Measures of Circles

• # Exploring Measures of Circles

Description

Explore relationships between the parts of a circle in order to discover the formulas for finding the circumference and area of circles.

### Hook

If you're going on a ten mile bike ride, which bike would you choose? Why?

### Lessons

Measure circular objects to explore the relationship between circumference and diameter of a circle in order to discover the ratio, Pi.
Discover the area formula of circles by separating into congruent shapes and using their understanding of other polygons.

### ARC Assessement

Have students revisit the Hook in the beginning of the ARC and ask students to reassess their answer. "Now that you have learned about the parts of a circle, and circumference and area of circles, would you change your answer? Why or why not? What is your mathematical justification for the bike you have chosen?"

• ## Ratings

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• ### ARC Global Essential Question(s)

How does understanding the relationship between the parts of a circle lead you to discovering the formulas for finding the circumference and area of a circle?

### Keywords

diameter, radius, circumference, pi, circle, area

### Vocabulary

• diameter
• circumference
• pi
• ratio
• circle
• area
• inscribed
• circle
• base
• height

### Standards

CCSS, Content Standards to Domain Level

• 7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems

CCSS, Standards for Mathematical Practices

• SMP 5 Use appropriate tools strategically.
• SMP 6 Attend to precision.

### Contributors

Original Sources: Illuminations Unit, Apple Pi
Original Author(s): Christopher Johnston
New Editors: Katelyn Albright, Suzanne Alejandre, Amber Condella, Cindy Hasselbring, Reba Hekker, Derek Pipkorn, Jennifer Plumb, AnnMarie Varlotta