7.9.A
The Standard
solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the base area of a solid, then use its perpendicular height to calculate volume. They decide when to include the one-third factor for a pyramid.
What Mastery Looks Like
- Students select the correct formula, identify the base area and perpendicular height, and show each step. They give reasonable answers in cubic units and explain why a pyramid has one-third the volume of a matching prism.
Common Misconceptions
- Students often forget the one-third factor for pyramids or the one-half factor when finding a triangular base area. They may use slant height instead of perpendicular height. Some label volume with square units instead of cubic units.
How to Assess It
- Give this exit ticket: A triangular prism and pyramid each have base legs 6 cm and 8 cm and height 9 cm. Find both volumes.
Lesson moves
Ways to Teach It
Build matching prism and pyramid models from nets, then use rice to test that three pyramid fills equal one prism fill.
Ask students to explain why slant height cannot replace perpendicular height in a volume calculation.
Play a card sort matching solid diagrams, dimensions, formulas, and calculated volumes.
Calculate the storage space in a cereal box and the air space inside a triangular prism tent.
Keep exploring
Related Standards
- 6.8.C
write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms wher...
- 8.7.A
solve problems involving the volume of cylinders, cones, and spheres
- 6.8.D
determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimens...
- 7.9.D
solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining...
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