MA.912.G.6.5Archived Standard

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Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

Remarks

Example: Which will give you more: three 6-inch pizzas or two 8-inch pizzas? Explain your answer.
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Geometry
Idea: Level 3: Strategic Thinking & Complex Reasoning
Standard: Circles - Define and understand ideas related to circles (radius, tangent, chord, etc.). Perform constructions, and prove theorems related to circles. Find measures of arcs and angles related to them, as well as measures of circumference and area. Relate geometry to algebra by finding the equation of a circle in the coordinate plane.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , FR item(s)
    • Also Assesses:

    MA.912.G.6.2 Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.

    MA.912.G.6.4 Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).
  • Clarification :
    Students will solve problems related to circles.
  • Content Limits :

    All angle measurements will be in degrees.

     Items may require statements and/or justifications to complete formal and informal proofs.

  • Stimulus Attributes :

    Items may be set in either real-world or mathematical contexts.

    Graphics should be used in most of these items, as appropriate.

Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question:

    Allison created an embroidery design of a stylized star emblem. The perimeter of the design is made by alternating semicircle and quarter-circle arcs. Each arc is formed from a circle with a 2 1/2 -inch diameter. There are 4 semicircle and 4 quarter-circle arcs, as shown in the diagram below.

     

    To the nearest whole inch, what is the perimeter of Allison’s design?

  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question:

    Kayla inscribed kite ABCD in a circle, as shown below.

     

    If the measure of arc ADC is 255° in Kayla’s design, what is the measure, in degrees, of ∠ADC ?

  • Difficulty: N/A
  • Type: FR: Fill-in Response

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

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Professional Development

Mathematical Modeling: Insights into Algebra, Teaching for Learning:

This professional development resource provides a rich collection of information to help teachers engage students more effectively in mathematical modeling. It features videos of two complete lessons with commentary, background information on effective teaching, modeling, and lesson study, full lesson plans to teach both example lessons, examples of student work from the lessons, tips for effective teaching strategies, and list of helpful resources.

  • In Lesson 1 students use mathematical models (tables and equations) to represent the relationship between the number of revolutions made by a "driver" and a "follower" (two connected gears in a system), and they will explain the significance of the radii of the gears in regard to this relationship.
  • In Lesson 2 students mathematically model the growth of populations and use exponential functions to represent that growth.

Type: Professional Development

Student Resources

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