Montana Math MT.5.MD.3
The Standard
Recognize volume as an attribute of solid figures and understand concepts of volume measurement by: Understanding that 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, and Understanding that 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.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use cubes with sides one unit long to measure how much space a solid takes up. They count the cubes needed to fill it, with no gaps or overlaps, and give the volume in cubic units.
What Mastery Looks Like
- A student identifies one unit cube as one cubic unit. They count all the cubes in a packed solid, including hidden cubes, and explain why that count is its volume.
Common Misconceptions
- Students may count only the cubes they can see and miss cubes in the back. Some count squares on the outside instead of cubes filling the solid, or think a shape with gaps is fully packed.
How to Assess It
- Show a drawing of a 2-by-2-by-2 block made of unit cubes. Ask students to write its volume and explain how they counted cubes they cannot see.
Lesson moves
Ways to Teach It
Give pairs eight wooden unit cubes to build a 2-by-2-by-2 block, then have them label its volume.
Show a cube drawing and ask students to explain why counting its outside squares will not give its volume.
Show three unit-cube stacks, one with a missing corner, and have partners count the cubes and check each other's answers.
Ask students to sketch how 1-inch cubes would fill a 2-inch by 3-inch by 1-inch shipping box.
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Printable MT.5.MD.3 Worksheet
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