After making an estimate of the number of sticky notes on the cabinet in the Warm-up, students now brainstorm ways to find that number more accurately. They then go about calculating an answer. The activity prompts students to transfer their understanding of the area of polygons to find the surface area of a three-dimensional object.

Students learn that the surface area of a three-dimensional figure is the total area of all its faces. Because the area of a region is the number of square units it takes to cover the region without gaps and overlaps, surface area can be thought of as the number of square units that are needed to cover all sides of an object without gaps and overlaps. The square sticky notes illustrate this idea in a concrete way.

As students work, notice the various approaches that they take to determine the number of sticky notes needed to tile the faces of the cabinet (excluding the bottom). Identify students with different strategies to share later.

Students may treat all sides as if they were congruent rectangles. That is, they find the area of the front of the cabinet and then just multiply by 5, or act as if the top is the only side that is not congruent to the others. If there is a real cabinet (or any other large object in the shape of a rectangular prism) in the classroom, consider showing students that only the sides opposite each other can be presumed to be identical.

Students may neglect the fact that the bottom of the cabinet will not be covered. Point out that the bottom is inaccessible because of the floor.

Invite previously identified students or groups to share their answer and strategy. On a visual display, record each answer and each distinct process for determining the surface area (that is, multiplying the side lengths of each rectangular face and adding up the products). After each presentation, poll the class on whether others had the same answer or process.

Play the video that reveals the actual number of sticky notes needed to cover the cabinet: "Act 3" at https://estimation180.com/filecabinet/

If students' answers vary from that shown on the video, discuss possible reasons for the differences. (For example, students may not have accounted for the cabinet's door handles. Some may have made a calculation error.)

Tell students that the question they have been trying to answer is one about the surface area of the cabinet. Explain that the surface area of a three-dimensional figure is the total area of all its surfaces. We call the flat surfaces on a three-dimensional figure its faces.

The surface area of a rectangular prism would then be the combined area of all six of its faces. In the context of this problem, we excluded the bottom face because it is sitting on the ground and will not be tiled with sticky notes. Discuss:

• “What unit of measurement are we using to represent the surface area of the cabinet?” (square sticky notes)
• “ Would the surface area, in terms of the number of square units, change if we used larger or smaller sticky notes? How?” (Yes, if we use larger sticky notes, we would need fewer. If we use smaller ones, we would need more.)

In this activity, students reason about the surface area of rectangular prisms built from cubes. To verify and find surface area, students may count the number of square units on the visible faces and double the number of squares on each face (or double the total number of squares on the three visible faces). They may also use the squares to determine the edge lengths of the prisms, multiply them to find the area of each face, and then combine the areas.

In Are You Ready for More? students are prompted to build a different prism from 12 cubes, draw it on isometric dot paper, and find its surface area. If physical cubes aren’t available, consider using the digital version, in which students can use an applet to build a prism.

Select 1 or 2 students to share how they know the surface area of the first prism is 32 square units. Use students’ explanations to highlight the meaning of surface area. Emphasize that the areas of all the faces need to be accounted for, including those we cannot see when looking at a two-dimensional drawing.

Select 1 or 2 students to briefly share their reasoning about the area of the second prism.

Point out that, in this activity, each face of their prism is a rectangle. We can find the area of each rectangle (by multiplying its base by its corresponding height) and then add the areas of all the faces to figure out the surface area. Explain that later, when we encounter non-rectangular prisms, we can likewise reason about the area of each face. We can find the areas of faces that are not rectangles the way we reasoned about the area of polygons earlier in the unit.