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IM® 6-8 Math v.360, an IM v.360 curriculum, is ©2024 by Illustrative Mathematics®, and licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

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6-8 Accelerated 6 Unit 1 Lesson 10

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K-5 Math •6-8 Math 9-12 Math

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•Accelerated 6 Accelerated 7

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•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 •Lesson 10 Lesson 11 Lesson 12 Lesson 13

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Lesson 10

10.1 Warm-up 10.2 Activity 10.3 Activity Student Lesson Summary Glossary

Unit 1, Lesson 10

What Is Surface Area?

Accelerated 6

10.1

Warm-up

Covering the Cabinet (Part 1)

Your teacher will show you a video about a cabinet or some pictures of it.

Estimate an answer to the question: How many sticky notes would it take to cover the cabinet, excluding the bottom?

Are You Ready for More?

10.2

Activity

Covering the Cabinet (Part 2)

Earlier you learned about a cabinet being covered with sticky notes.

How could you find the actual number of sticky notes it will take to cover the cabinet, excluding the bottom? What information would you need to know?
Use the information you have to find the number of sticky notes needed to cover the cabinet. Show your reasoning.

Are You Ready for More?

10.3

Activity

Prisms Built from Cubes

Standards Alignment

Building On

Addressing

6.G.4

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

View Full Standard

Building Toward

Here is a sketch of a rectangular prism built from 12 cubes. It has six faces, but you can see only three of them in the sketch.

Show that it has a surface area of 32 square units.
Here is a sketch of another rectangular prism built from 12 cubes. What is its surface area? Be prepared to explain or show your reasoning.

Are You Ready for More?

Student Lesson Summary

The surface area of a figure (in square units) is the number of unit squares it takes to cover the entire surface without gaps or overlaps.
If a three-dimensional figure has flat sides, the sides are called faces.
The surface area is the total of the areas of the faces.

For example, a rectangular prism has six faces. The surface area of the prism is the total of the areas of the six rectangular faces.

rectangular prism, length = 3 units, width = 2 units, height = 4 units.

So the surface area of a rectangular prism that has edge-lengths of 2 cm, 3 cm, and 4 cm has a surface area of

or 52 square centimeters.

Glossary

face

Each flat side of a polyhedron is called a face.

For example, a cube has 6 faces that are all squares.

surface area

The surface area of a polyhedron is the number of square units that covers all of its faces with no gaps or overlaps.

For example, the 6 faces of a cube each have an area of 9 cm². So, the surface area of the cube is , or 54 cm².

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Standards Alignment

Building On

Addressing

Building Toward

6.G.4

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

View Full Standard

Standards Alignment

Building On

Addressing

6.G.4

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

View Full Standard

Building Toward