 # Access Point #: MAFS.912.G-GMD.1.AP.1a (Archived Access Point)

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Describe why the formulas work for a circle or cylinder (circumference of a circle, area of a circle, volume of a cylinder) based on a dissection.

#### Essential Understandings

Concrete:

• Find the circumference and areas of a circle and volume of a cylinder using manipulatives.
• Create a ratio between the circumference and the diameter of a circle to determine the relationship using manipulatives.
• Create a ratio between the area and the diameter of a circle to determine the relationship using manipulatives.
Representation:
• Describe the relationship between the dimensions of the figures.
• Describe the relationship between the components of the formula (e.g., how to get the area, volume or circumference).

 Number: MAFS.912.G-GMD.1.AP.1a Category: Access Points Date Adopted or Revised: 07/14 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.

#### Related Standards

 Name Description 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.

#### Related Courses

 Name Description 1200400: Foundational Skills in Mathematics 9-12 1206300: Informal Geometry 1206310: Geometry 1206320: Geometry Honors 1298310: Advanced Topics in Mathematics (formerly 129830A) 7912060: Access Informal Geometry 1206315: Geometry for Credit Recovery 7912065: Access Geometry