Circles, Circumference and Area

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Objective

SWBAT give informal arguments for the circumference and area of circles.

Big Idea

Students dissect a circle in order to find its circumference and area.

Do Now

5 minutes

In the Do Now, students answer review questions about area and perimeter. They also describe the term sector of a circle which we go into greater detail during the Mini-Lesson.

After about three minutes, we will go over their responses. I expect that some of my students still have difficulty differentiating between area and perimeter. I make sure they can clearly describe the difference before we go on with the lesson. 

Mini-Lesson

5 minutes

Although the concepts in this lesson pertain to two-dimensional geometry, I have included this lesson in the three-dimensional geometry unit because it prepares students to understand how to find the volume of cylinders, cones and spheres.

We begin the Mini-Lesson by discussing area and circumference of a circle. I ask the students what they know about finding the area and circumference of a circle. Most students respond by stating formulas or they talk about the ratio, Pi. Then, I ask the students how we could find the area and circumference without using formulas. Few students can figure out the answer to this question. I direct them to look back to their Do Nows and think about why I included those questions. We discuss how we can use sectors to find the area of a circle. Students recognize that a sector of a circle appears to be triangular. We use this idea to figure out the area and circumference (G.GMD.1).

Activity

30 minutes

Summary

5 minutes

At the end of the lesson, students complete an exit ticket. They are asked to explain how to get a more accurate approximation for Pi using the dissection method. I collect the exit ticket and check to see that the students understand that slicing the circle into smaller sectors would give a better approximation for Pi.