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Content Area: Math
Index: 4.2E Grade 12 CPI 2
Standard: 4.2 - Geometry and Measurement
Strand: E - Measuring Geometric Objects
Cumulative Progress Indicator: 2 - The student will use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures · Approximation of area using grids of different sizes · Finding which shape has minimal (or maximal) area, perimeter, volume, or surface area under given conditions using graphing calculators, dynamic geometric software, and/or spreadsheets · Estimation of area, perimeter, volume, and surface area
Grade: 12
Sample Activities:
· Students find volumes of objects formed by combining geometric figures and develop formulas describing what they have done. For example, they might generate a formula for finding the volume of a silo composed of a cylinder of specified radius and height topped by a hemisphere of the same radius.
· Students construct models to show how the volume of a pyramid with a square base and height equal to a side of the base is related to the volume of a cube with the same base.
· Students develop and use a spreadsheet to determine what the dimensions should be for a cylinder with a fixed volume, in order to minimize the surface area. Similarly, they investigate what should be the dimensions for a rectangle having a fixed perimeter in order to maximize the enclosed area. They discuss how the symmetry of these figures relates to the solutions.
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