6.G.2: Volume with Fractional Edge Lengths
Also written as 6.G.A.2 and CCSS.MATH.CONTENT.6.G.A.2 · Cluster: Solve real-world and mathematical problems involving area, surface area, and volume.
The Official Wording
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, Grade 6, Geometry · Read it at the source · Checked October 14, 2026
What 6.G.2 Means in Plain English
Sixth graders find the volume of a box whose edges are fractions, like 3 by 2½ by 1½ inches. They pack it with ½-inch cubes, 6 by 5 by 3, count 90, and remember that 8 small cubes make one cubic inch, so the box holds 11¼ in³.
Then they multiply the edges, 3 × 5/2 × 3/2 = 45/4, and see the formula agree with the count. That is the point: the formula works for any lengths. 7th grade applies it to prisms with other bases (7.G.6), and 8th grade reaches cylinders and cones (8.G.9).
6.G.2 I Can Statements
- I can pack a box with unit-fraction cubes and count them.
- I can use V = l w h when the edges are fractions.
- I can show that counting cubes and multiplying edges give the same volume.
6.G.2 Worked Example
A gift box with half-inch edges, packed with cubes first and multiplied second, so both methods meet at 11¼.
A small gift box is 3 in long, 2½ in wide and 1½ in tall. What is its volume?
- The edges are halves, so pack with ½-inch cubes. Count how many fit along each edge.3 ÷ ½ = 6, 2½ ÷ ½ = 5, 1½ ÷ ½ = 3
- Multiply to count the cubes: a bottom layer of 6 by 5, stacked 3 high.6 × 5 × 3 = 90 cubes
- A ½-inch cube is not half a cubic inch. Eight of them make one cubic inch (2 × 2 × 2), so each is ⅛ in³.90 × ⅛ = 90/8 = 11¼ in³
- Now use the formula with the fractional edges and see that it lands in the same place.V = 3 × 5/2 × 3/2 = 45/4 = 11¼ in³
Check it: Multiply in two steps: 3 × 2½ = 7½, and 1½ of 7½ is 7½ + 3¾ = 11¼. It also sits between 3 × 2 × 1 = 6 and 3 × 3 × 2 = 18, where a box of this size belongs.
Common Mistakes with 6.G.2
Treating a ½-inch cube as ½ in³
90 cubes × ½ = 45 in³
Try this: Build one cubic inch from ½-inch cubes with real blocks: it takes 8 of them, so each small cube is ⅛ in³.
Multiplying only the whole parts
3 × 2½ × 1½ = 3 × 2 × 1 = 6 in³
Try this: Convert each mixed number to an improper fraction before multiplying, 5/2 and 3/2 here, or multiply in two steps and keep the halves.
Finding surface area instead
2(3 × 2½) + 2(3 × 1½) + 2(2½ × 1½) = 31½
Try this: Say what each formula measures: surface area is the wrapping paper in in², volume is the filling in in³. Packing with cubes settles it.
Where 6.G.2 Fits
Practice 6.G.2
Quick Check
- A box is 4 in by 2½ in by 2 in. How many ½-inch cubes fill it, and what is its volume?
- Find the volume of a prism 1½ ft by 1½ ft by 2 ft.
- A fish tank has a base of 2½ ft by 1 ft and holds 5 ft³ of water. How deep is the water?