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This The Volume of Prisms and Cylinders and Cavalieri’s Principle lesson plan also includes:
- Extending to Three Dimensions - Module Overview (PDF)
- Extending to Three Dimensions - Module Overview (Doc)
- The Volume of Prisms and Cylinders and Cavalieri’s Principle (Doc)
- The Volume of Prisms and Cylinders and Cavalieri’s Principle (PDF)
- The Volume of Prisms and Cylinders and Cavalieri’s Principle (Doc)
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Young mathematicians examine area of different figures with the same cross-sectional lengths and work up to volumes of 3D figures with the same cross-sectional areas. The instruction and the exercises stress that the two figures do not have to be the same but do need to have the same heights.
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CCSS:
Designed
Concepts
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Instructional Ideas
- Use two different solids that would have the same cross sectional areas, such as a cylinder and prism
Classroom Considerations
- Some pupils may have a problem with recognizing equal areas, especially if the shapes are different
- Parallel slices are the same as cross sections
- The tenth module in a 14-part series
Pros
- Provides concrete examples of Cavalieri's Principle
- The proof is not a complicated rigorous proof; it is more informal and can be understood at this grade level
Cons
- None