CCSS.Math.Content.5.MD.C.3b
The Standard
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.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use unit cubes to measure how much space a solid takes up. They count every cube and name the result in cubic units.
What Mastery Looks Like
- Students count all unit cubes in a packed solid, including cubes they cannot see directly. They state the volume with cubic units and explain why gaps or overlaps would make the measurement inaccurate.
Common Misconceptions
- Students may count only the visible cubes or report square units instead of cubic units. They may also think gaps, overlaps, or different cube sizes still give a valid volume count.
How to Assess It
- Exit ticket: A solid is packed with 18 unit cubes with no gaps or overlaps. What is its volume, and why?
Lesson moves
Ways to Teach It
Use snap cubes to build three rectangular prisms, then count the cubes and label each volume in cubic units.
Post this prompt: Explain why a cube model must have no gaps or overlaps when it represents volume.
Play Volume Match by pairing cards showing cube models, cube counts, and measurements in cubic units.
Pack a small box with centimeter cubes, then report how much space it holds in cubic centimeters.
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Printable 5.MD.C.3b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.5.MD.C.3b, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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