# 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:** 7
**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, 10:42pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/121 "2017-02-15T22:42:12Z")
> [@Darren\_Garrison](#): > > Of course I’d never say “five rabbit”–you capitalize [proper nouns](https://books.google.com/books?id=VdJYBQAAQBAJ&dq=%22five+rabbit%22). I thought that was surely going to be a link to a local [brewery](http://www.5rabbitbrewery.com/). ---
**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, 10:48pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/122 "2017-02-15T22:48:50Z")
> [@pulykamell](#): > > I thought that was surely going to be a link to a local brewery. Okay, if I drank beer, I think I’d drink [LINK REMOVED BY MODERATOR]. (But only if I could pour it into 3 cups.) ---
**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, 11:21pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/123 "2017-02-15T23:21:56Z")
> [@Darren\_Garrison](#): > > Okay, if I drank beer, I think I’d drink [this one](http://beerstreetjournal.com/5-rabbit-chinga-tu-pelo/). (But only if I could pour it into 3 cups.) What does “it” refer to? All of the beer, or just some of the beer? And will you be pouring it into the cups in equal amounts? These are all vital questions if you’re going to be sharing it (the beer, that is – preferably all of it) with the third-graders. Although at this point I think I’d prefer to go back to [the slightly more complicated math question](http://boards.straightdope.com/sdmb/showpost.php?p=19992401&postcount=50) involving John’s mom, the pimp, and the four liters of whiskey. ---
**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 15, 2017, 11:40pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/124 "2017-02-15T23:40:52Z")
> [@DSYoungEsq](#): > > 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. To avoid the ambiguity, change the words to “divide it among.” ---
**Author:** ![DSYoungEsq](https://avatars.discourse-cdn.com/v4/letter/d/c6cbf5/32.png) [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)\ **Post date:** [February 16, 2017, 1:31am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/125 "2017-02-16T01:31:59Z")
> [@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. > > 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. I think the subsequent discussion shows that it is you who have failed to understand the inherent ambiguity in your question. “It” as a pronoun can refer back to a number of possible nouns. The usual reference will be to the most proximal noun that matches the gender of the pronoun (here neuter). It’s not a “contrived unnatural interpretation” at all to do so; indeed, I think an English teacher would probably suggest it’s the most natural assumption. If you want a simple way to phrase the problem, try this: “Mary has a pitcher filled with four liters of water. If she pours all the water into three empty beakers so that each beaker holds the same amount of water when she is done pouring, how much water will have been poured into each beaker?” While there may be rather “contrived unnatural interpretations” that would cause some confusion, I think 99% of readers would understand the problem correctly, and could produce a correct answer (assuming they know how to do the math). The key is to make clear that a) we start with 4 units of water, b) we divide that water up into the beakers evenly, c) there is no water left in the pitcher. Any wording which clarifies those three points accomplishes the goal. Yours, sadly, was weighed and found wanting. > [@](#): > > 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. If you didn’t know what it was asking, I cannot help you. I think most everyone else knew upon reading it what was being asked. I certainly did. And I’m not particularly gifted. 😉 ---
**Author:** ![Girlundone](https://avatars.discourse-cdn.com/v4/letter/g/919ad9/32.png) [@Girlundone](https://boards.straightdope.com/u/Girlundone)\ **Post date:** [February 16, 2017, 2:05am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/126 "2017-02-16T02:05:14Z")
The problem with shitty questions like this is that if they are test questions, then the data becomes all skewed. We give quarterly benchmark assessments in my county (I teach third grade)and I have found at least two really poorly worded questions per test. Our county pulls these from a item test bank that they purchased. Usually the test has 19 questions covering 9 standards, evenly distributed so 2 questions or so testing mastery of a standard for an entire quarter of instruction. When one of the questions is like the one posted here, and 60% of the kids in the entire county miss that question, the data comes back and admins start freaking out “These kids don’t know fractions!!” and hours of meetings ensue on how to better instruct them in fractions. It’s stupid. How about this novel idea? If we want to find out what kids know/don’t know, and we want to get solid data that can further drive our instruction, we could begin by making sure the questions aren’t glaringly flawed. In addition to teaching content, more and more I now find myself having to strategically teach kids how to try and get through shitty test test questions. It’s like a core subject in itself anymore. It’s not a small issue when the county uses this data to determine promotion/retention status for students. ---
