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

Lesson 5.105.10 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, including ones with fractional edge lengths, using base area × 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. 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.

A jewelry box is 21/2 in long, 2 in wide, and 11/2 in tall. Find its volume.

  1. Write each mixed number as a fraction: 21/2 = 5/2; 11/2 = 3/2
  2. Find the base area: 5/2 × 2 = 5
  3. Multiply by the height: 5 × 3/2 = 15/2
  4. Write the answer as a mixed number: 15/2 = 71/2
  5. Check by packing cubes with 1/2-inch edges: 5 × 4 × 3 = 60; 60 × 1/8 = 71/2
  6. The volume is 71/2 cubic inches.

Now you trySame steps, your turn

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

A box is 4 units long, 2 units wide, and 0.5 units tall. Use the base area to find its volume.

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 5.105.10 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, including ones with fractional edge lengths, using base area × 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.
    112 in212 in4 in
    Two edges are mixed numbers.

    A box is 1 1/2 in long, 4 in wide, and 2 1/2 in tall. Find its volume.

    1. 1Write each mixed number as a fraction.
    2. 2What is the base area, 3/2 × 4?
    3. 3Multiply by the height, 5/2. What is the volume?
    Final answer:
  2. 2Complete each step, then write the final answer.
    34 ft2 ft12 ft

    A box is 3/4 ft long, 1/2 ft wide, and 2 ft tall. Find its volume. Then check it with cubes that have 1/4 ft edges.

    1. 1What is the base area, 3/4 × 1/2?
    2. 2Multiply by the height. What is the volume?
    3. 3How many 1/4 ft cubes fit? Use 3 × 2 × 8.
    4. 4Why do 48 small cubes give the same volume?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A box is 2 1/4 in long, 2 in wide, and 4 in tall. Find its volume.

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

    A box has a volume of 10 1/2 cubic feet. Its base is 3 ft by 2 ft. How tall is the box?

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

    A planter box is 4 1/2 ft long, 2/3 ft wide, and 1 1/2 ft tall. How much soil fills it?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Raj rounds a box that is 2 1/2 cm by 1 1/2 cm by 4 cm to 3 × 2 × 4 = 24. What is the real volume?

    Show your work
    Final answer:

Explain your thinkingWhy does V = B × h still work when the height is a fraction? Use layers of cubes to explain.

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