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This Use Cavalieri’s Principle to Compare Aquarium Volumes activity also includes:
- Answer Key
- Worksheet
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Learners are designing a stunning new water feature for an aquarium, but they soon discover that more than just a pretty home for their fishy friends is required. From calculating the volume of a composite shape through the abstract development of cross-sectional area formulas, these seemingly simple problems have some serious geometric chops! A capstone application of Cavalieri's principle ties the whole activity together, relating volumes of different shapes in a satisfying way.
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CCSS:
Designed
Concepts
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Instructional Ideas
- Aquarium filling could be simulated using physical models before abstract calculations are performed
- Could be linked with a science unit or lesson on Cavalieri's Principle
- Possible introduction problem to larger project on solid volumes and cross-sectional areas or volumes of rotation
Classroom Considerations
- Those not familiar with Cavalieri's principle will need an explanation of that key concept
- Student worksheet not separated from teacher notes and answer key
Pros
- Multi-step problem really encourages mathematical thinking and development of logical reasoning
- Application of volume formulas in an interesting context
Cons
- Right margin cut off by up to several letters in some places
- Described as leading students toward discovering the formula for the volume of a sphere, but this is not developed in the lesson