Finding the Surface Area of a Triangular Prism Using A Formula

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Objective

SWBAT find the surface area of triangular prisms using a formula

Big Idea

Students learn a more efficient method for finding surface areas other than using nets.

Lesson Author

Grant Harris

New Orleans, LA

Grade Level

Seventh grade

Subjects

Math

volume (3-D Geom)

Geometry

surface area

Standards

7.G.B.6

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP6

Attend to precision.

Lesson Beginning

5 minutes

Possible Changes to the Example

I’ll begin with some turn-and-talk questions to get students to generate what we have already learned about surface area of a triangular prism. I might ask “How did we find the surface area of a triangular prism in the previous lesson?” I will hold up a model of a triangular prism while asking this question so that students have a good visual. I want to hear a response that says to find the area of each face and add these areas. I want to lead students towards a general formula (Surface area = area of bases + areas of lateral face) for the surface area of a triangular prism (or any prism). So if necessary I will ask students to look at the prism as being composed of the bases and the lateral faces. How could we write a formula in terms of these terms? During this discussion, students are engaged in at least 2 of the mathematical practices. MP6 is evident as students are using precise language regarding prisms –bases & lateral faces. MP7 is evident as students are able to shift perspectives and see that all prisms are made up of bases and lateral faces, yet the specific base shapes may change.

Lesson Middle

35 minutes

This part of the lesson is the “I”, “WE”, and “YOU” of the lesson. In the “I” section I present two examples. Students are to watch my example and then fill in notes when instructed. In the “WE” section, students work together to solve problems that are similar to the examples. They are to show work in a manner similar to the model given in the “I” section. The reason for this is two-fold: 1) It gives students a step-by-step approach that will allow them to be successful; 2) It helps me to diagnose any misconceptions. In the “YOU” section, it is all independent work. I will have identified students who need support at this point. Struggling students will be reminded to follow the steps in the examples, first before asking for help. When nearly all have finished the main independent practice, we’ll go over solutions as needed.

Lesson End + Homework

10 minutes

I ask for a student to summarize a general formula for the surface area of any prism. We quickly discuss this, and then students take the exit ticket.