# Third Grade Math question **URL:** \ **Category:** Factual Questions\ **Created:** [February 10, 2017, 4:30pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477 "2017-02-10T16:30:27Z")\ **Posts on this page:** 20\ **Page:** 6
**Author:** ![yearofglad](https://avatars.discourse-cdn.com/v4/letter/y/b782af/32.png) [@yearofglad](https://boards.straightdope.com/u/yearofglad)\ **Post date:** [February 12, 2017, 5:22pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/101 "2017-02-12T17:22:06Z")
> [@Magiver](#): > > They could have added “equal amounts are poured from each bottle” but I suppose it’s assumed for the purposes of doing math. It appears the purpose of the question is to think logically about fractions. > > I truly think the problem is worded wrong. I agree - the problem is worded wrong. Nothing should be assumed. Especially when its third grade math - your assumptions, knowing the answer and what’s being tested, will be quite different from a third-graders. The “purpose” of the question is not apparent to a third-grader, so they won’t use that to inform the assumptions they should make. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [February 12, 2017, 5:39pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/102 "2017-02-12T17:39:27Z")
> [@yearofglad](#): > > The “purpose” of the question is not apparent to a third-grader, so they won’t use that to inform the assumptions they should make. Part of the frustration of high-stakes tests is that I have to spend a nontrivial amount of time teaching kids to get into the heads of the test-designers in order to unpack the assumptions the test designers are probably making. This may be a useful skill, but it is a desperately cynical and soul-crushing skill to have to learn at the age of eight. ---
**Author:** ![Magiver](https://avatars.discourse-cdn.com/v4/letter/m/4491bb/32.png) [@Magiver](https://boards.straightdope.com/u/Magiver)\ **Post date:** [February 12, 2017, 5:59pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/103 "2017-02-12T17:59:29Z")
> [@yearofglad](#): > > The “purpose” of the question is not apparent to a third-grader, so they won’t use that to inform the assumptions they should make. I agree. They’re lucky to find the classroom with a map and a line drawn on the floor. But the muckety mucks in charge of education are supposed to know the purpose of the question and the answer it’s suppose to elicit. Math is an educational odd duck. On a base level it’s absolute. the answers don’t change and we could use the same school books from 100 years ago. But it isn’t useful without problem solving skills and that involves throwing word problems at students. On that level it’s a class in language skills and that is not a precise science. Enter confusion stage left. ---
**Author:** ![Magiver](https://avatars.discourse-cdn.com/v4/letter/m/4491bb/32.png) [@Magiver](https://boards.straightdope.com/u/Magiver)\ **Post date:** [February 12, 2017, 6:10pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/104 "2017-02-12T18:10:39Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Part of the frustration of high-stakes tests is that I have to spend a nontrivial amount of time teaching kids to get into the heads of the test-designers in order to unpack the assumptions the test designers are probably making. > > This may be a useful skill, but it is a desperately cynical and soul-crushing skill to have to learn at the age of eight. I agree. When I was eight the emphasis was more on solving basic math and not logic. We were memorizing math tables and word problems were more direct. Personally, I’d still like to see a child exit high school with the ability to make change. I think it makes the logic part easier to understand. But that’s me. ---
**Author:** ![DSYoungEsq](https://avatars.discourse-cdn.com/v4/letter/d/c6cbf5/32.png) [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)\ **Post date:** [February 12, 2017, 6:52pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/105 "2017-02-12T18:52:08Z")
> [@wolfpup](#): > > Q: John’s mom has a pitcher that contains four pints of water. She needs to pour equal amounts of it into three containers. How much water must she pour into each container? > > A: 1 1/3 pints. > > An answer that should clarify the only possible presumed meaning of the very badly phrased question in the OP, an answer that should be clear to any adult and third-grader alike, and an answer that demonstrates how easy it is to set out this particular math problem without having to wonder about the capacity of the bottles, the capacity of the cups, or boggling the mind with confusing bullshit like what the hell “fraction of water bottles” is supposed to mean. And yet, your question is already ambiguous. You did not specify that there is to be no unpoured water left over. 😉 ---
