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MAFS.912.G-GMD.1.1

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Geometric Measurement & Dimension
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Explain volume formulas and use them to solve problems. (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.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

TEST ITEM SPECIFICATIONS

  • Item Type(s): This benchmark may be assessed using: MS item(s)

  • Assessment Limits :
    Informal arguments are limited to dissection arguments, Cavalieri’s
    principle, and informal limit arguments.

    Items may require the student to recall the formula for the
    circumference and area of a circle.

  • Calculator :

    Neutral

  • Clarification :
    Students will give an informal argument for the formulas for the circumference of a circle; the area of a circle; or the volume of a cylinder, a pyramid, and a cone.
  • Stimulus Attributes :
    Items may be set in a real-world or mathematical context. 

    Items may ask the student to analyze an informal argument to determine mathematical accuracy.

  • Response Attributes :
    Items may require the student to use or choose the correct unit of
    measure.

SAMPLE TEST ITEMS (1)

  • Test Item #: Sample Item 1
  • Question:

    Alejandro cut a circle with circumference C and radius r into 8 congruent sectors and used them to make the figure shown.

    Alejandro noticed that the figure was very close to the shape of a parallelogram. Select all the statements that apply to the figure..

  • Difficulty: N/A
  • Type: MS: Multiselect