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

Lesson 5.6Reading Nets and Solids

Start hereWords, worked example, and sentence starters

Name Date Period

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

Start hereWords for this lesson

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

WordWhat it meansExample
Surface areaSpanish: Área de superficie The total area of all the flat sides of a solid. A box 6 × 4 × 2: SA = 2(24) + 2(12) + 2(8) = 88 in² — like wrapping paper needed
NetSpanish: Plantilla (desarrollo plano) A flat shape that folds up into a solid. unfolded box
FaceSpanish: Cara One flat side of a solid shape. a cube has 6 faces
Two-dimensionalSpanish: Bidimensional A flat shape with length and width, but no thickness. A rectangle drawn on paper is 2D — it has length and width but no depth
EdgeSpanish: Arista The line where two flat sides of a solid meet. a cube has 12 edges
PyramidSpanish: Pirámide A solid with one base and triangular sides that meet at a point. A square base with 4 triangles.

How it worksWorked examplenaming the solid a net makes

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

A net is made of 2 identical triangles and 3 rectangles joined edge to edge. What solid does it fold into?

  1. Count the pieces. triangles: 2 rectangles: 3
  2. Two matching bases mean the solid is a prism, not a pyramid.
  3. The two bases are triangles, so the triangles name the solid.
  4. Fold it in your mind: five faces, nine edges, six vertices.

Answer: The net folds into a triangular prism.

Now you trySame steps, your turn

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

A net is made of 1 square and 4 identical triangles. What solid does it fold into?

  1. Count the pieces. squares: triangles:
  2. Only one base means the solid is a , not a prism.
  3. The base is a , so that shape names the solid.
  4. Fold it in your mind. faces edges vertices
Answer:name of the solid

Say it and write itSentence starters

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

  • The net has pieces shaped like .
  • It folds into a because .
  • The solid has faces, edges, and vertices.
  • I can tell a prism from a pyramid by .

Word bank netfoldfaceedgevertexbaseprismpyramidcubeidenticalsolidname

Watch outA common mistake

A common mistake in Surface Area Using Nets is finding the area of only one face from each of the 3 matching pairs and forgetting to double it, instead of counting all 6 faces. For a box that is 9 in × 4 in × 5 in, a student might add just one face from each pair: (9×4) + (9×5) + (4×5) = 36 + 45 + 20 = 101 in², but the net actually has two of each face, so the correct total is 2(36) + 2(45) + 2(20) = 72 + 90 + 40 = 202 in² — exactly double. Before you submit, ask: 'Did I count both matching faces in each pair, or only one from each pair?'

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

Lesson 5.6Reading Nets and Solids

Apply Day · Version ASupported 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.

  1. 1Complete each step, then write the final answer.
    bottomfrontbacktopleftright3 in1 in3 in

    A box is 3 in long, 3 in wide, and 1 in tall. Find its surface area.

    Show your work

    Hint Find each pair of faces: top and bottom, front and back, left and right.

    Final answer:
  2. 2Complete each step, then write the final answer.

    A cube has edges of 2 cm. Find its surface area.

    Show your work

    Hint A cube has 6 faces, and they are all the same square.

    Final answer:
  3. 3Complete each step, then write the final answer.

    A box is 6 cm long, 2 cm wide, and 2 cm tall. Find its surface area.

    Show your work

    Hint Find the area of each pair of faces. Then add.

    Final answer:
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 5.6Reading Nets and Solids

Apply Day · Version BCore 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.

  1. 1Complete each step, then write the final answer.

    Jin finds the surface area of a box that is 7 cm by 4 cm by 2 cm. He writes 28 + 14 + 8 = 50. Is he right? What is the surface area?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    A box is 4.5 cm long, 2 cm wide, and 3 cm tall. Find its surface area.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    A box is 6 ft long, 5 ft wide, and 3 ft tall. Find its surface area.

    Show your work
    Final answer:
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 5.6Reading Nets and Solids

Apply Day · ChallengeExtension

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.

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

    A net folds into a rectangular prism. How many rectangular faces does that net have?

    1. A4
    2. B6
    3. C8
    4. D12
    Show your work
  2. 2Complete each step, then write the final answer.

    Kim says boxes with the same volume need the same paper. Box A is 3 in × 3 in × 4 in. Box B is 9 in × 4 in × 1 in. Both hold 36 cubic inches. How much more paper does B need?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    A cube has a surface area of 384 square centimeters. How long is each edge?

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help