**Author:** ![Melbourne](https://avatars.discourse-cdn.com/v4/letter/m/b5e925/32.png) [@Melbourne](https://boards.straightdope.com/u/Melbourne)\ **Post date:** [February 15, 2017, 2:19am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/106 "2017-02-15T02:19:26Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Part of the frustration of high-stakes tests is that I have to spend a nontrivial amount of time teaching kids to get into the heads of the test-designers in order to unpack the assumptions the test designers are probably making. > > This may be a useful skill, but it is a desperately cynical and soul-crushing skill to have to learn at the age of eight. The greatest, best, most memorable part of going to university, was getting to a lab course where we were _expected to report and explain the results_. Not “get the right answer”. If the answer was wrong, the lab supervisor would come out and fix the equipment. If the answers didn’t make sense, they’d fix the question. My sister had medical exams like that too. If the smart educated students got 98% on the exam, they’d look at the other two questions and fix or replace them. It’s my engineering mindset. I never wanted my worksheets to be excercises in creative thinking. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 15, 2017, 2:37am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/107 "2017-02-15T02:37:46Z")
> [@DSYoungEsq](#): > > And yet, your question is already ambiguous. You did not specify that there is to be no unpoured water left over. 😉 Indeed. The correct answer is any amount 1 1/3 pints or less. 🙂 ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [February 15, 2017, 3:05am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/108 "2017-02-15T03:05:39Z")
> [@DSYoungEsq](#): > > And yet, your question is already ambiguous. You did not specify that there is to be no unpoured water left over. 😉 Actually, I did specify it. The problem statement was “John’s mom has a pitcher that contains four pints of water. She needs to pour equal amounts **of it** (i.e.- the aforementioned contents) into three containers.” That was actually precisely why the phrase “of it” was included; the problem could be construed to be ambiguous without it, but not with it, IMO. If that’s still deemed ambiguous because some nitpicker chooses to interpret “of it” as “of the contents or portion thereof” ;), then the clumsier construction “She needs to pour all of it into three containers in equal amounts” could be used, and the same simple question form remains. The point is that the problem presented in the OP was confusing not because there was some ambiguity about whether all the water had to be used, but because fundamentally it wasn’t clear what the hell the thing was even asking. It’s not hard to phrase it far more clearly, so that the question is clear to any reasonable interpretation, even if someone might still nitpick some theoretical ambiguity, like “it assumes that this is being done on the surface of the earth in the presence of gravity and at normal atmospheric pressure”. 🙂 ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 15, 2017, 3:16am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/109 "2017-02-15T03:16:39Z")
I do agree that it is better written using something along those lines. That “what fraction of water bottles” construction of the original question was annoying, and changing it to a pitcher with a volume removes the awkwardness of the phrasing. ---
**Author:** ![DSYoungEsq](https://avatars.discourse-cdn.com/v4/letter/d/c6cbf5/32.png) [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)\ **Post date:** [February 15, 2017, 5:47pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/110 "2017-02-15T17:47:16Z")
> [@wolfpup](#): > > Actually, I did specify it. The problem statement was “John’s mom has a pitcher that contains four pints of water. She needs to pour equal amounts **of it** (i.e.- the aforementioned contents) into three containers.” That was actually precisely why the phrase “of it” was included; the problem could be construed to be ambiguous without it, but not with it, IMO. If that’s still deemed ambiguous because some nitpicker chooses to interpret “of it” as “of the contents or portion thereof” ;), then the clumsier construction “She needs to pour all of it into three containers in equal amounts” could be used, and the same simple question form remains. > > The point is that the problem presented in the OP was confusing not because there was some ambiguity about whether all the water had to be used, but because fundamentally it wasn’t clear what the hell the thing was even asking. It’s not hard to phrase it far more clearly, so that the question is clear to any reasonable interpretation, even if someone might still nitpick some theoretical ambiguity, like “it assumes that this is being done on the surface of the earth in the presence of gravity and at normal atmospheric pressure”. 