8.MATH.6.B
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 8 · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.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 (the model to volume formulas for cylinders and cones) #dok3
- explain (the mathematical relationship between cylinder and cone volumes) #dok3
Learning Targets
- I can identify the parts of a cylinder and a cone needed to find volume. #dok1
- I can recall the formulas for finding the volume of a cylinder and a cone. #dok1
- I can use a model to show how the volumes of a cylinder and cone are related when they have congruent bases and heights. #dok2
- I can compare the volume of a cone to the volume of a cylinder with the same base and height. #dok2
- I can connect the physical or visual model to the algebraic formulas for cylinder and cone volumes. #dok3
- I can explain why the formula for the volume of a cone is one-third the volume of a cylinder with the same base and height. #dok3
Big Ideas
- The volume of a cone is one-third the volume of a cylinder with the same base and height.
- Models can be used to develop and connect geometric volume formulas.
Essential Questions
- How are the volumes of a cylinder and a cone with the same base area and height related?
- What does a physical or visual model reveal about the relationship between cylinder and cone volumes?
- Why is the volume of a cone one-third the volume of a cylinder with congruent bases and heights?
- How can geometric models help us understand and remember volume formulas for different shapes?
- In what real-world situations might you need to compare the volumes of cylinders and cones?