CCSS.Math.Content.6.G.A.2
The standard
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
Common Core State Standards for Mathematics · Geometry
What this standard means
Students need to understand volume as packing space, not just using a formula. They should build or picture a rectangular prism with fractional side lengths, choose a matching fractional unit cube, count how many fit, and connect that count to length times width times height.
Mastery means students can use both packing and multiplication to find volume with fractions, label cubic units, and solve word problems. Common snags are mixing up square and cubic units, multiplying only two dimensions, choosing the wrong unit fraction cube, and treating fractions as whole-number counts.
Ways to teach it
- Have students build prism models on grid paper using dimensions like 2 by 1/2 by 3/4, then count fractional cubes by layers.
- Ask students to explain why a box measuring 1/2 by 1/2 by 1/2 has volume 1/8 cubic unit.
- Give three prism problems with fractional edges and ask students to find volume, label units, and show one model or layer sketch.
- Use a small shipping box problem where students calculate how much space is inside when side lengths include halves or quarters of a foot.
Plan a lesson for CCSS.Math.Content.6.G.A.2
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- CCSS.Math.Content.5.NF.B.4b
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- CCSS.Math.Content.5.MD.C.5b
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