5.NF.B.4.B Tiling with Unit Squares

Home Forums Questions about the standards 3–5 Fractions 5.NF.B.4.B Tiling with Unit Squares

This topic contains 5 replies, has 3 voices, and was last updated by  Bill McCallum 3 months, 4 weeks ago.

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  • #3417 Reply

    ChristyG
    Member

    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.

    #3750 Reply

    dlward6
    Member

    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.

    #3751 Reply

    Bill McCallum
    Keymaster

    This is an error in the standards (I’ve noted it before in these pages, but, of course, that’s difficult to find!). It should say “squares with unit fraction side lengths.”

    #3752 Reply

    dlward6
    Member

    Thanks for the quick response. I am still a bit confused by the variations in lesson that address this topic. Dr. Wu’s example on Page 52 of the document found at the website below https://math.berkeley.edu/~wu/CCSS-Fractions_1.pdf offers a different approach than one found on Engage New York’s site at
    https://www.engageny.org/resource/grade-5-mathematics-module-5-topic-c-overview
    Do either of the approaches target this standard?
    Thank you!

    #3753 Reply

    Bill McCallum
    Keymaster

    Wu’s approach looks right to me. I’m not seeing the EngageNY approach, just a list of objectives. Am I missing something?

    #3754 Reply

    Bill McCallum
    Keymaster

    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.

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