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

Lesson 5.6Represent Three-Dimensional Figures in Two Dimensions

Set B · Version ASecond form · supported practice

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

Learning target I can find the surface area of a solid by using its net.

Why This Matters Your class is designing custom wrapping paper for time capsule boxes. To figure out how much paper you need, you have to find the total surface area of each box. The trick? Unfold the box into a net so you can see every face laid flat! One time capsule box is 6 inches long, 4 inches wide, and 2 inches tall. How much wrapping paper covers the whole box?

RememberRepresent Three-Dimensional Figures in Two Dimensions

Representing 3D Solids with Nets Surface area is the total area of all the flat faces of a solid. A net unfolds the box flat so you can see and add all 6 faces. The answer uses square units.

  1. A net is a 2D flat pattern that folds into a 3D solid without overlapping.
  2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs.
  3. Surface Area is the total sum of the areas of all flat faces on the net

Words: Surface area (Área de superficie)Net (Plantilla (desarrollo plano))Face (Cara)Two-dimensional (Bidimensional)Edge (Arista)

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

    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 in²
    4. D60 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?
  2. 2Circle the letter of the best answer. Show how you know.

    A box has a base area of 12 square cm and a height of 3 cm. What is its volume?

    1. A4 cm³
    2. B15 cm³
    3. C36 cm³
    4. D36 cm²
    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 box has a volume of 36 cm³. Its length is 6 cm and width is 3 cm. What is the height?

    1. A2 cm
    2. B3 cm
    3. C6 cm
    4. D12 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?
  4. 4Circle the letter of the best answer. Show how you know.

    How is volume different from area?

    1. AVolume uses cubic units; area uses square units
    2. BVolume uses square units; area uses cubic units
    3. CVolume only applies to cubes; area applies to all shapes
    4. DThere is no difference
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A gift shop wraps boxes with decorative paper. A box is 14 inches long, 10 inches wide, and 6 inches tall. One sheet of wrapping paper covers 400 square inches. What is the surface area of the box?

    1. A280 in²
    2. B284 in²
    3. C568 in²
    4. D840 in²
    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?
  6. 6Circle the letter of the best answer. Show how you know.

    A gift shop wraps boxes with decorative paper. A box is 14 inches long, 10 inches wide, and 6 inches tall. One sheet of wrapping paper covers 400 square inches. Why is each face pair multiplied by 2?

    1. AA rectangular box has two identical faces of each size
    2. BBecause you always double in geometry
    3. CBecause there are 2 sheets of paper
    4. DTo convert to square inches
    Show your work

Explain your thinkingThe total surface area is 158 in². Which face pair contributes the most area? Why does that make sense when you look at the dimensions?

Sentence starter The ___ faces contribute the most area (___ in²) because their dimensions ___ × ___ = ___ are the largest. The total SA is ___ + ___ + ___ = ___ in².

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.4

Lesson 5.6Represent Three-Dimensional Figures in Two Dimensions

Set B · Version BSecond form · core practice

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

Learning target I can find the surface area of a solid by using its net.

Why This Matters Your class is designing custom wrapping paper for time capsule boxes. To figure out how much paper you need, you have to find the total surface area of each box. The trick? Unfold the box into a net so you can see every face laid flat! One time capsule box is 6 inches long, 4 inches wide, and 2 inches tall. How much wrapping paper covers the whole box?

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

    Match each solid to the net it folds up from.

    1. Cube
    2. Rectangular prism
    3. Triangular prism
    4. Square pyramid
    5. Faces on any rectangular prism
    6. Square units (in², cm²)
    • ANet of 6 equal squares
    • BNet of 6 rectangles (3 matching pairs)
    • CNet of 2 triangles and 3 rectangles
    • DNet of 1 square and 4 triangles
    • E6 faces
    • FHow surface area is measured
  2. 2Write the name of the correct group on each line.

    Sort each flat shape: is it a valid net that folds into a closed time capsule box, or not a complete net?

    Groups: Valid net (folds into a closed box) Not a complete net
    • Six rectangles arranged in a cross shape
    • Six rectangles in a T shape (3 matching pairs)
    • Four rectangles in a straight row (top and bottom missing)
    • A single rectangle by itself
    • Two squares and four rectangles for a box
    • Seven rectangles (one extra face)
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A gift shop wraps boxes with decorative paper. A box is 14 inches long, 10 inches wide, and 6 inches tall. One sheet of wrapping paper covers 400 square inches. How many sheets of wrapping paper do you need?

    1. A1
    2. B2
    3. C3
    4. D568
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    You unfold a time capsule that is a cube. Its net shows 6 equal squares, and each square has an area of 4 cm². What is the cube's total surface area?

    1. A10 cm²
    2. B12 cm²
    3. C16 cm²
    4. D24 cm²
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 5Circle the letter of the best answer. Show how you know.

    Your team unfolds a rectangular time capsule box into a flat net. How many faces (flat sides) will the net show in all?

    1. A4
    2. B5
    3. C6
    4. D8
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    A time capsule box measures 2 in × 3 in × 4 in. Using its net, you add up all six faces. What is the total surface area?

    1. A24 in²
    2. B26 in²
    3. C48 in²
    4. D52 in²
    Formula
    Put the numbers in
    Work it out
    Answer with its unit

Explain your thinkingThe total surface area is 158 in². Which face pair contributes the most area? Why does that make sense when you look at the dimensions?

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