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Common Core: Standard
Common Core: ELA
Common Core: Math
- 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...
- 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 understand the definitions of a general prism and a cylinder and the distinction between a cross-section and a slice.
- 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 that given similar solids A and B so that the ratio of their lengths is a:b, then the ratio of their volumes is a3:b3. Students understand that if a solid with...
- 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 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 Visualize cross-sections of three-dimensional objects. Have an understanding of how a 3D printer works and its relation to Cavalieri’s principle.