Montana Math MT.CORE.GEOM.MEAS.4.b
The Standard
- MT.CORE.GEOM.MEAS.4
- Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: Modeling and solving problems with 2D shapes by using the perimeter and area of polygons, circles, and composite shapes with portions removed, Modeling and solving problems with 3D solids by using surface area and volume of solids, including composite solids and solids with portions removed, and Deriving and applying the relationships between the lengths, perimeters, areas, and volumes of similar figures in relation to their scale factor.
Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: Modeling and solving problems with 3D solids by using surface area and volume of solids, including composite solids and solids with portions removed, and
2026 Montana Mathematics Content Standards · Geometric Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students break an object into familiar 3D shapes, including any parts cut out of it. They use measurements to find its volume or exposed surface area and explain what the answer means.
What Mastery Looks Like
- A student draws a labeled model and uses the dimensions to calculate volume. For surface area, they leave out faces where solids meet and include surfaces exposed by a cutout.
Common Misconceptions
- Students may count faces hidden where two solids meet. They may subtract a hole's volume but forget the new surface inside it, or label volume in square units.
How to Assess It
- A 10 cm by 8 cm by 6 cm block has a cylindrical hole of radius 2 cm drilled through its 6 cm height. Find its remaining volume and total exposed surface area, and show which surfaces you counted.
Lesson moves
Ways to Teach It
Join two small boxes, measure them, and calculate the model's volume and exposed surface area without counting the joined faces.
Sketch a box with a cylindrical hole drilled through it, then explain which surfaces disappear and which new surfaces appear.
Give pairs dimension cards for a box and a cylindrical cutout, then have them calculate remaining volume and check each other's units.
For a proposed Montana tribal community garden, use a labeled sketch of a water tank to calculate its capacity and outside paint area.
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Related Standards
- MT.CORE.GEOM.MEAS.4
Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems in context. This standard should incorporate ...
- MT.7.G.5
Solve geometrical problems including problems in context that involve area, volume, and surface area of two- and three-dimensional objects composed of triangles...
- MT.CORE.GEOM.MEAS.4.a
Modeling and solving problems with 2D shapes by using the perimeter and area of polygons, circles, and composite shapes with portions removed,
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