**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 16, 2017, 2:32am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/127 "2017-02-16T02:32:54Z")
> [@DSYoungEsq](#): > > I think the subsequent discussion shows that it is you who have failed to understand the inherent ambiguity in your question. “It” as a pronoun can refer back to a number of possible nouns. The usual reference will be to the most proximal noun that matches the gender of the pronoun (here neuter). It’s not a “contrived unnatural interpretation” at all to do so; indeed, I think an English teacher would probably suggest it’s the most natural assumption. The natural assumption isn’t based on proximity to a referenced noun, nor to any other simplistic algorithmic factors, as I tried to say before, nor is it necessarily even based on a reference to any individual word at all, but potentially to the entirety of a noun phrase that it implicitly references. > [@DSYoungEsq](#): > > If you want a simple way to phrase the problem, try this: “Mary has a pitcher filled with four liters of water. If she pours all the water into three empty beakers so that each beaker holds the same amount of water when she is done pouring, how much water will have been poured into each beaker?” While there may be rather “contrived unnatural interpretations” that would cause some confusion, I think 99% of readers would understand the problem correctly, and could produce a correct answer (assuming they know how to do the math). Sure, and lawyers and linguists could have been enlisted, too. In the few seconds that I pondered how to phrase the question, a number of those variants crossed my mind, but they just seemed too awkward – there’s a difference between writing a math question and writing a legal contract. I took two seconds to write a simple example of how the OP question could have been phrased. If you want a more formal analysis, the word “that” following “pitcher” denotes a restrictive clause. If it was a non-restrictive clause beginning with “which”, the contents of the pitcher would be considered incidental information, but the restrictive clause denotes essential information – i.e.- the object of the verb is not just any pitcher, but is specially called out as one that contains four pints of water. The components of the noun phrase are in effect inseparable and it functions as a whole. I wouldn’t expect children to have developed the level of language nuance to be able to express that formally, but I’m pretty sure that they would understand the question. > [@DSYoungEsq](#): > > If you didn’t know what it was asking, I cannot help you. I think most everyone else knew upon reading it what was being asked. I certainly did. And I’m not particularly gifted. 😉 So you instantly grasped the problem described in the linguistic shambles described in the OP, but you found my example sadly ambiguous? Is that correct? 😃 ---
**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 16, 2017, 3:36am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/128 "2017-02-16T03:36:08Z")
> [@Girlundone](#): > > If we want to find out what kids know/don’t know, and we want to get solid data that can further drive our instruction, we could begin by making sure the questions aren’t glaringly flawed. In addition to teaching content, more and more I now find myself having to strategically teach kids how to try and get through shitty test test questions. It’s like a core subject in itself anymore. It’s not a small issue when the county uses this data to determine promotion/retention status for students. I think I have finally, fully grasped the meaning of the expression “misery loves company.” ---
**Author:** ![ZurBob](https://avatars.discourse-cdn.com/v4/letter/z/71e660/32.png) [@ZurBob](https://boards.straightdope.com/u/ZurBob)\ **Post date:** [February 16, 2017, 6:20am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/129 "2017-02-16T06:20:00Z")
> [@Left\_Hand\_of\_Dorkness](#): > > I think I have finally, fully grasped the meaning of the expression “misery loves company.” You are not alone. Not an educator here, but I understand what you and Girlundone are saying, and I agree. Fortunately for me, I was a perceptive kid in the '60s and 70’s, and understood the game when it came to test-taking. I could always determine the “drift” of my teachers and their tests, be it formulated in house, or by the State… And I always tested well. The remainder (majority) of the time, I failed miserably in class. I had no clue as to what was expected of me. I was fortunate to be a good test-taker with a moderate intellect. It’s a shame for those who held a superior intellect to mine who did not test out as well as me. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [February 16, 2017, 9:46am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/130 "2017-02-16T09:46:16Z")
> [@ZurBob](#): > > You are not alone. > > Not an educator here, but I understand what you and Girlundone are saying, and I agree. > > Fortunately for me, I was a perceptive kid in the '60s and 70’s, and understood the game when it came to test-taking. I could always determine the “drift” of my teachers and their tests, be it formulated in house, or by the State… And I always tested well. The remainder (majority) of the time, I failed miserably in class. I had no clue as to what was expected of me. > > I was fortunate to be a good test-taker with a moderate intellect. It’s a shame for those who held a superior intellect to mine who did not test out as well as me. I’m sure the 1580 SAT score helped get you into university … ---
**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\ **Post date:** [February 16, 2017, 3:24pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/131 "2017-02-16T15:24:37Z")
> [@Darren\_Garrison](#): > > Okay, if I drank beer, I think I’d drink [this one]([LINK REMOVED). (But only if I could pour it into 3 cups.) **Moderator Note** **Darren Garrison** , political jabs are not allowed in GQ. No warning issued, but don’t do this again. I have removed the link. Colibri General Questions Moderator ---
