The term "improper" fractions

[kgartland]

We had a professional development session yesterday and had a lively discussion about the use of the term “improper” fraction. I mentioned that this vocabulary was no longer used in the standards and that led to a discussion of what should be used as an alternative to this term – I thought that we were now calling them “fractions greater than one” but one teacher insisted that a fraction had to be less than one.
Would someone mind clarifying these definitions and what the writers of the standards intended for teachers to use to describe “13/8”

Thank you in advance.

[Bill McCallum]

A fraction does not have to be less on than one, that’s for sure! As for improper fractions, there is no prohibition on writing things like 2 1/2. Indeed, it would be hard to avoid. But the standards do not use the term “improper fraction” because it promotes the misconception that a “proper” fraction must be less than 1. The notation 2 1/2 is just a shorthand for the sum 2 + 1/2, and should be read that way. Then rewriting it in the form 5/2 is accomplished the same way as for any sum of fractions (with the understanding that 2 = 2/1).

The standards also avoid talking about converting between proper and improper fractions, because the word “convert” suggests you are actually changing the number. The number stays the same, there are just different ways of writing it, depending on your purpose. Students should be able to deal with fractions written in any form, but there is no need to insist they write them in one particular way.

I’m not sure you can avoid the term “improper fraction” entirely. I’d be interested to try though.

[Jeffrey Zivkovic]

I was looking for an alternative name to use with my students. I don’t like the term, “Improper Fraction” because it implies that less-than-one fractions are proper. There’s a connotation that there’s something wrong with 13/8 and that it should not be used.

For this coming year, I’m going to try using the term, “Overflow Fraction.”

[Bill McCallum]

That’s better than “improper.” But I’m wondering why you need a separate term at all. My first instinct would be to use the term “fraction” and point out that some fractions are less than 1 and some are greater than 1 (and, for that matter, some are equal to 1 . . . 5/5 = 1 is an important thing to know).

[Karen Gartland]

I completely agree – both 1/4 and 5/4 are fractions. For all intensive purposes and clarity for students, I think that having them recognize that both are fractions is truly important. I used to have so many Algebra students wanting to change 5/4 to 1 1/4 and the only way that I could convince them that it wasn’t necessary and actually “mathematically detrimental” was when we were using 5/4 as slope – WAY easier to graph! 🙂

[Bill McCallum]

Beautiful example!

[muneeryachb]

I am parent, software engineer by profession, trying to teach my son, who is in 3rd grade, fractions. I believe terminology used for describing any concept plays a very critical role in the comprehension of the concepts. I see everyday where simple straight forward concepts are unnecessarily made ambiguous by naming things the wrong way.

When you hear the word fraction, you would understand it as part of a whole. For example: I ate a fraction of the cake. But it is difficult to think naturally that a fraction can also be greater than a whole. If we call quantities less than 1 fractions then for quantities greater than 1 may be we should call them conglomerates (my two cents!!) 🙂

Thanks!!

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