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7-GM-3-1

Page history last edited by Brenda Butz 6 years, 2 months ago

7.GM.3.1 Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is π and can be approximated by rational numbers such as 22/7 and 3.14.


In a Nutshell

Know that when the diameter of a circle is multiplied by pi the product is the circumference of the circle. Know that when the circumference of a circle is divided by pi or the diameter of the circle then the quotient is the other (diameter or pi). Acceptable rounded values of pi are 22/7 and 3.14.

Student Actions

Teacher Actions

  • Develop the ability to make predictions, conjectures and draw conclusions when discovering the relationship between diameter and circumference through measurement.

  • Develop strategies for problem solving when given one measurement of a circle to find the other. Example : If given the diameter, find the circumference.  If given the circumference, find the diameter. 

  • Provide the opportunity to use and connect mathematical representations through measuring diameters and circumferences of circles and making meaningful comparisons.

  • Implement tasks that promote reasoning about the relationship between the proportional relationship between the diameter and the circumference of a circle.

  • Use and connect mathematical representations by engaging students in meaningful tasks by creating relationships between the radius, diameter and circumference. 

Key Understandings

Misconceptions

  • The diameter of a circle is the distance from one side to another through the center.

  • The circumference is the entire distance around the outside of a circle with no overlapping.

  • The diameter of any circle multiplied by pi produces the circumference of that circle.
  • Students may not understand that pi is a constant.

  • Students may struggle to differentiate between pi and its approximations.

  • Students may struggle to generalize the relationship between the diameter and circumference of all circles.

 


OKMath Framework Introduction

7th Grade Introduction

 

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