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

Lesson 5.55.5 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

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. 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.

  1. Name the three dimensions. l = 8 cm w = 6 cm h = 9 cm
  2. Find the base area first — that is one layer of cubes. 8 × 6 = 48
  3. 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.

  1. Name the three dimensions. l = ft w = ft h = ft
  2. Find the base area. × = ft²
  3. 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 5.55.5 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    7 inh = ?4 in
    The base is 7 by 4. The height is unknown.

    A storage box has a volume of 168 cubic inches. It is 7 inches long and 4 inches wide. How tall is it?

    1. 1Find the area of the base.
    2. 2Divide the volume by the base area. How tall is the box?
    3. 3Check by multiplying all three edges.
    Final answer:
  2. 2Complete each step, then write the final answer.
    l = ?4 cm5 cm

    A box has a volume of 180 cubic centimeters. It is 5 cm wide and 4 cm tall. How long is it?

    1. 1Multiply the two edges you know.
    2. 2Divide the volume by 20. How long is the box?
    3. 3Why can you divide by 5 × 4, even if that face is not the bottom?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A box has a base area of 35 square centimeters. Its height is 6 cm. Find its volume.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    A box is 2 ft long, 5 ft wide, and 3 ft tall. You double only the height. What is the new volume?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A raised garden bed is 9 ft long and 3 ft wide. It holds 54 cubic feet of soil. How deep is the soil?

    Show your work
    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    Box A is 8 in by 5 in by 3 in. Box B is 6 in by 4 in by 5 in. Which box holds more?

    1. ABox A
    2. BBox B
    3. CThey hold the same amount
    Show your work

Explain your thinkingVolume = base area × height. Explain why dividing the volume by the base area tells you how many layers tall a box is.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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