Montana Math MT.7.G.5
The Standard
Solve geometrical problems including problems in context that involve area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 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 split compound shapes into triangles, quadrilaterals, and other polygons to find area. They find the volume and exposed surface area of cubes and right prisms, including joined solids. They use these calculations in community plans.
What Mastery Looks Like
- Given a floor plan, a student finds each piece's area without counting any region twice. For joined prisms, they find total volume and exposed surface area, using square and cubic units correctly.
Common Misconceptions
- Students may use a slanted side instead of the perpendicular height of a triangle. They may count joined faces as exposed surface area or label volume in square units.
How to Assess It
- Draw two cubes with 2 cm edges joined face to face. Ask students to find the total volume and exposed surface area, with units, and explain what happens to the joined faces.
Lesson moves
Ways to Teach It
Tape two cereal boxes together, measure them, and calculate their total volume and exposed surface area.
Ask partners why the joined faces of two cubes do not count in surface area; have them draw the exposed faces.
Draw composite floor plans and prism stacks on cards; have pairs match each drawing to an area, volume, or surface-area calculation.
Calculate planting area for a proposed Fort Peck Tribes garden: a 6-by-4-meter rectangle and a triangle with 4-meter base and 3-meter height.
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