NY Next Generation Math NY-7.G.6
The Standard
Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles and trapezoids.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decompose flat figures into triangles and trapezoids, treating quadrilaterals with at least one pair of parallel sides as trapezoids, and combine the areas. They use nets or labeled faces to find surface area of right prisms and pyramids, and use base area times height to find volumes of triangular prisms and joined rectangular prisms.
What Mastery Looks Like
- Given a compound figure, the student identifies perpendicular heights and calculates each nonoverlapping part once. For solids, the student accounts for every exposed face, chooses the correct base area and perpendicular height, and separates composite volume into nonoverlapping rectangular prisms.
Common Misconceptions
- Students may use slanted lengths as heights, omit the one-half factor for triangles, or overlook that parallelograms count as trapezoids under the inclusive definition. They may count hidden faces, confuse surface area with volume, or use a rectangular-base formula for a triangular prism.
How to Assess It
- Give a four-section exit ticket with labeled dimensions: composite triangle-trapezoid area; surface area of a right prism and right pyramid; triangular-prism volume; and composite rectangular-prism volume.
Lesson moves
Ways to Teach It
Build prism and pyramid nets, label exposed triangular and trapezoidal faces, then fold the nets to check the surface-area total.
Ask students why surface area uses square units while the same solid's volume uses cubic units.
Run a card sort matching composite figures and solids with decompositions, formulas, units, and completed calculations.
Estimate material and storage needs for a package made from joined prism-shaped sections, then calculate its surface area and volume.
Keep exploring
Related Standards
- NY-6.G.1
Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in ...
- NY-6.G.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these tech...
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