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Geometry Resources & Lesson Plans7 chapters | 194 lessons

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Instructor:
*Marques Herrington*

I have taught both middle school math and science for 10 years and I have a master's degree in education

This lesson plan derives the formula for finding the surface area of a cylinder. Students will work in pairs to practice using the formula to calculate the surface area of a cylinder.

Upon completion of this lesson, students will be able to:

- Derive the formula for the surface area of a cylinder by combining the areas of two circles and a rectangle.
- Calculate the surface area of a cylinder using the correct units of measurement.

- 60-70 minutes

- Math Journals/notebook
- Cutout sheet of two identical circles and a rectangle, where the length of the rectangle is equivalent to the circumference of the two circles.
- Formula derivation sheet for the surface area of a cylinder.
- Surface area of a cylinder practice sheet (should consist of four cylinder problems; two that use whole number measurements, two that use decimal measurements)
- Exit ticket slip
- Class set of scissors
- Tape
- Printed copies of the lesson quiz

CCSS.MATH.CONTENT.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.

CCSS.MATH.CONTENT.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.

Begin by giving students three warm-up problems on the board as they enter the classroom. Students should answer the questions in their math notebook/journals. These questions should review finding the area of a circle, the circumference of a circle, and the area of a rectangle. Make sure students are writing down the formulas for each of these. Go over the solutions to these questions to check for understanding of these concepts.

Pass out the cutout sheets of circles and rectangles, and instruct students to cut out both the circles and rectangle. Play the video lesson How to Find the Surface Area of a Cylinder and stop it at 1:10.

- Divide students into pairs.
- Prompt students to discuss and write in their journals about how the length of the rectangle is related to the length around the circle (circumference).
- Pass out the formula derivation forms.
- As you monitor each group, make sure students understand the length of the rectangle is being 'wrapped around the circle.' This means the length of the rectangle is equal to the circumference of the circle, 2 * pi * the radius of the circle.
- Have the students construct an expression for the area of a rectangle in terms of the height of the rectangle and the circumference of the circle. Give the students 5 minutes to do this.
- Check to see that students have the right expression.
- Lead the class in discussion by asking the following questions:

*What else do we need to calculate the total surface area of the cylinder? (The 2 circles)

*What is the formula for finding the area of a circle? (A = pi times the radius squared)

*What can we write to account for both circles? (A = 2 times pi times the radius squared) - After making these connections, prompt the student pairs to combine the expressions to get the final formula for the surface area of a cylinder. Give students 5 minutes to do this.
- Play the rest of the video lesson.
- Instruct the student groups to finish taping together the rectangle and circles to make a paper cylinder. Model this for students if necessary.
- Pass out the surface area cylinder quiz, and give them 10 minutes to complete.
- Go over the solutions to check for understanding.

Pass out exit tickets. Prompt student to describe, in their own words, what they learned in the class. Make sure they use diagrams and/or math work in their explanation.

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Geometry Resources & Lesson Plans7 chapters | 194 lessons

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