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

Lesson 5.65.6 Small Group · Group 2

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, 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
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 net on paper
EdgeSpanish: Arista The line where two flat sides of a solid meet. A cube has 12 edges — the lines where two flat faces connect
PyramidSpanish: Pirámide A solid with one base and triangular sides that meet at a point. square base + 4 triangles

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 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 5.65.6 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

Part 1Understand the ideamodels and meaning
  1. 1Complete each step, then write the final answer.

    A toy chest is 3 ft long, 2 ft wide, and 2.5 ft tall. Paint costs $3 for each square foot. What does it cost to paint every face of the chest?

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    ? cm
    6 congruent squares share the 150 square centimeters.

    A cube has a surface area of 150 square centimeters. How long is each edge?

    1. 1How many faces does a cube have? Are they the same size?
    2. 2What is the area of one face?
    3. 3Which edge length makes a square with area 25?
    Final answer:
  2. 3Complete each step, then write the final answer.
    bottomfrontbacktopleftright5 in? in4 in

    A box is 5 in long and 4 in wide. Its surface area is 112 square inches. How tall is the box?

    1. 1What is the area of the top and bottom together?
    2. 2How much area is left for the four side faces?
    3. 3The four sides unfold into one rectangle 18 in long. How tall is the box?
    4. 4Why is that long rectangle 18 in long?
    Final answer:
  3. 4Complete 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:
  4. 5Complete each step, then write the final answer.

    A cube-shaped box needs 216 square inches of paper to cover it with no overlap. How long is each edge?

    Show your work
    Final answer:
  5. 6Complete 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:

Explain your thinkingA net can work backward. How can a surface area help you find a missing edge? Use the cube or the box you solved together.

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