# Lesson 12

What is Surface Area?

### Lesson Narrative

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 three-dimensional figure without gaps or overlaps (MP6).

Later in the lesson, students use cubes to build rectangular prisms and then determine their surface areas.

### Learning Goals

Teacher Facing

• 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 three-dimensional object.

### Student Facing

Let’s cover the surfaces of some three-dimensional objects.

### 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 cool-down.

### Student Facing

• I know what the surface area of a three-dimensional object means.

Building Towards

### Glossary Entries

• 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 cm2, then the surface area of the cube is $$6 \boldcdot 9$$, or 54 cm2.

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