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 In this installment of the video professional development series, there are two videos for small groups of educators to learn from the Common Core in practice. The first video does not include...

 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 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...

 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...

 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 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 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.

 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 the definitions of a general prism and a cylinder and the distinction between a crosssection and a slice.

 Student Outcomes Students understand the definition of a general pyramid and cone and that their cross sections are similar tothe base. Students show that if two cones have the same base area and the...

 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 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 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 crosssections of threedimensional objects. Have an understanding of how a 3D printer works and its relation to Cavalieri’s principle.

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...

 Student Outcomes Students will be able to give an informal argument using Cavalieri’s principle for the formula for the volume of a sphere and other solid figures.