Measures of Circles

  • Exploring Measures of Circles

    7th grade


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


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


    Lesson 1 of 2
    Measure circular objects to explore the relationship between circumference and diameter of a circle in order to discover the ratio, Pi.
    Lesson 2 of 2
    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?"

    Technology Resources

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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?


    diameter, radius, circumference, pi, circle, area


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


    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.



    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