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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the volume of rectangular prisms whose edge lengths include fractions. They model the prism with fractional cubes, multiply its dimensions, and use the result to solve problems.
What Mastery Looks Like
- Students partition a prism into equal fractional cubes and account for each cube's volume. They multiply the three edge lengths, label the result in cubic units, and explain why both methods agree.
Common Misconceptions
- Students may count each small cube as one cubic unit, even when its edges are fractional units. They may add edge lengths, multiply only two dimensions, or label volume with square units.
How to Assess It
- Exit ticket: A prism measures 1 1/2 by 1 by 1/2 units. Show its volume using half-unit cubes and multiplication.
Lesson moves
Ways to Teach It
Build a 1 1/2 by 1 by 1/2 prism from half-unit cubes, then compare the cube count with the product of its dimensions.
Ask students to explain why six half-unit cubes have a total volume of 3/4 cubic unit, not six cubic units.
Match cards showing prism dimensions, fractional-cube diagrams, multiplication expressions, and volumes, then justify each completed set to a partner.
Measure a small storage box to the nearest half inch, then calculate how many cubic inches it can hold.
Free download
Printable 6.G.A.2 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.6.G.A.2, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetBefore This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.5.MD.C.5b
Students extend prism volume formulas and base-area reasoning from whole-number edges to fractional edge lengths and unit-fraction cubes.
- CCSS.Math.Content.5.MD.C.5a
Students extend unit-cube packing and length times width times height from whole-number edges to fractional edge lengths.
- CCSS.Math.Content.5.NF.B.4b
Fractional rectangle area and unit-fraction tiling carry into prism volume as base area, unit-cube packing, and multiplying fractional edges.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.7.G.B.6
Rectangular prism volume with fractional edges supports later volume and surface area work for prisms and composite 3D objects.
- CCSS.Math.Content.8.G.C.9
Rectangular prism volume develops volume units, fractional dimensions, and formula use that support applying cylinder, cone, and sphere formulas.
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