In grade 6, students used nets made up of rectangles and triangles to find the surface area of threedimensional figures. In this lesson they find surface areas of prisms, and see that structure of a prism allows for shortcuts in adding up the areas of the faces. They see that if the prism is sitting on its base, then the vertical sides can be unfolded into a single rectangle whose height is the height of the prism and whose length is the perimeter of the base. The purpose of the lesson is not to come up with a formula for the surface area of a prism, but to help students see and make use of the structure of the prism to find surface area efficiently (MP7).
Lesson overview
 14.1 Warmup: Multifaceted (5 minutes)
 14.2 Activity: So Many Faces (15 minutes)

14.3 Activity: Revisiting a Pentagonal Prism (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 14.4 Cooldown: Surface Area of a Hexagonal Prism (5 minutes)
Learning goals:
 Calculate the surface area of a prism, and explain (in writing) the solution method.
 Comprehend that surface area and volume are two different attributes of threedimensional objects and are measured in different units.
 Interpret different methods for calculating the surface area of a prism, and evaluate (orally and in writing) their usefulness.
Learning goals (student facing):
 Let’s look at the surface area of prisms.
Learning targets (student facing):
 I can picture the net of a prism to help me calculate its surface area.
 I can find and use shortcuts when calculating the surface area of a prism.
Required materials:
 materials assembled from the blackline master
Required preparation:
 Assemble the net from the blackline master to make a prism with a base in the shape of a plus sign.
 Make sure to print the blackline master at 100% scale so the dimensions are accurate.
 This prism will be used for both the warmup and the following activity.
Glossary:
 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 \(6 \cdot 9\), or 54 \(cm^2\).
 Access the complete Grade 7 glossary.
Standards:
 This lesson builds on the standards:CCSS.3.MD.C.5MS.3.MD.5MO.3.GM.C.9 CCSS.3.MD.D.8MS.3.MD.8MO.3.GM.D.15MO.3.GM.D.16CCSS.6.G.A.4MS.6.G.4MO.6.GM.A.4aMO.6.GM.A.4b
 This lesson builds towards the standard:CCSS.7.G.B.6MS.7.G.6MO.7.GM.B.6aMO.7.GM.B.6b
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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