Maryland Math 5.GR.C.5.c
The Standard
- 5.GR.C.5
- Relate volume to the operations of multiplication and addition and solve problems in context.
Determine the volumes of composite figures by decomposing them into non-overlapping right rectangular prisms and adding their volumes together to solve problems in context
Maryland College and Career Ready Standards for Mathematics (2025) · UNDERSTAND CONCEPTS OF VOLUME AND RELATE VOLUME TO MULTIPLICATION.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students split a stepped solid into rectangular prisms that do not overlap. They find each prism’s volume, then add the volumes to answer a question about the whole solid.
What Mastery Looks Like
- A student can mark a clear split on a drawing and use the dimensions to find each part’s volume. Their total includes every part once and uses cubic units.
Common Misconceptions
- Some students count the same section twice or leave part of the solid out. Others add side lengths instead of finding each prism’s volume, or label the answer in square units.
How to Assess It
- Exit ticket: A stepped storage box has two non-overlapping parts measuring 3 × 2 × 2 inches and 2 × 2 × 1 inches. Find its total volume and show the volume of each part.
Lesson moves
Ways to Teach It
Build 3 × 2 × 2 and 2 × 2 × 1 blocks with snap cubes, join them, and count the cubes two ways.
Sketch a stepped solid on the board and ask, “Where would you split it so no cubes overlap or go missing?”
Give pairs four dimensioned sketches of stepped solids; partners mark the splits, calculate the volumes, and check each other’s totals.
Draw a stepped planter with soil sections measuring 4 × 2 × 1 feet and 2 × 2 × 2 feet; find the soil volume.
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Related Standards
- 6.GR.A.2.a
By packing prisms with unit cubes and using estimation to show that the volume can be found by multiplying the edge lengths of the prism.
- 3.GR.C.7.c
Determine the area of composite rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas.
- 5.GR.C.5.a
Find the volume of a right rectangular prism with whole-number side lengths by filling it with unit cubes in layers and show that the volume is the same as woul...
- 6.GR.A.2
Find the volume of a right rectangular prism with fractional edge lengths.
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