Third Grade Math question

My son got this question in a class assignment and it’s been messing with my head all morning. So, I’d check with doperati.

John’s mom has 4 water bottles. She needs to fill three cups with water. What fraction of water bottles will she put into each cup?

The answer choices are:
a) 3/4 (three quarters)
b) 1 3/4 (one and three quarters)
c) 1/3 (one thirds)
d) 1 1/3 (one and one thirds)

That’s the exact question - no edits.

I do not want to bias the discussion with my inferences, so I will wait for your comments.

Assuming there’s nothing left over, D. I think another way to reword it would be “I have three containers of water that combine to 4 [units] of water. How many [units] of water are in each container?” 1 1/3 * 3 = 4

Obviously, the question needs to tell the volume of the water bottles and the cups.

Meaningless without a concept of how much water is in each bottle and each cup, or at least their relative volumes.

I’d imagine there’d be no point asking the teacher if they’d read Piaget…

The word “fill three cups” threw me off, as well as the notion that water from 4 bottles will fit into 3 cups.

But I think the intent is to divide the water from 4 bottles equally into 3 cups, and we are supposed to assume that the cups are big enough (and the bottles small enough) for you to do this. If so, obviously the answer is (d).

I concur with D, and am filled with quiet rage at whomever wrote that question. (Not necessarily the teacher.)

Was this question given in a country where English is the primary language? Besides the wording being terribly ambiguous, there’s the “one thirds” phrasing that happens twice.

After looking at the responses, I agree that they were looking for the “d” answer, but on first reading, I didn’t know what they were asking.

Terribly written, I agree, and it took me a minute or so to parse it, but based on what I believe they’re asking, it’s 4/3 or 1 1/3 or (d).

Assuming 1 water bottle fills 1 cup she needs 3 of the 4 water bottles or (a). That’s my assumption based on it being for a 3rd grader.

And the notation “1 1/3” is obsolete. It should be either a proper fraction (4/3) or decimal (1.33).

Thanks people - that was quick!

We live in a suburb of Houston, TX - so yes, the first language is English. And my son reads at least at a 8th grade level, so comprehension is not an issue.

The one thing I did add here was describing the factions in the answer choices because I was not sure how it would read online.

The thing that gets my goat is that answering this question requires you to make at least one major assumption (4 bottles = 3cups). Why they could not state it clearly, I don’t quite understand.

Yes I had to read the question several time to figure out what they were trying to do. When I read 3 cups my mind went to 3 eight Oz cups. And the confusion started.

Simple solution to problem.
John’s mom has 4 smallwater bottles. She needsdivide the water into three largecups (Or containers) with water. What fraction of water bottles will she put into each cup?
No on second thought the whole question should be scraped and rewritten from scratch.

Since when? My kids are still learning mixed numbers (1 1/3) and improper fractions (4/3) in school, and how to convert between them. Mixed numbers are harder to do math in, but much easier to visualize what’s going on - how much is 27/4 anyway?

The question sucks but the way I read it, you take all the water from all the bottles and it exactly fills three cups. Therefore D) 1-1/3. But the question sucks.

4/3 is an improper fraction. And there is nothing obsolete about the 1-1/3 notation (most style guides require a hyphen, not a space).

Do the bottles need to be half full, or half empty?

Obviously, 1/3 will go into each cup, regardless of where the water comes from, or how many bottles it is originally in.

The question should explicitly say that

  1. The water bottle’s volume is significantly smaller than the cup’s.
  2. The three cups should be filled equally.

If that is true, the answer is 1 1/3 (I was not aware that this notation is obsolete - anyone have a cite for this?).

Another couple of nitpicks are

  1. “what fraction of water bottles” should be “what fraction of a water bottle”, since otherwise it can be construed as what fraction of the four bottles should be put in each cup (in which case the answer is 1/3).

  2. “fraction” implies, in English if not strictly in math, I guess, smaller than a whole. Which leads away from the 1 1/3 answer. 1 1/3 is not a “fraction” it is a “mixed number”.

And lastly, one of the possible answers was listed as “one thirds (sic)”. Are you sure you copied it correctly?

No, it’s not obsolete. “1 1/3” is how one numerically writes the words “one and a third”. Proper fractions are useful for doing mathematics, but aren’t used in colloquial speech. For example, see Google Ngram. Kids need to learn how to do the math and put the answer in an accessible form.

Yes, I suppose based on reasonable assumptions about what this horror really means, the answer should be (d). But whoever wrote the question should be fired for incompetence and never allowed to work in a school again, or possibly taken out back and shot. It’s not just confusingly ambiguous, but contains bad English – not just “one thirds”, but the jarringly bad phrasing “what fraction of water bottles …”.

A meaningful question would be constructed in terms of units, not bottles. John’s mom has 4 liters of water (or pints, or hogsheads, or whatever suits the locally familiar units of measure). She needs to divide it equally among three containers. How much will she pour into each container?

Nothing obsolete about it. And 1.33 is not equal to 1 1/3.

This question was part of a packet of math assignments by the school district (one of the largest, if not the largest in Texas). This is not the first time I am seeing a poorly worded math or science question. I see at least one in every assignment.

While my son is quite bright and does very well in school, I shudder to think of the kids who normally struggle with math concepts. My wife also tutors kids at my son’s school and she often says that many kids, after some initial struggle with math, give up on themselves by the time they get to 5th grade. They don’t even want to try any more. And that is really really sad.

Never seen it except for in old cookbooks (and, yes, schoolbooks on arithmetic!)

Feel free to add “3”:s to the limit of your measuring accuracy!