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

Lesson 5.10Volume 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, 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!

RememberVolume of Rectangular Prisms

Volume of Rectangular Prisms with Fractional Edges. Formula: V = l × w × h = B × h Volume is the space inside a rectangular prism. There are two ways to write the same rule. You can multiply all three edges, V = length × width × height. Or you can find the base area first, B = length × width, and then stack that base up the height: V = B × h. Both give the same number, and both work when an edge is a fraction or a decimal.

  1. Convert mixed numbers to improper fractions before multiplying.
  2. Multiply numerators across, multiply denominators across: V = (l · w · h).
  3. Simplify the fraction and label with cubic units

Words: Volume (Volumen)Rectangular prism (Prisma rectangular)Cubic units (Unidades cúbicas)Dimensions (Dimensiones)Base area (Área de la base)

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

    A cube has an edge length of 5 cm. What is its volume?

    1. A15 cm³
    2. B25 cm³
    3. C75 cm³
    4. D125 cm³

    Hint A cube's edges are all equal, so its length, width, and height are each 5 cm.

    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.

    A regular hexagon splits into 6 identical triangles, each with an area of 8 square cm. What is the area of the hexagon?

    1. A8 square cm
    2. B14 square cm
    3. C48 square cm
    4. D48 cm
    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. 3Circle the letter of the best answer. Show how you know.

    A regular pentagon is decomposed into triangles from its centre. How many triangles are there?

    1. A3
    2. B5
    3. C6
    4. D10
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A regular octagon has an area of 96 square inches and splits into 8 identical triangles. What is the area of one triangle?

    1. A8 square inches
    2. B12 square inches
    3. C24 square inches
    4. D768 square 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?
  5. 5Circle the letter of the best answer. Show how you know.

    Why does decomposing a regular polygon into triangles help you find its area?

    1. ATriangles have no area
    2. BEvery triangle's area is easy to find, and the parts add to the whole
    3. CIt turns the polygon into a rectangle
    4. DIt makes the perimeter shorter
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    An aquarium store sells fish tanks. A small tank is 24 inches long, 12 inches wide, and 16 inches tall. One gallon of water takes up about 231 cubic inches. What is the tank's volume?

    1. A52 in³
    2. B576 in³
    3. C4,608 in³
    4. D4,806 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 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
Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.2

Lesson 5.10Volume 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, 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!

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

    Match each box's dimensions to its correct volume.

    1. 2 × 3 × 4
    2. 5 × 2 × 2
    3. 3 × 3 × 3
    4. 6 × 1 × 5
    • A24 cubic in
    • B20 cubic in
    • C27 cubic in
    • D30 cubic in
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    An aquarium store sells fish tanks. A small tank is 24 inches long, 12 inches wide, and 16 inches tall. One gallon of water takes up about 231 cubic inches. About how many gallons does the tank hold?

    1. Aabout 2
    2. Babout 20
    3. Cabout 200
    4. Dabout 231
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    An aquarium store sells fish tanks. A small tank is 24 inches long, 12 inches wide, and 16 inches tall. One gallon of water takes up about 231 cubic inches. Why divide by 231 instead of multiplying?

    1. ABecause dividing always makes numbers smaller
    2. BBecause you are finding how many 231-in³ gallons fit inside the tank
    3. CBecause 231 is bigger than 24
    4. DBecause gallons are bigger than inches
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    A time-capsule box measures 6 in long, 4 in wide, and 3 in tall. What is its volume?

    1. A13 cubic in
    2. B24 cubic in
    3. C72 cubic in
    4. D72 square in
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  4. 5Circle the letter of the best answer. Show how you know.

    Two storage boxes are ready to pack. Box A is 5 × 5 × 2 inches and Box B is 4 × 4 × 3 inches. Which box holds more?

    1. ABox B, because 48 cubic in is more than 50 cubic in
    2. BBox A, because 50 cubic in is more than 48 cubic in
    3. CThey hold the same amount
    4. DBox B, because it is taller
    Show your work
  5. 6Circle the letter of the best answer. Show how you know.

    A keepsake box is 4 in long, 3 in wide, and 1½ in tall. What is its volume?

    1. A8.5 cubic in
    2. B12 cubic in
    3. C18 cubic in
    4. D36 cubic in
    Formula
    Put the numbers in
    Work it out
    Answer with its unit

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

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