Circles, Circumference and Area

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. 

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).

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.