Virginia SOL 7.MG.1.d
The Standard
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 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 a rectangular prism's volume changes when one dimension is multiplied by one-fourth, one-third, one-half, 2, 3, or 4. They apply the same factor to the original volume and explain the result in context.
What Mastery Looks Like
- Students state that the volume changes by the same factor as the one changed dimension. They calculate the new volume and explain that the other two dimensions remain fixed.
Common Misconceptions
- Students may multiply the volume by the factor three times because volume uses three dimensions. They may change all dimensions instead of only one. They may also confuse multiplying by one-fourth with decreasing by one-fourth.
How to Assess It
- Exit ticket: A 6-by-4-by-9 storage bin has its height multiplied by one-third. Find the new volume and explain how it compares with the original volume.
Lesson moves
Ways to Teach It
Build a cube model of a rectangular prism, double one dimension, and compare the original and new cube counts.
Ask students to explain why tripling one dimension triples volume, while tripling all three dimensions does not.
Match cards showing dimension changes, such as one-half or four times, with cards showing the resulting volume change.
Compare shipping boxes when one dimension changes, then calculate how much packing space is gained or lost.
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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.e
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 contextua...
- 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.
- 4.CE.3.d
Apply the inverse property of multiplication in models (e.g., use a visual fraction model to represent 4 4 or 1 as the product of 4 × 1 4 ).
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