Teacher Resources

## Collection Contents

### Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

by Allen Wolmer

Exercises from Illustrative MathematicsA set of 4 exercises, commentary, and solutions
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### Students understand the definitions of a general prism and a cylinder and the distinction between a cross-section and a slice.

by Allen Wolmer

Teacher and Student versions of full lesson from engageNY
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### Students understand the precise language that describes the properties of volume.

by Allen Wolmer

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×height.Teacher and Student versions of full lesson from engageNY
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### Students use Cavalieri’s principle

by Allen Wolmer

Students use Cavalieri’s principle and the cone cross section theorem to show that a general pyramid or cone has volume (1/3)Bh where B is the area of the base and h is the height by comparing it with a right rectangular pyramid with base area B and height h.Teacher and Student versions of full lesson from engageNY
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### Students give an informal argument using Cavalieri’s principle for the volume formula of a sphere

by Allen Wolmer

Students give an informal argument using Cavalieri’s principle for the volume formula of a sphere and use the volume formula to derive a formula for the surface area of a sphere.Teacher and Student versions of full lesson from engageNY
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### Visualize cross-sections of three-dimensional objects. Have an understanding of how a 3D printer works and its relation to Cavalieri’s principle.

by Allen Wolmer

Visualize cross-sections of three-dimensional objects.Have an understanding of how a 3D printer works and its relation to Cavalieri’s principle.Teacher and Student versions of full lesson from engageNY
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### Areas and Volumes

by Allen Wolmer

A link to a page containing many lessons, videos, exercises, and text from CK-12. Additional resources available at this site.
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