🙂 No, No, No. “It” refers to the water. But if I pour 1/10 of a cup of the water into each of the three containers, I have done precisely what you asked. And this points out that the real problem in the question was not what was intended (which everyone reading the question has grasped), but rather the fact that the writer proceeds with unstated assumptions (and clumsy, less-than-clear writing) which obscure the true intention. And speaking as someone who teaches, and who writes questions for his students, I know first-hand exactly how difficult writing a question that avoids mis-interpretation can be. And if you want to see the ultimate in “nit-picking” such a question, just search around here for the most recent “airplane on a treadmill” thread. :p:eek: ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [February 15, 2017, 6:49pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/111 "2017-02-15T18:49:00Z")
> [@DSYoungEsq](#): > > “It” refers to the water. You’re not wrong, but rather, you’re advancing a contrived unnatural interpretation to try to show ambiguity. What does John’s mom have – what is the object of the verb? It could be construed to be “a pitcher”, or it could be understood to be “water”, or some pints of water, but the most natural interpretation of the object of the verb is the _noun phrase_ “a pitcher that contains four pints of water”. That’s the _relevant_ description of what she has, and the natural parsing of a native English speaker would have “it” refer to that noun phrase, and not to some arbitrary quantity of water. So yes, a lawyer striving to weasel out of a contract might try your interpretation out on the jury, but a natural reading seems to me to yield a fairly clear interpretation. There’s a good reason that contracts often have clumsy and redundant language – it’s often the only way to truly eliminate all ambiguity when you have someone actively looking for it. My point was not to show how brilliantly phrased this question is, as I only devoted a few seconds to it and I’m sure it could be written much better, but to show how easy it is to write something that’s readily comprehensible and how truly bad the original question was in comparison. > [@DSYoungEsq](#): > > And this points out that the real problem in the question was not what was intended (which everyone reading the question has grasped), but rather the fact that the writer proceeds with unstated assumptions (and clumsy, less-than-clear writing) which obscure the true intention. The real problem with the original question, as I said and as was noted earlier, is not some theoretical ambiguity but the fact that it’s so poorly written that it’s a near-incomprehensible linguistic dog’s breakfast. On first reading I genuinely did not know what the hell it was asking. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [February 15, 2017, 7:01pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/112 "2017-02-15T19:01:14Z")
> [@pulykamell](#): > > Indeed. The correct answer is any amount 1 1/3 pints or less. 🙂 [This is either a nitpick OR a critical issue of what we’re talking about. Your call:] Fewer. [/This is either a nitpick OR a critical issue of what we’re talking about. Your call:] ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [February 15, 2017, 7:03pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/113 "2017-02-15T19:03:58Z")
It’s been a week, are we taking evaporation into account? ---
**Author:** ![yearofglad](https://avatars.discourse-cdn.com/v4/letter/y/b782af/32.png) [@yearofglad](https://boards.straightdope.com/u/yearofglad)\ **Post date:** [February 15, 2017, 7:12pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/114 "2017-02-15T19:12:53Z")
> [@wolfpup](#): > > You’re not wrong, but rather, you’re advancing a contrived unnatural interpretation to try to show ambiguity. What does John’s mom have – what is the object of the verb? It could be construed to be “a pitcher”, or it could be understood to be “water”, or some pints of water, but the most natural interpretation of the object of the verb is the _noun phrase_ “a pitcher that contains four pints of water”. That’s the _relevant_ description of what she has, and the natural parsing of a native English speaker would have “it” refer to that noun phrase, and not to some arbitrary quantity of water. So yes, a lawyer striving to weasel out of a contract might try your interpretation out on the jury, but a natural reading