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Common Core: Math
CCLS - Math: G.GMD.1
- Geometric Measurement And Dimension
- 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.
- 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 cross-section and a slice.
- Students study the basic properties of two-dimensional and three-dimensional 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 3-dimensions 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...