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.

Why This Matters Your class is building a time capsule to bury on school grounds. The capsule is a rectangular prism that is 2 feet long, 1.5 feet wide, and 1 foot tall. You need to figure out how much stuff can fit inside — that means calculating the volume!

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. 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.

  1. I put in the numbers: V = 2 × 1.5 × 1.
  2. First I multiply 2 × 1.5 = 3.
  3. Then 3 × 1 = 3.
  4. 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 out!A 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

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

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

Why This Matters Your class is building a time capsule to bury on school grounds. The capsule is a rectangular prism that is 2 feet long, 1.5 feet wide, and 1 foot tall. You need to figure out how much stuff can fit inside — that means calculating the volume!

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.

  1. I put in the numbers: V = 2 × 1.5 × 1.
  2. First I multiply 2 × 1.5 = 3.
  3. Then 3 × 1 = 3.
  4. So the volume is 3 ft³. A fractional edge like 1.5 did not change my steps at all.
Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Find the volume of each rectangular prism.

    LengthWidthHeightVolume
    8 in5 in2 in
    4 cm4 cm4 cm
    10 ft3 ft6 ft
    Steps to try
    1. Each row lists a length, width, and height. The blank Volume cell needs a number with cubic units.
    2. For every row use V = l × w × h: multiply the first two numbers, then multiply by the third.
    3. Row 1: multiply 8 × 5 = 40 first, then multiply by the height, 2. Include 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 = 4 in, w = 3 in, h = 5 in?

    1. A12 in³
    2. B24 in³
    3. C60 in³
    4. D60 in²
    Steps to try
    1. Spot the three edges: l = 4 in, w = 3 in, h = 5 in. Volume fills the whole box, so all three matter.
    2. Use V = l × w × h and remember the answer needs cubic units (in³), not square units.
    3. Multiply 4 × 3 = 12 for the base, then multiply that result by the height, 5 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 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
    Steps to try
    1. You're given the volume (36 cm³) plus two edges (6 cm and 3 cm). The height is what's missing.
    2. Work backward: divide the volume by the base area (length × width) to uncover the height.
    3. Find the base area first: 6 × 3 = 18 cm². Then ask what number times 18 gives 36.
    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.

    How is volume different from area?

    1. AVolume uses cubic units; area uses 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
    Steps to try
    1. Think dimensions: area covers a flat 2D surface, while volume fills a 3D space.
    2. Match each measurement to its unit: flat surfaces get square units (²), filled space gets cubic units (³).
    3. Picture a rug (flat) versus a fish tank (filled). Decide which is area and which is volume, then check each choice.
    Show your work

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 ___.

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