Alexei is right, I think it makes sense to replace “unit cubes” with “rectangular prisms with unit fraction side lengths” here. One of these days I will publish my glitch file!

Although I would point out that you could use unit cubes. For example, you can pack a $\frac13$ by $\frac15$ by $\frac17$ rectangular prism with unit cubes with side length $\frac1{3\times5\times7}$, forming a $5 \times 7$ by $3 \times 7$ by $3 \times 5$ array. But in the end you still have to find the volume of the cube, and the natural way to do that is by seeing how many of them fit into a cube with side length 1. Since that’s also the way you would find the volume of a rectangular prism with unit fraction side lengths, I think it makes more sense to do the latter directly.

Probably way more answer than you wanted!

Bill,

Your reply above seems to suggest that 6.G.2 is calling for some sort of hands-on manipulative activity, which seems wildly impractical to me. Your reply above is also at odds with the answer you gave us in July 2010 when we asked essentially the same question. Your answer then was, “Certainly the intention was not to mandate any manipulative activity,
but rather to describe how to conceive of the volume of a prism with
fractional side lengths. This could be aided by manipulatives,
drawings, computer animation, verbal description … how to bring
about the conceptual understanding is not mandated.” Jason Zimba also responded to us at that time, saying, “I myself at least always thought of this as a pencil and paper diagrammatic argument, not a manipulative activity.”
So, which is it? Are you proposing that teachers try to obtain actual “unit cubes of the appropriate unit fraction edge lengths”? Or even, as you now seem to be proposing, “rectangular prisms with unit fraction side lengths”? Or is this a thought experiment, as we thought you and Jason were saying three years ago?

Andy