7.MATH.8.B

Explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular 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
volumetriangular prismtriangular pyramidcongruent basesheightsrelationshipformulasverbal explanationsymbolic explanation
Skills
  • explain (the relationship between the volume of triangular prisms and triangular pyramids) #dok2
  • describe (how congruent bases and heights relate to volume formulas) #dok2
  • connect (the relationship to the appropriate volume formulas) #dok3
  • represent (the volume relationship verbally and symbolically) #dok3
Learning Targets
  • I can identify the formulas for the volume of a triangular prism and a triangular pyramid. #dok1
  • I can define congruent bases and heights in three-dimensional shapes. #dok1
  • I can explain the relationship between the volume of a triangular prism and a triangular pyramid with congruent bases and heights. #dok2
  • I can describe verbally and symbolically how the volumes of these shapes are connected. #dok2
  • I can connect the relationship between a prism’s and a pyramid’s volume to their respective formulas. #dok3
  • I can justify why the volume of a triangular pyramid is one-third the volume of a triangular prism with the same base and height. #dok3
Big Ideas
  • The volume of a triangular pyramid is one-third the volume of a triangular prism with the same base and height.
  • Understanding how formulas for volume are related helps students apply reasoning to new three-dimensional shapes.
Essential Questions
  • How are the volumes of a triangular prism and a triangular pyramid with the same base and height related?
  • Why is the volume of a triangular pyramid one-third the volume of a triangular prism with congruent bases and heights?
  • How do we explain the relationship between these volumes both verbally and symbolically?
  • How does understanding this relationship help us remember and apply volume formulas?
  • What real-world situations might require comparing the volumes of prisms and pyramids?