Access Point #: MAFS.912.G-C.2.AP.5b (Archived Access Point)


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Derive the fact that the length of the arc intercepted by an angle is proportional to the radius.

Clarifications:

Essential Understandings

Concrete:

  • Identify the formula for the circumference of a circle.
  • Identify the radius of a circle.
  • Construct a circle with a specified radius.
  • Use a protractor to measure angles.
  • Use geometry software to manipulate circles based on their radius and circumference.
Representation:
  • Set up a proportion using dimensions of the circle.
  • Use appropriate tools to calculate.
  • Convert degrees to radians and radians to degrees.
  • Use appropriate tools to calculate the arc length of a circle.
  • Calculate the circumference of a circle.
  • Understand the following concepts and vocabulary: circle, radian, degree, arc, arc length, circumference, diameter.

Number: MAFS.912.G-C.2.AP.5b Category: Access Points
Date Adopted or Revised: 07/14 Cluster: Find arc lengths and areas of sectors of circles. (Geometry - Additional Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Related Standards

Name Description
MAFS.912.G-C.2.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.



Related Courses

Name Description
1200400: Foundational Skills in Mathematics 9-12
1206310: Geometry
1206320: Geometry Honors
1206315: Geometry for Credit Recovery
7912065: Access Geometry