5th Grade · Measurement & Data
5.MD.C.3: Understand volume: how many cubes it takes to fill a solid shape
5.MD.C.3 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
Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
In plain words
Understand volume: how many cubes it takes to fill a solid shape.
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
Hana stacks 12 unit cubes into a tall tower. Then she takes it apart and uses all 12 cubes to build a long, low wall. How does the volume of the wall compare with the volume of the tower?
- They have the same volume
- The tower has more volume
- The wall has more volume
Where students can get stuck
- Confusing volume with area, counting the squares on one face of a box instead of the cubes inside.
- Ignoring gaps and overlaps, estimating a box's volume by tossing in cubes loosely and counting them.
- Assuming the taller container always holds more, when a short, wide box can hold more than a tall, narrow one.
Effective teaching strategies
- Have students fill an open paper box with unit cubes one layer at a time, count the cubes in each layer, and say that volume is the space inside the box and not the faces outside.
- Give students a tall, narrow open paper box and a short, wide one, and have them predict which holds more before filling each with unit cubes.
- Ask students to pack cubes with no gaps and no overlaps, and explain why cubes dropped in loosely cannot give the volume.
Units that teach this standard
Find where 5.MD.C.3 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 Volume: how much space is inside a solid 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.
See how it works for teachers
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.