Expressing a whole number as a fraction before 5th grade

[zdeluna4]

Hi!

How should fractions equivalent to whole numbers be expressed before 5 grade? For example, how should “3/1” be expressed? If I said “3 divided by one”, I feel it would confuse the students since they aren’t learning the connection between fractions and division until 5.NF.3.

Would “3 over 1” or “3 oneths” be more appropriate?

Thanks!

[Anonymous]

Students will have experience in 3rd grade seeing whole numbers as fractions – more than likely as they experiment with number line diagrams and notice that many fractions can label the same point. On the number line, the whole is the unit interval from 0 to 1. So using the language of the 3rd grade standards I would think that 3/1 would be verbalized as “3 wholes” or “3 units” or “the quantity you get by putting 3 wholes together.” Just like 9/3 is the quantity you get by putting 9 copies of 1/3 together or 7/6 is 7 shares of size 1/6. I would steer clear of language like “3 over 1″ or “4 out of 5″ since it does not support the unit fraction idea that is the root of all the fraction standards.

[Bill McCallum]

Agree with abieniek, and I would only add that this is an explicit requirement in Grade 3.

3.NF.3c: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

[dmcdonald]

I have a question similar to the original one, in regards to how to say a particular fraction when it comes up with my students. The Progression documents have a number of examples of fractions in which the numerator is an addition or multiplication expressions, such as 5 + 4/9 (5 + 4 as a numerator and 9 as a denominator). How would this be read exactly? If I were to say 5 + 4 ninths, it would seem to be indicating a mixed number. Would I repeat the word “ninths”, reading it as five-ninths plus four-ninths, as it were two different fractions?

Thank you for your help.

[Bill McCallum]

I guess I would just say “five plus four over nine.” Well, that could still be interpreted as a mixed number. People sometimes say something like “quantity five plus four,” with a pause afterwards, to indicate they are referring to a single quantity. So you could say “quantity five plus four [slight pause] over nine.” Probably I would just avoid having to say this verbally at all.

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