Lesson 12: What is Surface Area?
About this lesson
This lesson introduces students to the concept of surface area. They use what they learned about area of rectangles to find the surface area of prisms with rectangular faces.
Students begin exploring surface area in concrete terms, by estimating and then calculating the number of square sticky notes it would take to cover a filing cabinet. Because students are not given specific techniques ahead of time, they need to make sense of the problem and persevere in solving it (MP1). The first activity is meant to be open and exploratory. In the second activity, they then learn that the surface area (in square units) is the number of unit squares it takes to cover all the surfaces of a threedimensional figure without gaps or overlaps (MP6).
Later in the lesson, students use cubes to build rectangular prisms and then determine their surface areas.
Lesson overview
 12.1 Warmup: Covering the Cabinet (Part 1) (5 minutes)

12.2 Activity: Covering the Cabinet (Part 2) (20 minutes)
 Includes "Are you Ready for More?" extension problem

12.3 Activity: Building with Snap Cubes (20 minutes)
 There is a digital applet in this activity.
 Lesson Synthesis
 12.4 Cooldown: A Snap Cube Prism (5minutes)
Learning goals:
 Calculate the surface area of a rectangular prism and explain (orally and in writing) the solution method.
 Comprehend that the term “surface area” (in written and spoken language) refers to how many square units it takes to cover all the faces of a threedimensional object.
Learning goals (student facing):

Let’s cover the surfaces of some threedimensional objects.
Learning targets (student facing):
 I know what the surface area of a threedimensional object means.
Required materials:
 geometry toolkits
 snap cubes
Required preparation:
 Prepare 12 cubes per student and extra copies of isometric dot paper for Building with Snap Cubes activity.
 Build several rectangular prisms that are each 2 cubes by 3 cubes by 5 cubes for the cooldown.
Glossary:
 face  Each flat side of a polyhedron is called a face. For example, a cube has 6 faces, and they are all squares.
 surface area  The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps. For example, if the faces of a cube each have an area of 9 cm\(^2\), then the surface area of the cube is \(6\cdot9\), or 54 cm\(^2\).
 Access the complete Grade 6 glossary.
Standards

This lesson builds towards the standards:CCSS.6.G.A.4MS.6.G.4MO.6.GM.A.4aMO.6.GM.A.4b
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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