Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.4

Lesson 5.65.5 · 5.6 · 5.10 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 5.5 · 5.6 · 5.10 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Volume with Whole-Number EdgesSpanish: Volumen con aristas de números enteros The number of unit cubes inside a rectangular prism. Formula: V = l × w × h. V = l × w × h; 3 × 4 × 5 = 60 cubic units.
VolumeSpanish: Volumen How much space is inside a solid shape. A box 3 × 2 × 4 holds 24 unit cubes, so V = 24 cubic units
Rectangular prismSpanish: Prisma rectangular A solid box shape with six flat rectangle sides. A cereal box or shoe box — it has length, width, and height
Cubic unitsSpanish: Unidades cúbicas The units used to measure space inside, like cubic inches. A tiny cube that is 1 in × 1 in × 1 in = 1 in³ (one cubic inch)
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. unfolded box

How it worksWorked exampledrawing a net from a solid's attributes

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A triangular prism has 2 triangle bases and 3 rectangular side faces. Draw and describe its net.

  1. List the attributes. bases: 2 triangles side faces: 3 rectangles
  2. Draw the 3 rectangles in a row — these wrap around the outside.
  3. Attach 1 triangle to the top edge of the row and 1 to the bottom edge.
  4. Check: five flat pieces, and every folding edge has a partner.

Answer: The net is a row of 3 rectangles with a triangle on the top edge and one on the bottom.

Now you trySame steps, your turn

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

A square pyramid has a square base and 4 triangular faces that meet at one point. Draw its net.

  1. List the attributes. base: square side faces: triangles
  2. Draw the base shape first, near the middle of your page.
  3. Attach one triangular face to each side of the base, folding outward.
  4. Check: total flat pieces Any overlaps?
Answer:sketch and description of the net

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • This solid has faces shaped like .
  • The net needs flat pieces because .
  • I attached each to a side of the .
  • When the net folds up, the meets the .

Word bank netfacefoldunfoldbasepyramidprismcubetrianglesquarerectangletwo-dimensionalthree-dimensional

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.4

Lesson 5.65.5 · 5.6 · 5.10 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 5.5 · 5.6 · 5.10 by using each lesson's big idea in mixed practice.

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

    (Lesson 5.5) What is the volume of a rectangular prism with l = 7 in, w = 3 in, h = 4 in?

    1. A14 in³
    2. B42 in³
    3. C84 in³
    4. D84 in²

    Hint Notice the three edge lengths: l = 7 in, w = 3 in, h = 4 in. Volume asks how much space fills the whole box.

    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.

    (Lesson 5.5) A time capsule box has a volume of 120 cm³. Its length is 10 cm and width is 4 cm. What is its height?

    1. A3 cm
    2. B4 cm
    3. C6 cm
    4. D12 cm

    Hint You already know the volume (120 cm³) and two edges (10 cm and 4 cm). The height is the missing piece.

    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.

    (Lesson 5.6) A rectangular prism has l = 6 in, w = 4 in, h = 2 in. What is its surface area?

    1. A44 in²
    2. B48 in²
    3. C88 in²
    4. D88 in³

    Hint Surface area covers all 6 faces of the 6 × 4 × 2 box — it's not the same as the space inside.

    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.

    (Lesson 5.6) How many faces does a rectangular prism have?

    1. A4
    2. B6
    3. C8
    4. D12

    Hint Picture a cereal box in your hands. Turn it: there's a front, a back, two sides, a top, and a bottom.

    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    (Lesson 5.10) What is the volume of a rectangular prism with l = 4 in, w = 3 in, h = 5 in?

    1. A12 in³
    2. B24 in³
    3. C60 in³
    4. D60 in²

    Hint Spot the three edges: l = 4 in, w = 3 in, h = 5 in. Volume fills the whole box, so all three matter.

    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 ___.

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