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
What this standard means
Students need to understand volume as the count of unit cubes that fill a solid shape. They should see that each cube takes up one cubic unit, and a shape’s volume is the total number of those cubes when they fit with no gaps or overlaps.
Mastery looks like building or viewing a rectangular prism and naming its volume in cubic units. Students can explain why the count matches the space filled. Common trouble spots are counting visible cubes only, leaving hidden cubes out, mixing up square units and cubic units, and not noticing gaps or overlaps.
Ways to teach it
- Have students pack small boxes with centimeter cubes, then record the total cubes used and the volume in cubic centimeters.
- Ask students to explain why a layer of 12 cubes stacked 3 layers high has a volume of 36 cubic units.
- Show three cube models, one with a gap, and ask students which one shows a correct volume count and why.
- Bring in a shipping box and ask students how cube packing could help estimate how many small items fit inside.
Plan a lesson for CCSS.Math.Content.5.MD.C.3b
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Related standards
- CCSS.Math.Content.5.MD.C.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
- 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.3.MD.C.5b
A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
- CCSS.Math.Content.5.MD.C.3a
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.