3.NF.2 Fractions

How big is three-eighths?

In the student’s work below, what is “it” and why does the student think that matters?


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5 replies on “How big is three-eighths?”

The best that I can make out of this is that the student doesn’t understand the role of the numerator and is focusing overly on the denominator in thinking about the size of the fraction.

@Michael P: I think you are right about this student’s work. It almost seems like the student thinks that all of the 8th’s are smaller than 1/4. I would be curious to see where he would place 3/4 in relation to 1/2 or 1/3. Would the same mistake be evident?

I think they are saying that 3/8 must be A, because A is smaller than 1/4 (and they know where 1/4 is.) Agreeing with abshores, maybe “anything with an eighth is smaller than a quarter.”

I would ask the student “why does 3/8 seem smaller than 1/4? do we have a way of comparing them to be sure?”
It is particularly interesting that this student focused on the denominator’s impact on fraction size when it seems a more common mistake is “3 > 1 therefore 3/8 is more things than 1/4 and so 3/8 > 1/4”. Perhaps this student had made a numerator-based mistake in the past and was “overcorrecting”?

I know I’m commenting on a really old post BUT I’m looking around at fractions stuff so …
I’m wondering if we might glean more about the students’ thinking if we asked them to identify all of the points A through E on the number line.

As I think this year more about ‘what is the student’s understanding’ I also think more about the questions I ask.

We are doing some stuff with Sherry Parrish’s Number Talks, hopefully we are teaching kids to articulate their math thoughts.
For 15 years I looked at 7th & 8th grade test and thought wth was he/she thinking as I graded the tests. Wouldn’t it be nice to think the kid might even be able to explain it to me. Of course, I do need to ask the question.

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