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Mathematics > Course Model Mathematics II (Integrated Pathway) > Circles
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - Circles

Cluster - Find arc lengths and areas of sectors of circles.

[MII.G-C.B.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.

Resources:

    Predecessor Standards:

    • 7.RP.A.2
      Recognize and represent proportional relationships between quantities.
    • 7.RP.A.2.a
      Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
    • 7.RP.A.2.b
      Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
    • 7.RP.A.2.c
      Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
    • 7.RP.A.2.d
      Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
    • 7.G.B.4
      Circles and measurement
    • 7.G.B.4.a
      Know that a circle is a two-dimensional shape created by connecting all of the points equidistant from a fixed point called the center of the circle.
    • 7.G.B.4.b
      Understand and describe the relationships among the radius, diameter, circumference and circumference of a circle.
    • 7.G.B.4.c
      Understand and describe the relationship among the radius, diameter, and area of a circle.
    • 7.G.B.4.d
      Know the formulas for the area and circumference of a circle and use them to solve problems.
    • 7.G.B.4.e
      Give an informal derivation of the relationship between the circumference and area of a circle.

    Successor Standards:

    No Successor Standards found.

    Same Level Standards:

    • MII.G-SRT.A.2
      Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
    • MIII.F-TF.A.1
      Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.