Finding the Surface Area of Cylinders Using a Formula

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Objective

SWBAT solve problems about the surface area of cylinders using a formula

Big Idea

Students have already discovered the formula for themselves. Now they put it to use solving problems.

Lesson Author

Grant Harris

New Orleans, LA

Grade Level

Seventh grade

Subjects

Math

volume (3-D Geom)

Geometry

surface area

circumference (Determining Measurements)

Standards

7.EE.A.1

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients

7.G

Geometry

7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

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.

MP4

Model with mathematics.

MP7

Look for and make use of structure.

Lesson Beginning

10 minutes

I will state the essential question: how can you find the surface area of a cylinder using a formula?Next, I will remind students that they have already explored cylinders and discovered for themselves the surface area formula. I’ll ask “How could you explain in simple terms how to find the surface area of cylinder without resorting to formulas?” I’ll ask students if they can recreate the formula based on this explanation. Then I’ll post the standard formula. Using the general surface area formula, I’ll cold call students to identify the various parts of the formula and to what part of the cylinder they belong. This is an opportunity again for students to develop MP7. In addition, we are now going to use a formula that we understand to model and solve a problem (MP4). Then, I’ll say today we will use the formula to solve problems about surface area of cylinders. Then, we’ll work through 1-2 examples.

Lesson Middle

30 minutes

Problem 7 - Visualizing Cheese Minus the Wedge

Students now work with their partner(s) to solve about 6 surface area problems. This is guided practice. One of the first problems requires students to describe to each other what the parts of the formula mean. I will circulate and listen in on these discussions. After about 10 minutes, we’ll discuss some of the problems as needed. Be on guard for common mistakes: forgetting to include the area of both bases; doubling a radius as opposed to squaring it; using the diameter instead of the radius; etc. Students are then to work independently on a similar set of problems followed by the extension. I will focus my attention on students who are still struggling during guided practice. I will provide guided questions to students who have reached the extension. We will then quickly go over various students solutions.