Maryland Math 5.GR.C.5.a
The Standard
- 5.GR.C.5
- Relate volume to the operations of multiplication and addition and solve problems in context.
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 would be found by multiplying the edge lengths, or by multiplying the height by the area of the base. Represent products of three whole numbers as volumes, (e.g., to represent the associative property of multiplication).
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 build rectangular prisms from unit cubes and count the cubes in each layer. They multiply the cubes per layer by the number of layers, then compare that result with multiplying all three edge lengths.
What Mastery Looks Like
- For a 3 by 4 by 2 prism, a student finds 12 cubes per layer and 24 cubes total. They show that (3 × 4) × 2 and 3 × (4 × 2) both give 24 cubic units.
Common Misconceptions
- Some students count only visible cubes and miss cubes hidden inside. Others stop at the base area, add the three side lengths, or label the volume in square units.
How to Assess It
- Exit ticket: Draw a prism with a 3 by 4 base and height 2. Show the cubes in one layer and find the volume using two different groupings of the three edge lengths.
Lesson moves
Ways to Teach It
Build a 3 by 4 by 2 prism with linking cubes, separate its layers, and count the cubes in each layer.
Show a drawing of a 2 by 3 by 4 prism and ask, “Why do (2 × 3) × 4 and 2 × (3 × 4) match?”
Give each pair three number cards; have them sketch a prism and write two grouped products for its volume.
Draw a shipping box with inside dimensions 20 by 10 by 5 centimeters; calculate how many centimeter cubes could fill it.
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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.
- 5.GR.C.5.b
Apply the formulas V = (l)(w)(h) and V = (B)(h) for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve probl...
- 5.GR.C.5.c
Determine the volumes of composite figures by decomposing them into non-overlapping right rectangular prisms and adding their volumes together to solve problems...
- 6.GR.A.2
Find the volume of a right rectangular prism with fractional edge lengths.
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