Grade: 7^th / 8^th Grade
Subject: Math/Pre-Algebra
Unit: Geometry and Measurement
Topic: Surface Area of Cylinders

Objectives: By the end of the lesson, the students will:
1.) Discover and create the formula for the surface area of a cylinder
2.) Calculate the surface area of a cylinder

Activities:
Bell Work: As students enter the room, have the following problems on the board as review from the previous lessons. When students are complete, review the answers and answer any questions that may arise.

1. Calculate the area of a rectangle with l = 12.2 in. and w = 6.4 in.
2. Calculate the area and circumference of a circle with r = 3.4 cm

Small Group: (3 or 4) Separate the students into groups of 3 or 4. Each group gets a copy of the handout, a can of pringles, a sheet of construction paper or colored paper, tape, markers or colors, and a ruler. The students are to create a label for their own brand of potato chips. Their labels must fit the can perfectly. {a rectangular label for the body of the can, and two circular labels for the top and bottom of the can} Students may decorate and color their labels to their likings. When the labels are complete, they are to leave them off and answer the questions on the handout.

Whole Group:
T: Would a group like to share their formula?
T: Is ___________'s formula similar or the same as the formula anyone else discovered?
T: Can we all agree that the formula for the surface area of a cylinder should be 2pr² + 2prh ?

Individual: Students should be given one or two sample problems to complete individually.

Conclusion: Students get a partner and sit back to back. Set up this situation for the students. You are at home trying to complete your homework. You reach a problem you cannot work. You call the emergency 7-1-1 math line. You explain the problem to the person on the other end of the line (your partner). The 7-1-1 operator describes to you how to work the problem. You and your partner are to replay this situation with this problem. Calculate the surface area of a cylinder with a height of 7 in. and a radius of 11 in.

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Group # _____________
Leader: _____________________________ Reporter: _____________________________
Recorder: ___________________________ Runner: _______________________________

Directions: You and your friends have made your own type of potato chips. Create a label for your can of chips that fits your can perfectly. You can decorate your label with any title and symbols that are school appropriate. Do not attach your label until you reach the direction that tells you to!! Answer the questions on this handout.
1. What shape is the top and the bottom of the can?
2. What formula do you use to find the area of the label you used for the top and the bottom?
3. The formula for total area of the label for the top and the bottom of the can is _______________ .
4. Now, look at the label for the body of the can. What shape is this label?
5. How is the length of the label related to the can? Explain.
6. How is the width of the label related to the can? Explain.
7. Using h for the height of the can and r for the radius of the circle, what formula can you create to find the  area of the rectangular label?
8. Draw a sketch of what your label looks like flattened out on your desk.
9. From this drawing, what formula can you create for the total surface area of the can?
10. Now, with the label flattened out, calculate the area of the two circles and the rectangle by using your ruler. Then find the sum of the area of the 3 figures.
11. Tape your label onto your can. Use your ruler to find the needed measurements for your formula and calculate the surface area using your formula.
12. Compare the two areas from #'s 11 and 12. Are they the same or close to the same? Is your formula correct?