5th Grade · Measurement & Data
5.MD.C.5: Find the volume of a box by multiplying its length, width, and height
5.MD.C.5 is a 5th grade Common Core math standard in Measurement & Data. Here’s what it really covers, and how you can help your students learn it.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
The standard
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. 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 in the context of solving real world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
In plain words
Find the volume of a box by multiplying its length, width, and height.
Sample questions from student practice
These questions from Bobby's Math Club are the kinds of questions your students will see. You can try answering them to see what a student might see.
Question 1 of 3
Pablo knows the area of the bottom of his toy chest. What else does he need to know to find the volume of the chest?
- Nothing more, because the area is the volume
- Its height
- The distance around its bottom
Where students can get stuck
- Adding the three dimensions instead of multiplying, so a 4 by 3 by 2 box gets a volume of 9, not 24.
- Multiplying only two dimensions, finding the area of the base and forgetting to multiply by the height.
- Counting the overlap twice when splitting an L-shaped solid into two boxes, or using the whole shape's length for one part.
Effective teaching strategies
- Have students fill a box layer by layer, find that a 4 by 3 base holds 12 cubes per layer, and multiply by the 2 layers to get 24.
- Write the volume of a box as length × width × height and as base area × height, and ask students what each factor counts.
- Split an L-shaped solid into two boxes in a drawing with students, find each volume, and add them while checking that no part is counted twice.
Units that teach this standard
Find where 5.MD.C.5 lands in the program you teach. Each unit has a guide written for families. Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence.
Bridges in Mathematics
enVision Mathematics
Eureka Math²
Everyday Mathematics
i-Ready Classroom Mathematics
Illustrative Mathematics
Math Expressions
Reveal Math
Don’t see your curriculum? Contact Bobby and we’ll see if we can help!
Share it with families
Families can read Finding the volume of a box for a plain-language look at this skill, with three questions to try together and ideas for helping at home.
Help every student practice measurement and data at home
In Bobby's Math Club, students practice at just the right level, with a hint when they need one, a clear explanation after every question, and kid-friendly videos. Unlimited practice is free for every family.
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Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.