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
What this standard means
Students need to see a solid figure as parts that do not overlap. They should split an irregular rectangular solid into two rectangular prisms, find each volume with length times width times height, then add the volumes. They also need to choose a sensible split when more than one is possible.
Mastery looks like cleanly decomposing the shape, labeling dimensions, calculating both smaller volumes, and explaining why the total is the sum. Students often get stuck using outside edge lengths that do not belong to one prism, double-counting a shared space, or adding all visible numbers instead of finding each prism’s volume.
Ways to teach it
- Build an L-shaped solid with unit cubes, have students split it into two rectangular prisms, then record both volume equations.
- Prompt students to explain which two prisms they see in an irregular solid and why the parts do not overlap.
- Show a composite prism diagram with labeled edges and ask students to write the two volume expressions before solving.
- Use a storage closet sketch with two rectangular sections and ask students to find how many cubic feet of supplies it can hold.
Plan a lesson for CCSS.Math.Content.5.MD.C.5c
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.5.MD.C.3
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
- CCSS.Math.Content.5.MD.C.5a
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