Maryland Math 7.GR.B.4.a
The Standard
- 7.GR.B.4
- Solve mathematical problems with and without context involving area, surface area, and volume of two- and three-dimensional objects.
Solve problems involving area, surface area, and volume of polygonal figures and polyhedral solids, including triangles, quadrilaterals, other polygons, cubes, right prisms, and pyramids—figures defined by edges and flat faces.
Maryland College and Career Ready Standards for Mathematics (2025) · REASON WITH AND ABOUT GEOMETRIC FORMULAS TO SOLVE PROBLEMS AND JUSTIFY SOLUTIONS IN CONTEXT.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students split polygons into familiar shapes to find area. They add the areas of flat faces to find surface area. They use base area and perpendicular height to find the volume of prisms and pyramids.
What Mastery Looks Like
- A student can break an irregular polygon into triangles and rectangles and add their areas. They can account for every face of a solid, divide by three for pyramid volume, and use square or cubic units correctly.
Common Misconceptions
- Students may use slant height instead of perpendicular height for pyramid volume. They may leave out a hidden face when finding surface area or forget to divide by three for pyramid volume.
How to Assess It
- Exit ticket: A right triangular prism has a base with legs of 3 cm and 4 cm and a hypotenuse of 5 cm; its length is 8 cm. Find its surface area and volume, with units.
Lesson moves
Ways to Teach It
Cut and fold a grid-paper net of a 3 by 4 by 5 cm prism; find its surface area and volume.
Show two ways to split an L-shaped polygon into rectangles; explain why both give the same area.
Match volume cards marked 72 and 24 cm³ to a 6 by 4 by 3 cm prism and a pyramid with the same base and height.
Draw a closed square-pyramid gift box with a 6 cm base edge and 5 cm slant height; calculate the paper needed.
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Printable 7.GR.B.4.a Worksheet
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Related Standards
- 6.GR.A.4
Represent three-dimensional figures (triangular prism, rectangular prism, pyramid) using nets made up of rectangles and triangles, and use the nets to find the ...
- 7.GR.B.4
Solve mathematical problems with and without context involving area, surface area, and volume of two- and three-dimensional objects.
- 6.GR.A.1
Find the area of triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and quadrilaterals to solve problems.
- 7.GR.B.4.b
Solve problems involving volume of curved-surface solids, including cones, cylinders, and spheres—figures without edges.
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