In 5.NF.B.4.B it states, “Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths…”
My question is about the phrase “unit squares.”
Is the intention that the area must be tiled by squares rather than simply rectangles?
In the Progressions document (p. 13) 3/4 x 5/3 is shown tiled with rectangles that are each 1/4 by 1/3 (not squares).
The area could be tiled with 1/12 by 1/12 squares (resulting in an area of 9/12 x 20/12 = 180/144) but this seems like it would unnecessarily complicate the problem.
My office has the same question. The language “tiling with unit squares” is the issue. Activities found online that address this standard seem to indicate that there are a variety of interpretations of this standard. Any insights would be appreciated.
So anyway, the basic idea here is this: I know that rectangle which is 1/n by 1/m has area 1/nm because I can fit nm of them in a unit square. So then I know that a rectangle with dimensions a/n and b/m has ab of those little rectangles, so its area is ab x 1/nm = ab/nm. In other words, the area of a rectangle with fractional side lengths is the product of the side lengths. Of course, curricula often treat this as completely obvious, which is a shame, because the reasoning is fun.