Virginia SOL 7.MG.1.e
The Standard
Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a factor of 1 2 or 2, including those in contextual situations.
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 determine how halving or doubling one dimension changes a rectangular prism’s surface area. They explain that only the faces using that dimension change, while the other pair stays the same.
What Mastery Looks Like
- Students correctly compare the original and changed surface areas when one dimension is halved or doubled. They use a formula, net, or face areas to explain which faces change and which stay the same.
Common Misconceptions
- Students may think doubling one dimension always doubles the total surface area, or halving one dimension halves it. They may also change every dimension or forget that one pair of faces stays unchanged.
How to Assess It
- Exit ticket: A prism measures 8 by 3 by 2 units. Find its surface area, then halve the height and explain why the new surface area is not half the original.
Lesson moves
Ways to Teach It
Build 4-by-3-by-2 and 8-by-3-by-2 prisms from cubes, then count and compare the exposed square faces.
Write a response to: Why does doubling one edge of a rectangular prism not always double its surface area?
Sort cards showing original prisms, changed dimensions, and matching surface area calculations, then check each match with a partner.
Compare packaging boxes when one dimension doubles, and calculate how much extra cardboard each redesigned box requires.
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Printable 7.MG.1.e Worksheet
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Related Standards
- 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.b
Develop the formulas for determining the surface area of rectangular prisms and right cylinders and solve problems, including those in contextual situations, us...
- 7.MG.1.d
Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a factor of 1 4 , 1 3 , 1 2 , 2, 3, or 4, including thos...
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