Montana Math MT.6.G.4
The Standard
Represent three-dimensional figures using nets made up of rectangles and triangles and use the nets to find the surface area of these figures in problems including 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 draw nets that show every rectangular and triangular face of a solid. They find each face's area and add them to work out how much material covers the solid.
What Mastery Looks Like
- A student can draw and label a net that folds into the given solid, with matching edges and no missing faces. They calculate the total area and label it in square units.
Common Misconceptions
- Students may leave off a face they cannot see, such as the bottom or a triangle end. Some forget to halve the area of a triangle or add edge lengths instead of face areas.
How to Assess It
- Exit ticket: A triangular prism has right triangle ends with sides of 3, 4, and 5 cm. Its length is 8 cm. Draw its net and find its surface area.
Lesson moves
Ways to Teach It
Give pairs grid paper and a cardboard triangular prism; have them trace and cut a net, then label each face's area.
Ask students to sketch two nets for the same triangular prism and explain why both give the same surface area.
Give pairs three dimensioned net cards, one missing a face; have them spot the error and calculate the complete nets' areas.
Draw a net for a 30 by 20 by 10 cm display case for a Montana Indigenous artist's public exhibition; calculate plastic needed.
Free download
Printable MT.6.G.4 Worksheet
A ready-to-print activity worksheet aligned to MT.6.G.4, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- 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.5.G.2
Represent problems including problems in context by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in t...
- MT.6.G.1
Find the area of triangles, quadrilaterals, and other polygons by composing them into rectangles or decomposing them into triangles and other shapes. This stand...
- MT.5.NF.6
Solve problems in context that involve multiplication of fractions and mixed numbers. This standard should incorporate cultural context relating to Montana Indi...
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.
Also for this standard:Make a WorksheetMake a QuizMake a Sub Lesson