units (in²) or plain units (in).

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

Lesson 5.5Determine the Volume of Rectangular Prisms

Version ASupported practice

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.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Find the volume of each rectangular prism.

Length Width Height Volume
5 in 3 in 4 in
6 cm 6 cm 2 cm
9 ft 2 ft 5 ft

Hint Each row gives a length, width, and height. The empty Volume cell wants one number with cubic units.
Show your work
2Write the name of the correct group on each line.
Put these steps in order for finding the volume of a box that is 8 in long, 5 in wide, and 3 in tall.

Groups:
- Identify: l = 8, w = 5, h = 3
- Write the formula: V = l × w × h
- Multiply: 8 × 5 = 40
- Multiply: 40 × 3 = 120
- Answer: V = 120 in³
Hint Read each step card. One identifies numbers, one writes a formula, two multiply, and one states the answer.

Length	Width	Height
5 in	3 in	4 in
6 cm	6 cm	2 cm
9 ft	2 ft	5 ft

Part 2Apply itreal-world problems

3Circle 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
Hint Notice the three edge lengths: l = 7 in, w = 3 in, h = 4 in. Volume asks how much space fills the whole box.
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?
4Circle 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
Hint You already know the volume (120 cm³) and two edges (10 cm and 4 cm). The height is the missing piece.
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?
5Circle 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 (°)
Hint Re-read each unit and think dimensions: volume fills 3D space — length, width, AND height.
Show your work

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
The Forgotten Height
1. 1DimensionsA time capsule box is 4 long, 3 wide, and 5 tall
2. 2FormulaV = length × width × height
3. 3CalculateV = 4 × 3 = 12 cubic units
4. 4AnswerVolume = 12 cubic units
Which step has the mistake? Explain what went wrong, then show the correct work.

Hint Look at the Calculate step. How many edges did the student multiply?
Correct work
Correct answer:

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 ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

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

Lesson 5.5Determine the Volume of Rectangular Prisms

Version BCore practice

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.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Complete the table. Find the missing dimension or volume for each time capsule.

Capsule Length Width Height Volume
Capsule X 9 in 5 in 2 in
Capsule Y 6 ft 4 ft 168 ft³
Capsule Z 12 cm 5 cm 360 cm³

Show your work
2Use the model to solve. Show your work.

Each section holds how many cubic inches?
Show your work
Answer:
3Write the name of the correct group on each line.
Sort these rectangular prisms from LEAST volume to GREATEST volume.

Groups:
- 3 × 3 × 3
- 10 × 2 × 2
- 5 × 4 × 3
- 6 × 6 × 2
- 8 × 5 × 4

Capsule	Length	Width	Height	Volume
Capsule X	9 in	5 in	2 in
Capsule Y	6 ft	4 ft		168 ft³
Capsule Z	12 cm		5 cm	360 cm³

Part 2Apply itreal-world problems

4Circle the letter of the best answer. Show how you know.
Two storage bins: Bin A is 8 × 6 × 5 inches. Bin B is 9 × 4 × 7 inches. Which holds more and by how much?
1. ABin B by 12 in³
2. BBin A by 12 in³
3. CBin B by 24 in³
4. DThey hold the same
Show your work
5Circle the letter of the best answer. Show how you know.
A rectangular prism has length 8 cm, width 5 cm, and height 4 cm. What is its volume?
1. A17 cm³
2. B80 cm³
3. C120 cm³
4. D160 cm³
Formula

Put the numbers in

Work it out

Answer with its unit

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
Added the Last Edge
1. 1DimensionsA capsule is 6 long, 5 wide, and 3 tall
2. 2FormulaV = length × width × height
3. 3CalculateV = 6 × 5 + 3 = 33 cubic units
4. 4AnswerVolume = 33 cubic units
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:

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?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

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

Lesson 5.5Determine the Volume of Rectangular Prisms

ChallengeExtension

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.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

If you double ONE dimension of a 3 × 4 × 5 box, how does the volume change?

Change New Dimensions New Volume How did it change?
Double the length 6 × 4 × 5
Double the width 3 × 8 × 5
Double the height 3 × 4 × 10

Show your work

Change	New Dimensions	New Volume	How did it change?
Double the length	6 × 4 × 5
Double the width	3 × 8 × 5
Double the height	3 × 4 × 10

Part 2Apply itreal-world problems

2Circle the letter of the best answer. Show how you know.
A shipping crate is 12 ft long, 3 ft wide, and 2 ft tall. How many 1-foot cubes exactly fill it?
1. A17 cubes
2. B36 cubes
3. C72 cubes
4. D144 cubes
Show your work
3Circle the letter of the best answer. Show how you know.
Two prisms have the same volume of 48 cm³. Prism A is 4 × 4 × 3. Prism B is 8 × 3 × h. What is h?
1. A2 cm
2. B3 cm
3. C4 cm
4. D6 cm
Formula

Put the numbers in

Work it out

Answer with its unit

Part 3Explain and correctreasoning

4Find the mistake. Explain it, then show the correct work.
Find the Volume Error
1. 1Dimensionsl = 9 ft, w = 4 ft, h = 6 ft
2. 2FormulaV = l × w × h
3. 3CalculateV = 9 × 4 × 6 = 9 × 10 = 90 ft³
4. 4AnswerVolume = 90 ft³
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:
5Answer in complete sentences.

A box needs to hold exactly 60 cubic inches. Give three different sets of whole-number dimensions that work. Which set would make the box closest to a cube shape? Why might that matter?
Write your answer

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?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help