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Standard 3.MD.4 asks students to generate and record lengths in halves and quarters of an inch. Presumably this means they are to use mixed numbers and the bottom example in the margin on page 10 of the MD Data Progressions certainly shows this. This seems to go beyond any explicit expectations for fractions in Grade 3 – neither the Standards nor Progressions suggest mixed numbers in Grade 3 (general comments about “fractions” notwithstanding). Is this measurement standard the expected extent of mixed numbers in Grade 3?
Good points, Duane. The measurement standard in question is
3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.
It’s a very interesting question whether this is introducing mixed numbers or not. A ruler marked in halves and quarters doesn’t generally label the marks with the numbers they represent, and the bamboo shoot diagram you refer to works equally well with only the whole number marks labelled. So you could avoid mentioning mixed numbers altogether in Grade 3. On the other hand, examples like this are clearly pointing in that direction, and provide a good opportunity to talk about them if, for example, a student asks how to label the marks. But work with mixed numbers is not required until Grade 4.
Here’s the diagram for others’ convenience:
Thanks Bill. Would labeling the whole numbers only be confusing in the context of a line plot? My understanding was that each mark had to be labeled.
I was thinking that since rulers generally don’t have each mark labeled, there’s no particular reason why that has to be the case here.
There’s a discussion of this point here.
Bill, did you mean to post that here instead?
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