7adv.MATH.10.E
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 (Advanced) · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
volumetriangular prismtriangular pyramidcongruent basescongruent heightsformulasrelationship
Skills
- explain (relationship between the volume of a triangular prism and a triangular pyramid) #dok3
- connect (geometric relationships to volume formulas) #dok3
- describe (congruent bases and heights for three-dimensional figures) #dok2
- express (relationships verbally and symbolically) #dok3
Learning Targets
- I can describe the relationship between the volume of a triangular prism and a triangular pyramid with congruent bases and heights. #dok2
- I can explain the connection between the geometric relationship of prisms and pyramids and their volume formulas. #dok3
- I can express verbally and symbolically how the volume of a triangular prism compares to the volume of a triangular pyramid with the same base and height. #dok3
Big Ideas
- The volume of different three-dimensional figures with congruent bases and heights are related in predictable ways.
- Understanding and expressing geometric relationships helps connect concrete models to abstract volume formulas.
Essential Questions
- How is the volume of a triangular pyramid related to the volume of a triangular prism with the same base area and height?
- Why do the formulas for the volume of a prism and a pyramid differ?
- In what ways can geometric relationships be expressed both verbally and symbolically?
- How can models help you understand and explain volume formulas for three-dimensional figures?
- What must be true about the bases and heights of prisms and pyramids to compare their volumes meaningfully?