Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
Give students 3 minutes of quiet think time to match nets to polyhedra and then another 2 minutes to discuss their response and reasoning with a partner. Encourage students to use the terminology that they learned in prior lessons.
To support students who need more time or help in visualization, prepare physical models of the polyhedra and copies of the nets from the blackline master. Pre-cut the nets or have scissors available so that students can assemble the nets and test their ideas.
Each of the nets can be assembled into a polyhedron. Match each net with its corresponding polyhedron, and name the polyhedron. Be prepared to explain how you know the net and polyhedron go together.
If students have trouble distinguishing between Figures A, C, and D, remind them that prisms and pyramids can both contain faces that are triangles. In a pyramid, all triangular faces that are not the base meet at a one vertex and have shared edges. In a prism, there can be a triangular base, but the other faces are quadrilaterals.
Invite a few students to share their matching decisions and reasoning with the class. Ask students: “What clues did you use to help you match? How did you check if you were right?” If there is not unanimous agreement on any of the nets, ask students with differing opinions to explain their reasoning. Discuss to come to an agreement.
Using Nets to Find Surface Area Cutouts
In this activity, students cut and assemble nets into polyhedra. They use nets to find surface area, applying what they learned earlier about areas of triangles and parallelograms. The presence of a grid supports students in their calculations. It also reinforces the idea of area as the number of unit squares in a region and the connection between area and surface area.
As they find surface area, students have an opportunity to look for and make use of structure (MP7). For instance, they may identify multiple copies of the same polygon and find the combined area with a single calculation. They may also group rectangles with a common side length into a larger rectangle and find the area of the latter.
Monitor for the different approaches that students take. Here are some likely approaches, starting from less systematic to more systematic:
Also monitor for how students organize their work, such as whether they record the measurements of each face, label the shapes in the net and the associated calculations, and account for all the faces of their polyhedron. Encourage students with disorganized or scattered work to take a more methodical approach.
Arrange students in groups of 3. Give each group one of each net (A, B, and C), tape, and access to their geometry toolkits (especially scissors). Explain to students that they will cut some nets, assemble them into polyhedra, and calculate their surface areas. Remind students that the surface area of a three-dimensional figure is the sum of the areas of all of its faces. Ask students to complete the first question before cutting anything.
Point out that the net has shaded and unshaded polygons. Explain that only the shaded polygons in the nets will show once the net is assembled. The unshaded polygons are “flaps” to make it easier to glue or tape the polygons together. They will get tucked behind the shaded polygons and are not really part of the polyhedron. Tell students that creasing along all of the lines first will make it easier to fold up the net and attach the various polygons together. A straightedge can be very helpful for making the creases.
Tell students that it is easy to miss or double-count the area of a face when finding surface area. Ask them to think carefully about how to record their calculations to ensure that all faces are accounted for, correct measurements are used, and errors are minimized.
When students have completed their calculations, ask them to compare and discuss their work with another student who has the same polyhedron.
For whole-class discussion, select 1 or 2 polyhedra whose surface area is found using different approaches, including different ways to keep track of calculations. Select students who use different strategies to share later.
Name the polyhedron that each net would form when assembled.
Three nets on a grid, labeled A, B, and C. Net A is composed of two rectangles that are 5 units tall by 6 units wide, two that are 5 units high and one unit wide, and two that are one unit high and six units wide. Net B is a square with a side length of 4 units and is surrounded by triangles that are four units wide at the base and four units high. Net C is a square with a side length of 3, a rectangle 3 units wide and 5 units high, another rectangle that is 3 units wide and 4 units tall, and two triangles, one on either side, that are three units tall by four units across.
Your teacher will give you the nets of three polyhedra. Cut out the nets and assemble the three-dimensional shapes.
Invite previously selected students to share their responses and reasoning. For each polyhedron, sequence the discussion of the strategies in the order listed in the activity narrative. If possible, record and display their work for all to see.
Connect the different responses to the learning goals by asking questions such as:
If methods for organizing the work—such as listing measurements and labeling polygons and computations—are not mentioned, bring them up. If needed, demonstrate these organizational methods and discuss their benefits.
Connect the approaches used here to those used earlier in the unit by asking students: “How is finding the surface area of a polyhedron like finding the area of a polygon? How is it different?”
Highlight that even though polyhedra are three-dimensional figures, surface area is a two-dimensional measure, so the same strategies we used to find area—such as decomposing and rearranging—still apply here.
A net of a pyramid has one polygon that is the base. The rest of the polygons are triangles. A pentagonal pyramid and its net are shown here.
A net of a prism has two copies of the polygon that is the base. The rest of the polygons are rectangles. A pentagonal prism and its net are shown here.
In a rectangular prism, there are three pairs of parallel and identical rectangles. Any pair of these identical rectangles can be the bases.
Because a net shows all the faces of a polyhedron, we can use it to find its surface area. For instance, the net of a rectangular prism shows three pairs of rectangles: 4 units by 2 units, 3 units by 2 units, and 4 units by 3 units.
The surface area of the rectangular prism is 52 square units because .
If students do not identify the specific type of prism or pyramid, remind them that they should also name each figure by the shape of its base.