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# Circles, Circumference and Area

Lesson 3 of 5

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

*45 minutes*

#### Do Now

*5 min*

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.

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#### Mini-Lesson

*5 min*

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).

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#### Summary

*5 min*

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.

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment