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

Lesson 5.75.7 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find the surface area of rectangular and triangular prisms — one step at a time, with support.

Why This Matters This is your support small group for Lesson 5.7. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

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. add every face
Rectangular prismSpanish: Prisma rectangular A solid box shape with six flat rectangle sides. 3 congruent pairs
Triangular prismSpanish: Prisma triangular A solid with two triangle ends and three flat rectangle sides. Shaped like a tent or a wedge of cheese — 2 triangle ends + 3 rectangle sides
FaceSpanish: Cara One flat side of a solid shape. top, side, end
NetSpanish: Plantilla (desarrollo plano) A flat shape that folds up into a solid. unfolded box
Lateral faceSpanish: Cara lateral The side faces of a solid, not the top or bottom. On a triangular prism, the 3 rectangles that wrap around the sides are lateral faces

How it worksWorked example

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

A closed box is 6 cm × 4 cm × 3 cm.

  1. Faces: 6 × 4 = 24, 6 × 3 = 18, 4 × 3 = 12.
  2. Double each: 48, 36, 24.
  3. Add: 48 + 36 + 24 = 108.

Answer: SA = 108 cm²

Now you trySame steps, your turn

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

A rectangular prism is 5 cm long, 4 cm wide, and 3 cm tall. Find its surface area.

Answer:

Say it and write itSentence starters

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

  • The prism has faces in matching pairs.
  • The three different face areas are , , and .
  • I doubled each face area because .
  • The surface area is square units.

Word bank surface areanetfacecongruentpairprismunfoldadddoublesquare unitstopside

Watch out!A common mistake

A common mistake in Surface Area of Prisms is confusing surface area with volume

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

Lesson 5.75.7 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, I can find the surface area of rectangular and triangular prisms — one step at a time, with support.

Why This Matters This is your support small group for Lesson 5.7. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

  1. 1Complete each step, then write the final answer.
    8 in5 in10 in12 in
    The net has 2 triangles and 3 rectangles.

    A triangular prism is 5 in long. Each triangle end has a base of 12 in and a height of 8 in. The two slanted sides are 10 in each. Find the surface area.

    1. 1What is the area of one triangle end?
    2. 2What is the area of both triangle ends?
    3. 3The rectangles are 12 × 5, 10 × 5 and 10 × 5. Add them.
    4. 4Add the triangles and the rectangles. What is the surface area?
    Final answer:
  2. 2Complete each step, then write the final answer.
    10 in5 in12 in13 in

    A ramp is a triangular prism 10 in long. Each triangle end has sides of 5 in, 12 in and 13 in. The 5 in and 12 in sides meet at a square corner. Find the surface area.

    1. 1Which two sides are the base and height of the triangle?
    2. 2What is the area of both triangle ends?
    3. 3Each rectangle is one side × 10. What do the three rectangles add to?
    4. 4What is the surface area?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A rectangular prism is 4 cm long, 2 cm wide, and 1 cm tall. Find its surface area.

    Show your work

    Hint A rectangular prism has 3 pairs of matching faces. Find each pair, then add.

    Final answer:
  4. 4Complete each step, then write the final answer.
    10 cm8 cm15 cm17 cm

    A triangular prism is 10 cm long. Its triangle ends have sides of 8 cm, 15 cm and 17 cm. The 8 cm and 15 cm sides meet at a square corner. Find the surface area.

    Show your work

    Hint Use the two sides at the square corner for the triangles. Use all three sides for the rectangles.

    Final answer:
  5. 5Complete each step, then write the final answer.

    A tent with a floor is a triangular prism 5 ft long. Each triangle end has a base of 16 ft and a height of 6 ft. The slanted sides are 10 ft. How much fabric covers the whole tent?

    Show your work

    Hint The fabric covers 5 faces: 2 triangles, the floor and 2 slanted sides.

    Final answer:
  6. 6Complete each step, then write the final answer.

    Rosa finds the surface area of a triangular prism. The rectangles are 12, 16 and 20 square inches. Each triangle end is 24 square inches. She adds 12 + 16 + 20 + 24 = 72. What is the correct surface area?

    Show your work

    Hint Count the faces Rosa added. How many faces does a triangular prism have?

    Final answer:

Explain your thinkingHow is the surface area of a triangular prism like the surface area of a box? How is it different?

Sentence starter Both are the same because ___. · A triangular prism has ___ faces, so ___.

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