7adv.MATH.10.F

Model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas.

Grade 7 (Advanced) · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
modelrelationshipvolumecylinderconecongruent basesheightsformulas
Skills
  • model (the relationship between the volume of a cylinder and a cone with congruent bases and heights) #dok2
  • compare (formulas for volume of cylinders and cones) #dok2
  • connect (models to volume formulas) #dok3
  • explain (how the volume changes from cylinder to cone) #dok2
Learning Targets
  • I can model the relationship between the volume of a cylinder and a cone with congruent bases and heights. #dok2
  • I can compare the formulas for the volume of a cylinder and a cone. #dok2
  • I can explain how using the same base and height affects the volumes of cylinders and cones. #dok2
  • I can connect models to the formulas for volume of a cylinder and a cone. #dok3
  • I can justify why the cone’s volume is one-third of the cylinder’s with the same base and height. #dok3
Big Ideas
  • The volume of a cone with a given base and height is one-third the volume of a cylinder with the same base and height.
  • Using models helps clarify and justify the volume formulas for cylinders and cones.
Essential Questions
  • How does the volume of a cone compare to the volume of a cylinder with the same base and height?
  • Why is modeling important in understanding geometric formulas?
  • What happens to the volume when the base or height changes for both cylinders and cones?
  • How do you connect your model to the actual formula for volume?
  • Why do you think the cone holds less volume than the cylinder with congruent bases and heights?