7.8.B
The Standard
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
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare the volumes of a triangular prism and triangular pyramid with the same base area and perpendicular height. They explain why the pyramid's volume is one-third of the prism's volume using words and equations.
What Mastery Looks Like
- Students state that the prism holds three times as much as the matching pyramid. They write the relationship as Vprism = Bh and Vpyramid = 1/3 Bh, then justify it.
Common Misconceptions
- Students may use the triangle area factor of one-half twice. They may forget the one-third factor for a pyramid or use slant height instead of perpendicular height.
How to Assess It
- Give students a triangular prism with volume 90 cubic units. Ask them to find and explain the volume of a matching triangular pyramid.
Lesson moves
Ways to Teach It
Fill an open triangular pyramid with rice, pour it into a matching prism, and count the three fills needed.
Write words and equations explaining why the one-third factor changes volume even when base area and height stay the same.
Play a card match using solid diagrams, dimensions, formulas, volumes, and prism-to-pyramid relationships.
Compare shipping packages shaped as triangular prisms and pyramids with equal base areas and heights, then calculate each package's capacity.
Keep exploring
Related Standards
- 7.8.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...
- 8.6.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
- 5.4.G
use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V...
- 7.9.A
solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.