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.

Why This Matters This is your challenge small group for Lesson 5.10. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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 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 5.105.10 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.

Why This Matters This is your challenge small group for Lesson 5.10. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  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.

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