CCSS.Math.Content.5.MD.C.5c
The Standard
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.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students split a composite solid into two rectangular prisms with no gaps or overlap. They find each prism’s volume, add the volumes, and solve related measurement problems.
What Mastery Looks Like
- Students draw or mark a valid split that covers the whole solid without overlap. They calculate each prism’s volume, add the results, and label the answer in cubic units.
Common Misconceptions
- Students may add all side lengths instead of multiplying length, width, and height for each prism. They may count an overlapping region twice, omit part of the solid, or label volume with square units.
How to Assess It
- Exit ticket: An L-shaped solid is split into prisms measuring 4 by 3 by 2 units and 2 by 3 by 5 units. Find the total volume and show an equation.
Lesson moves
Ways to Teach It
Build an L-shaped solid with linking cubes, draw a partition into two rectangular prisms, then calculate and add both volumes.
Show two different partitions of the same solid and ask students to explain in writing why both totals must match.
Play Composite Volume Match: students pair solid diagrams with dimension cards and volume expressions, then check each match with a partner.
Use a stepped storage-box diagram and ask how many one-cubic-foot cartons fit when each rectangular section is filled.
Free download
Printable 5.MD.C.5c Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.5.MD.C.5c, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.5.MD.C.5b
Students must calculate each rectangular prism’s volume before adding the non-overlapping parts of a composite solid.
- CCSS.Math.Content.5.MD.C.3
Students must understand volume as measurable cubic space before adding volumes of rectangular-prism parts in a composite solid.
- CCSS.Math.Content.3.MD.C.7d
Decomposing composite area into rectangles directly supports decomposing composite volume into rectangular prisms and adding the parts.
Keep exploring
Related Standards
- CCSS.Math.Content.5.MD.C.5a
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 foun...
- CCSS.Math.Content.6.G.A.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show ...
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