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

Lesson 5.10Volume of Rectangular Prisms

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the volume of a rectangular prism, including ones with fractional edge lengths, using base area × 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.	A box 2 × 1.5 × 1 = 3 ft³ — it holds 3 cubic feet of stuff
Rectangular prismSpanish: Prisma rectangular	A solid box shape with six flat rectangle sides.	A tissue box, a fish tank, a brick — all rectangular prisms
Cubic unitsSpanish: Unidades cúbicas	The units used to measure space inside, like cubic inches.	1 ft³ = a cube that is 1 foot on every edge
DimensionsSpanish: Dimensiones	How long, how wide, and how tall a shape is.	A box with dimensions 4 × 3 × 2 means l = 4, w = 3, h = 2
Base areaSpanish: Área de la base	The area of the bottom of a solid. Volume = base area × height.	If the base is 6 × 4 = 24 cm² and h = 3, then V = 24 × 3 = 72 cm³

How it worksWorked example

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

My capsule is 2 ft long, 1.5 ft wide, and 1 ft tall. I write V = length × width × height.

I put in the numbers: V = 2 × 1.5 × 1.
First I multiply 2 × 1.5 = 3.
Then 3 × 1 = 3.
So the volume is 3 ft³. A fractional edge like 1.5 did not change my steps at all.

Now you trySame steps, your turn

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

Now try a box that is 4 long, 2 wide, and 0.5 tall. Let's do it the base-area way. What is the base, 4 × 2?

Answer:

Say it and write itSentence starters

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

Capsules A and B both have V = because × × = × × . I'd choose because .

Word bank VolumeRectangular prismCubic unitsDimensionsBase area3volumesamedifferentdimensionsshapelength

Watch outA common mistake

A common mistake in Volume of Rectangular Prisms is rounding a fractional edge length to the nearest whole number before multiplying, instead of using the exact fraction or decimal. For a box that is 2 ft × 1.5 ft × 1 ft, a student might round 1.5 down to 1 and compute 2 × 1 × 1 = 2 ft³, but the correct volume uses the exact edge length: 2 × 1.5 × 1 = 3 ft³ — a full cubic foot larger. Before you submit, ask: 'Did I multiply using the exact fractional or decimal edge length, or did I round it off first?'

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

Lesson 5.10Volume 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, including ones with fractional edge lengths, using base area × 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
8 in 5 in 2 in
4 cm 4 cm 4 cm
10 ft 3 ft 6 ft

Hint Each row lists a length, width, and height. The blank Volume cell needs a number with cubic units.
Show your work
2Write the name of the correct group on each line.
Sort these boxes from SMALLEST volume to LARGEST volume.

Groups:
- 4 × 4 × 4
- 10 × 2 × 3
- 6 × 5 × 3
- 2 × 2 × 5
- 7 × 3 × 4
Hint Each card gives a box's three measurements. Multiply all three to get its volume, then sort by that total.

Length	Width	Height
8 in	5 in	2 in
4 cm	4 cm	4 cm
10 ft	3 ft	6 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 = 4 in, w = 3 in, h = 5 in?
1. A12 in³
2. B24 in³
3. C60 in³
4. D60 in²
Hint Spot the three edges: l = 4 in, w = 3 in, h = 5 in. Volume fills the whole box, so all three matter.
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 box has a volume of 36 cm³. Its length is 6 cm and width is 3 cm. What is the height?
1. A2 cm
2. B3 cm
3. C6 cm
4. D12 cm
Hint You're given the volume (36 cm³) plus two edges (6 cm and 3 cm). The height is what's missing.
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.
How is volume different from area?
1. AVolume measures 3D space (cubic units); area measures 2D surface (square units)
2. BVolume uses square units; area uses cubic units
3. CVolume only applies to cubes; area applies to all shapes
4. DThere is no difference
Hint Think dimensions: area covers a flat 2D surface, while volume fills a 3D space.
Show your work

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
1. 1DimensionsA box is 5 in long, 4 in wide, and 2 in tall.
2. 2FormulaV = length × width × height
3. 3CalculateV = 5 + 4 + 2 = 11 cubic in
4. 4AnswerVolume = 11 cubic in
Which step has the mistake? Explain what went wrong, then show the correct work.

