7.MATH.8.A

Model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas.

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

Standard Unwrapping

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Vocabulary
modelrelationshipvolumerectangular prismrectangular pyramidcongruent basescongruent heightsformulas
Skills
  • model (relationship between the volume of rectangular prisms and rectangular pyramids with congruent bases and heights) #dok2
  • connect (the relationship to the volume formulas for these shapes) #dok3
  • compare (volumes of prisms and pyramids with congruent bases and heights) #dok2
  • generalize (how formulas relate to the modeled relationships) #dok3
Learning Targets
  • I can identify the bases and heights of rectangular prisms and pyramids. #dok1
  • I can recognize congruent bases and heights in prisms and pyramids. #dok1
  • I can model the relationship between the volumes of a rectangular prism and a rectangular pyramid with congruent bases and heights. #dok2
  • I can compare the volume of a rectangular prism to the volume of a rectangular pyramid when their bases and heights are congruent. #dok2
  • I can explain how the volume of a rectangular pyramid relates to the volume of a rectangular prism using models. #dok3
  • I can connect the relationship observed in models to the actual volume formulas for prisms and pyramids. #dok3
Big Ideas
  • The volume of a rectangular pyramid is one-third the volume of a rectangular prism when they have congruent bases and heights.
  • Modeling with concrete or visual representations helps in understanding and justifying volume formulas for three-dimensional shapes.
Essential Questions
  • How is the volume of a rectangular pyramid related to the volume of a rectangular prism with the same base and height?
  • Why does a rectangular pyramid have less volume than a prism with the same base and height?
  • How can models help us understand the mathematical formulas for volume?
  • What real-world situations might require knowing the relationship between the volumes of prisms and pyramids?
  • In what ways can we justify the formula for the volume of a rectangular pyramid?