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Common Core: Math
CCLS  Math: G.GMD.1
 Category
 Geometric Measurement And Dimension
 SubCategory
 Explain Volume Formulas And Use Them To Solve Problems
 State Standard:
 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.
12 Results

 Student Outcomes Students give an informal argument using Cavalieri’s principle for the volume formula of a sphere and use thevolume formula to derive a formula for the surface area of a sphere.

 Student Outcomes Students use Cavalieri’s principle and the cone cross section theorem to show that a general pyramid or cone has volume 1/3Bh where B is the area of the base and h is the height by...

 Student Outcomes Students understand the principle of parallel slices in the plane, and understand Cavalieri’s principle as ageneralization of the principle of parallel slices. Students use Cavalieri...

 Student Outcomes Students understand the precise language that describes the properties of volume. Students understand that the volume of any right cylinder is given by the formula area of base×...

 Student Outcomes Students understand the definitions of a general prism and a cylinder and the distinction between a crosssection and a slice.

 Students study the basic properties of twodimensional and threedimensional space, noting how ideas shift between the dimensions. They learn that general cylinders are the parent category for...

 Student Outcomes Students use inscribed and circumscribed polygons for a circle (or disk) of radius r and circumference C to showthat the area of a circle is 1/2Cr or as it is usually written, πr2.

 Student Outcomes Students understand that a similarity transformation with scale factor r multiplies the area of a planar region bya factor of r2. Students understand that if a planar region is...

 Student Outcomes Students understand properties of area: 1.Students understand that the area of a set in the plane is a number greater than or equal to zero thatmeasures the size of the set and not...

 Student Outcomes Students review the area formula for rectangles with rational side lengths and prove the area formula for anarbitrary rectangle. Students use a square grid to estimate the area of a...

 Students begin their work with 3dimensions by first developing a stronger sense of area in two dimensions. They find approximated areas of curved figures by “squeezing” them between inscribed and...

 Geometry Module 3: Extending to Three Dimensions Module 3, Extending to Three Dimensions, builds on students’ understanding of congruence in Module 1 and similarity in Module 2 to prove volume...