Virginia SOL 7.MG.1.b
The Standard
Develop the formulas for determining the surface area of rectangular prisms and right cylinders and solve problems, including those in contextual situations, using concrete objects, two-dimensional diagrams, nets, and formulas.
Virginia Standards of Learning for Mathematics · The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students unfold or draw rectangular prisms and right cylinders as nets, then connect each part to an area formula. They use those formulas to find surface area in diagrams and real situations.
What Mastery Looks Like
- Students can use a net to explain why a rectangular prism has paired rectangular faces and why a cylinder includes two circles and one rectangle. They select dimensions correctly, calculate total surface area, and label answers in square units.
Common Misconceptions
- Students may use volume formulas when surface area is needed. They may omit a base, use diameter as radius, or treat the cylinder's curved surface as a circle. Some give cubic units instead of square units.
How to Assess It
- Give a rectangular prism measuring 3 by 4 by 8 and a cylinder with radius 3 and height 8. Ask students to sketch each net, write each surface area formula, and calculate both totals.
Lesson moves
Ways to Teach It
Build a rectangular prism and right cylinder from paper nets, label each dimension, then add the areas of all faces.
Ask students to explain why the cylinder's curved surface becomes a rectangle with length equal to the base circumference.
Match cards showing solids, nets, dimensions, formulas, and surface areas, then have partners justify each completed set.
Calculate the cardboard needed for a closed cereal box and a cylindrical oatmeal container using measurements from actual packages.
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Printable 7.MG.1.b Worksheet
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Related Standards
- 5.MG.2.d
Investigate and develop a formula for determining the volume of rectangular prisms using concrete objects.
- 5.MG.2.e
Solve problems, including those in context, to estimate and determine the volume of a rectangular prism using concrete objects, diagrams, and formulas when the ...
- 7.MG.1.c
Determine if a problem in context, involving a rectangular prism or right cylinder, represents the application of volume or surface area.
- 7.MG.1.a
Develop the formulas for determining the volume of right cylinders and solve problems, including those in contextual situations, using concrete objects, diagram...
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