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Common Core: Math
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 Student Outcomes Visualize crosssections of threedimensional objects. Have an understanding of how a 3D printer works and its relation to Cavalieri’s principle.

 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 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 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 understand how the Greeks measured the distance from the earth to the moon and solve related problems.

 Student Outcomes Students understand that parallel lines cut transversals into proportional segments. They use ratios between corresponding line segments in different transversals and ratios within...

 Students learn what it means for two figures to be similar in general, and then focus on triangles and what criteria predict that two triangles will be similar. Length relationships within and...

 Student Outcomes Students create scale drawings of polygonal figures by the Ratio Method. Given a figure and a scale drawing from the Ratio Method, students answer questions about the scale factor...

 Students revisit what scale drawings are and discover two systematic methods of how to create them using dilations. The comparison of the two methods yield the Triangle Side Splitter Theorem and the...

 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...

 Geometry Module 2: Similarity, Proof, and Trigonometry Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2. To be able to discuss...