Virginia SOL 5.MG.2.d
The Standard
Investigate and develop a formula for determining the volume of rectangular prisms using concrete objects.
Virginia Standards of Learning for Mathematics · The student will use multiple representations to solve problems, including those in context, involving perimeter, area, and volume.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students build rectangular prisms with unit cubes and count the cubes by rows and layers. They connect the count to multiplying length, width, and height.
What Mastery Looks Like
- Students can find the volume of a rectangular prism from a cube model or its dimensions. They explain that length times width counts one layer, then multiplying by height counts all layers.
Common Misconceptions
- Students may count only the visible cubes or confuse volume with the area of one face. Some add the three dimensions instead of multiplying them, or label answers with square units.
How to Assess It
- Give each student 24 cubes and ask them to build a 4 by 3 by 2 prism. Have them write a multiplication equation and explain how it matches the layers.
Lesson moves
Ways to Teach It
Give pairs 24 linking cubes to build every rectangular prism possible, then record length, width, height, cube count, and each dimension product.
Display a prism with a 4 by 3 base and 5 layers; ask students to explain why multiplication counts all cubes.
Play Dimension Draw: students draw three number cards, calculate the prism's volume, and earn a point after checking with cubes.
Measure a small storage box, calculate its volume, then test the result by filling it with identical cubes.
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Printable 5.MG.2.d Worksheet
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Determine the volume of cones and square-based pyramids, using concrete objects, diagrams, and formulas.
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