Montana Math MT.5.MD.5
The Standard
Relate volume to the operations of multiplication and addition and volume problems including problems in context by: Finding the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and showing that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base and representing the product of three whole numbers using the associative property of multiplication. Applying the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths including problems in context, and Recognizing volume as additive and finding volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve problems in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students pack rectangular prisms with unit cubes and count the cubes in each layer. They multiply three edge lengths, or multiply base area by height, to find volume. For a solid made of two joined prisms, they find each volume and add.
What Mastery Looks Like
- A student can show that four layers of six cubes give a 3 by 2 by 4 prism a volume of 24 cubic units. They can group the three factors in either order. They can split an L-shaped solid into two prisms, add their volumes, and label the answer in cubic units.
Common Misconceptions
- Students may add the three edge lengths or multiply only two of them. Some count squares on the outside instead of cubes inside. Others draw overlapping parts when splitting a solid and count the shared space twice.
How to Assess It
- Exit ticket: A 4 by 3 by 2 cm prism touches a 2 by 3 by 2 cm prism with no overlap. Find their total volume, showing each base area and your sum.
Lesson moves
Ways to Teach It
Build a 3 by 2 by 4 prism with unit cubes; count cubes by layer, then compare the count with 3 × 2 × 4.
Draw a 3 by 2 by 4 prism and explain why multiplying its base area by 4 gives the cube count.
Give pairs drawings of two joined prisms with labeled edges; partners mark the split, calculate each volume, and check each other's sum.
Sketch joined 4-by-3-by-2-foot and 2-by-3-by-2-foot soil beds for a hypothetical Blackfeet community garden; calculate their combined soil volume in cubic feet.
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