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

Lesson 5.5Determine the Volume of Rectangular Prisms

Set B · Version ASecond form · supported 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.

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?

RememberDetermine the Volume of Rectangular Prisms

Volume of Rectangular Prisms (Whole Numbers). Formula: V = Length × Width × Height = Base Area × Height (V = l · w · h = B · h) Volume is how much space is inside a 3D shape. For a rectangular prism (a box), volume = length × width × height, measured in cubic units.

  1. Identify the length, width, and height of the box.
  2. Multiply base area (l × w) by height (h).
  3. Label answer in cubic units (e.g. in³, cm³, ft³)

Words: Volume (Volumen)Rectangular prism (Prisma rectangular)Cubic units (Unidades cúbicas)Length, width, height (Largo, ancho, altura)Net (Plantilla (desarrollo plano))

  1. 1Circle the letter of the best answer. Show how you know.

    A box has a volume of 72 in³. Its base is 6 in by 4 in. What is its height?

    1. A2 in
    2. B3 in
    3. C12 in
    4. D18 in

    Hint You know the volume (72 in³) and the base (6 in by 4 in). Only the height is unknown.

    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. 2Circle the letter of the best answer. Show how you know.

    To find the area of a composite figure, you first…

    1. Ameasure around the outside
    2. Bmultiply all the side lengths
    3. Cfind the longest side
    4. Dbreak it into basic shapes you know
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    A figure is a 6 by 4 rectangle with a 2 by 3 rectangle attached. What is the total area?

    1. A15 square units
    2. B24 square units
    3. C30 square units
    4. D144 square units
    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?
  4. 4Circle the letter of the best answer. Show how you know.

    A 10 by 8 rectangular garden has a 3 by 3 square patio cut out of it. What area is left?

    1. A62 square units
    2. B71 square units
    3. C80 square units
    4. D89 square units
    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?
  5. 5Circle the letter of the best answer. Show how you know.

    A shape is made of a 5 by 4 rectangle joined to a triangle with base 5 and height 4. What is the total area?

    1. A20 square units
    2. B25 square units
    3. C30 square units
    4. D40 square units
    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?
  6. 6Circle the letter of the best answer. Show how you know.

    A moving company uses rectangular boxes. A large box is 24 inches long, 18 inches wide, and 18 inches tall. A medium box is 18 inches long, 14 inches wide, and 12 inches tall. What is the volume of the large box?

    1. A60 in³
    2. B3,024 in³
    3. C4,752 in³
    4. D7,776 in³
    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?

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

Lesson 5.5Determine the Volume of Rectangular Prisms

Set B · Version BSecond form · core 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.

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?

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each capsule's dimensions to its volume. Use V = length × width × height.

    1. 7 × 2 × 3
    2. 6 × 5 × 2
    3. 9 × 4 × 2
    4. 5 × 3 × 2
    • A42 cubic units
    • B60 cubic units
    • C72 cubic units
    • D30 cubic units
  2. 2Write the name of the correct group on each line.

    A capsule is filled with unit cubes. Sort each statement by whether it describes COUNTING cubes by layers or finding volume with the FORMULA.

    Groups: Counting Cubes by Layers Using the Volume Formula
    • Count 4 layers of 6 cubes each
    • Add up the cubes in every layer
    • Stack layers until the box is full, then count
    • Use V = length × width × height
    • Multiply the three edge lengths together
    • Compute 6 × 5 × 2 = 60 cubic units
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A moving company uses rectangular boxes. A large box is 24 inches long, 18 inches wide, and 18 inches tall. A medium box is 18 inches long, 14 inches wide, and 12 inches tall. What is the volume of the medium box?

    1. A2,520 in³
    2. B3,024 in³
    3. C3,240 in³
    4. D4,752 in³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 4Circle the letter of the best answer. Show how you know.

    A moving company uses rectangular boxes. A large box is 24 inches long, 18 inches wide, and 18 inches tall. A medium box is 18 inches long, 14 inches wide, and 12 inches tall. How many more cubic inches does the large box hold?

    1. A1,728 in³
    2. B3,024 in³
    3. C4,752 in³
    4. D10,800 in³
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    A time capsule box is 5 units long, 3 units wide, and 2 units tall. How many unit cubes fill it?

    1. A10 cubic units
    2. B15 cubic units
    3. C25 cubic units
    4. D30 cubic units
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    You stack unit cubes in a capsule: each layer has 6 cubes, and there are 4 layers. What is the volume?

    1. A10 cubic units
    2. B12 cubic units
    3. C18 cubic units
    4. D24 cubic units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit

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?

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