Hint Check Step 3: should you add the dimensions or multiply them?
Correct work
Correct answer:

Explain your thinkingCapsules A and B have the same volume (3 ft³) but different dimensions. Why? Which design would you choose and why?

Sentence starter Capsules A and B both have V = ___ because ___ × ___ × ___ = ___ × ___ × ___. I'd choose ___ 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 5.10Volume 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, including ones with fractional edge lengths, using base area × height.

Part 1Understand the ideamodels and meaning

1Use the model to solve. Show your work.

The container is half full. How many cubic feet of space are left?
Show your work
Answer:
2Complete the table. Show how you found each value.

Find the missing dimension or volume for each container.

Container Length Width Height Volume
Box A 12 in 5 in 3 in
Box B 7 cm 4 cm 168 cm³
Box C 8 ft 5 ft 240 ft³

Show your work
3Write the name of the correct group on each line.
A pool is 12 ft × 8 ft × 5 ft. Sort the statements from FALSE to TRUE.

Groups:
- The pool volume is 96 ft³
- The pool holds 400 ft³
- The pool volume is 480 ft³
- V = 12 × 8 × 5

Container	Length	Width	Height	Volume
Box A	12 in	5 in	3 in
Box B	7 cm		4 cm	168 cm³
Box C		8 ft	5 ft	240 ft³

Part 2Apply itreal-world problems

4Circle the letter of the best answer. Show how you know.
Two boxes: Box A is 10 × 5 × 4 inches. Box B is 8 × 6 × 5 inches. Which has more volume and by how much?
1. ABox B by 40 in³
2. BBox A by 40 in³
3. CBox B by 60 in³
4. DThey're equal
Show your work
5Circle the letter of the best answer. Show how you know.
What is the volume of a prism with edge lengths 1/2 m, 3 m, and 4 m?
1. A3 m³
2. B6 m³
3. C7.5 m³
4. D12 m³
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.
Spot the Common Mistake
1. 1DimensionsA box is 6 in long, 4 in wide, and 1/2 in tall.
2. 2FormulaV = length × width × height
3. 3CalculateV = 6 × 4 × 1/2, and the student dropped the 1/2: V = 6 × 4 = 24 cubic in
4. 4AnswerVolume = 24 cubic in
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:

Explain your thinkingCapsules A and B have the same volume (3 ft³) but different dimensions. Why? Which design would you choose and why?

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 5.10Volume 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, including ones with fractional edge lengths, using base area × height.

Part 1Understand the ideamodels and meaning

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

Two L-shaped containers are each made from two rectangular prisms joined together. Find the total volume of each.

Container Prism 1 Dimensions Prism 2 Dimensions Total Volume
L-shape A 6 × 4 × 3 6 × 2 × 3
L-shape B 10 × 5 × 2 4 × 5 × 4

Show your work

Container	Prism 1 Dimensions	Prism 2 Dimensions	Total Volume
L-shape A	6 × 4 × 3	6 × 2 × 3
L-shape B	10 × 5 × 2	4 × 5 × 4

Part 2Apply itreal-world problems

2Circle the letter of the best answer. Show how you know.
A fish tank measures 2 1/2 ft by 2 ft by 3 ft. What is its volume?
1. A7.5 ft³
2. B12 ft³
3. C15 ft³
4. D30 ft³
Formula

Put the numbers in

Work it out

Answer with its unit
3Circle the letter of the best answer. Show how you know.
A prism with a 3/4 ft by 2 ft base has a volume of 9 ft³. What is its height?
1. A4 ft
2. B6 ft
3. C9 ft
4. D12 ft
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 = 5 m, w = 3 m, h = 2.5 m
2. 2FormulaV = l × w × h
3. 3CalculateV = 5 × 3 × 2.5 = 5 × 5.5 = 27.5 m³
4. 4AnswerVolume = 27.5 m³
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:
5Answer in complete sentences.

A toy company ships action figures in boxes that are 4 × 3 × 6 inches. A shipping crate is 24 × 12 × 18 inches. How many action figure boxes fit in the crate? Explain your reasoning step by step.
Write your answer

Explain your thinkingCapsules A and B have the same volume (3 ft³) but different dimensions. Why? Which design would you choose and why?

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