Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments

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Objective

SWBAT find the area and perimeter of shapes composed of arcs and line segments

Big Idea

These shapes look really cool.

Lesson Author

Grant Harris

New Orleans, LA

Grade Level

Seventh grade

Subjects

Math

volume (3-D Geom)

Geometry

circumference (Determining Measurements)

Standards

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.

MP1

Make sense of problems and persevere in solving them.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

Warm Up

10 minutes

Problem Solving

25 minutes

Making Sense!

I will remind students to show work as they solve and be prepared to discuss their solutions. As noted in the comments section of the task, there will be some discussion and perhaps confusion over finding the perimeter of the green and red shapes. I think it will be simplest just to have students find the total distance of the border around the shaded regions including the holes.

When students struggle, I will ask questions like the opener: What fraction of a circle is present? What fraction of the square is shaded or not shaded?

Summary

15 minutes

We will share out our findings. I will call on groups to present their solutions. I will try to make time to discuss at least two different solution methods per problem. Here is an opportunity for students to critique the reasoning of others or construct a viable argument for their solutions (MP3).

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