seems to me to yield a fairly clear interpretation. There’s a good reason that contracts often have clumsy and redundant language – it’s often the only way to truly eliminate all ambiguity when you have someone actively looking for it. Let’s assume, as you do, that “it” means “a pitcher that contains four pints of water.” In that case, I can’t pour any of “it” into cups, because “it” is a pitcher, a solid object that cannot be poured. So now “it” means “the four pints of water that are contained within the pitcher”? If I now pour 1/8 of a pint of water into each cup, are you saying I have NOT poured equal amounts of it [the four pints of water that are contained within the pitcher] into each cup? Then what HAVE I done? At a third-grade level, and I would say at ANY level, you need to specify you are pouring all the water. ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [February 15, 2017, 7:24pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/115 "2017-02-15T19:24:04Z")
> [@Leo\_Bloom](#): > > Fewer. Less. “Fewer marbles”, “fewer bottles of water”, but “less water”. Water here would be regarded as a continuous quantity notwithstanding the reference to a unit of measure. “The main reservoir holds ten million gallons of water. The auxiliary reservoir holds less.” ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [February 15, 2017, 7:45pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/116 "2017-02-15T19:45:34Z")
> [@yearofglad](#): > > At a third-grade level, and I would say at ANY level, you need to specify you are pouring all the water. What if I took offense to that analysis and said that “I could care less about it”? Does that mean that I must care about it at least a moderate amount? We’ve had some lively discussions about such matters here, and while some cases of such usage serve no discernible purpose, the fact remains that if we based our comprehension of language on this kind of algorithmic micro-analysis we would constantly have to communicate in legalese. The great difficulties with computer language translation have stemmed from the fact that humans take a holistic and experience-based, context-based view of language, and even a third-grader has a wealth of this experience. I’m not an expert on the mind of a third-grader, but I would suspect that she would unconsciously associate the pronoun with the entire noun phrase in the question, simply because that’s the only possible way that it reads as a problem in arithmetic. ---
**Author:** ![Patx2](https://avatars.discourse-cdn.com/v4/letter/p/73ab20/32.png) [@Patx2](https://boards.straightdope.com/u/Patx2)\ **Post date:** [February 15, 2017, 10:03pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/117 "2017-02-15T22:03:07Z")
> [@watchwolf49](#): > > It’s been a week, are we taking evaporation into account? Nice! 😂 ---
**Author:** ![Darren\_Garrison](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/darren_garrison/32/92_2.png) [@Darren\_Garrison](https://boards.straightdope.com/u/Darren_Garrison)\ **Post date:** [February 15, 2017, 10:12pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/118 "2017-02-15T22:12:05Z")
> [@wolfpup](#): > > “Fewer marbles”, “fewer bottles of water”, but “less water”. Water here would be regarded as a continuous quantity notwithstanding the reference to a unit of measure. “The main reservoir holds ten million gallons of water. The auxiliary reservoir holds less.” But a container of water consists of a large but discrete number of water molecules, and as everyone knows, like moose, buffalo, and rabbit, the plural of water is water. Therefore, you would have fewer water. (Not to be confused with Frewer Water, the short-lived product marketed by the former _Max Headroom_ star.) ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [February 15, 2017, 10:28pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/119 "2017-02-15T22:28:01Z")
> [@Darren\_Garrison](#): > > … like moose, buffalo, and rabbit … Do you really say “five rabbit” rather than “five rabbits” ? ---
**Author:** ![Darren\_Garrison](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/darren_garrison/32/92_2.png) [@Darren\_Garrison](https://boards.straightdope.com/u/Darren_Garrison)\ **Post date:** [February 15, 2017, 10:38pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/120 "2017-02-15T22:38:09Z")
> [@Xema](#): > > Do you really say “five rabbit” rather than “five rabbits” ? Of course I’d never say “five rabbit”–you capitalize [proper nouns](https://books.google.com/books?id=VdJYBQAAQBAJ&dq=%22five+rabbit%22). [Previous page](https://boards.straightdope.com/t/third-grade-math-question/779477.md?page=5) [Next page](https://boards.straightdope.com/t/third-grade-math-question/779477.md?page=7)