**Author:** ![ZurBob](https://avatars.discourse-cdn.com/v4/letter/z/71e660/32.png) [@ZurBob](https://boards.straightdope.com/u/ZurBob)\ **Post date:** [February 17, 2017, 5:05pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/132 "2017-02-17T17:05:03Z")
> [@watchwolf49](#): > > I’m sure the 1580 SAT score helped get you into university … I’m curious as to what prompted your snarky reply. BTW: I took the ACT. If memory serves me correctly, I had a 30 composite. Is that good enough to grovel in your presence? ---
**Author:** ![excavating\_for\_a\_mind](https://avatars.discourse-cdn.com/v4/letter/e/e8c25b/32.png) [@excavating\_for\_a\_mind](https://boards.straightdope.com/u/excavating_for_a_mind)\ **Post date:** [February 19, 2017, 2:15pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/133 "2017-02-19T14:15:05Z")
I suspect the subject problem results more from the guidelines that must be followed than anything else. I suspect the question 1. cannot be ethnocentric (for example, people’s names–Why John instead of Juan?) 2. cannot mention unit of measure (avoid the whole metric/US standard issue) 3. cannot mention illegal/immoral/controversial issues (don’t want angry parents being insulted) 4. must demonstrate the concept being taught 5. must include items/issues the intended audience has been exposed to Of course, like most sets of guidelines, they are contradictory (as in #1 and #5) , which makes it difficult, but not impossible. Of course, when those who write the questions are paying more attention to these guidelines, they pay less attention to whether or not the question actually makes sense as written. ---
**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 19, 2017, 2:33pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/134 "2017-02-19T14:33:08Z")
> [@excavating\_for\_a\_mind](#): > > I suspect the subject problem results more from the guidelines that must be followed than anything else. I suspect the question > > 1. cannot be ethnocentric (for example, people’s names–Why John instead of Juan?) > 2. cannot mention unit of measure (avoid the whole metric/US standard issue) > 3. cannot mention illegal/immoral/controversial issues (don’t want angry parents being insulted) > 4. must demonstrate the concept being taught > 5. must include items/issues the intended audience has been exposed to > > Of course, like most sets of guidelines, they are contradictory (as in #1 and #5) , which makes it difficult, but not impossible. Of course, when those who write the questions are paying more attention to these guidelines, they pay less attention to whether or not the question actually makes sense as written. 1 and 2 are almost certainly not part of the guidelines. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [February 19, 2017, 3:14pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/135 "2017-02-19T15:14:03Z")
> [@ZurBob](#): > > I’m curious as to what prompted your snarky reply. > > BTW: I took the ACT. If memory serves me correctly, I had a 30 composite. Is that good enough to grovel in your presence? It wasn’t snark … it was fellowship … didn’t your school have a secret club of those who tested well … helping each other find the right classes to boost the GPA … hells bells I took a solid year of chemistry solely because the tests were easy in that way … I had to go to lab but I mostly skipped lecture … straight A’s … Maybe that was back-in-the-day and educators have gotten smarter about this … ---
**Author:** ![yearofglad](https://avatars.discourse-cdn.com/v4/letter/y/b782af/32.png) [@yearofglad](https://boards.straightdope.com/u/yearofglad)\ **Post date:** [February 19, 2017, 5:21pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/136 "2017-02-19T17:21:19Z")
> [@Left\_Hand\_of\_Dorkness](#): > > 1 and 2 are almost certainly not part of the guidelines. I agree - as someone who writes assessments for a living, multi-culturalism is something that is DESIRABLE - just because one item uses John instead of Juan doesn’t mean it’s something that’s avoided. Questions can certainly mention units of measure - both US and UK units are typically tested in the US - it’s not an “issue” at all. ---
**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 19, 2017, 8:42pm UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/137 "2017-02-19T20:42:41Z")
> [@yearofglad](#): > > I agree - as someone who writes assessments for a living, multi-culturalism is something that is DESIRABLE - just because one item uses John instead of Juan doesn’t mean it’s something that’s avoided. Right. The solution isn’t to avoid names, it’s to avoid always using John and Mary as names. Sometimes use those, sometimes use Malik and Graciela, sometimes use Filipe and Oshun. > [@](#): > > Questions can certainly mention units of measure - both US and UK units are typically tested in the US - it’s not an “issue” at all. Not only that–common core _requires_ students to learn various measures. Third grade focuses on metric liquid measurements, thus liter and milliliter. I think second focuses on customary measurements, and fourth does both. ---
**Author:** ![Ulf\_the\_Unwashed](https://avatars.discourse-cdn.com/v4/letter/u/b4bc9f/32.png) [@Ulf\_the\_Unwashed](https://boards.straightdope.com/u/Ulf_the_Unwashed)\ **Post date:** [February 20, 2017, 1:41am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/138 "2017-02-20T01:41:34Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Right. The solution isn’t to avoid names, it’s to avoid always using John and Mary as names. Sometimes use those, sometimes use Malik and Graciela, sometimes use Filipe and Oshun. > Not only that–common core _requires_ students to learn various measures. Third grade focuses on metric liquid measurements, thus liter and milliliter. I think second focuses on customary measurements, and fourth does both. Second grade CC actually leaves out volume/capacity measurements entirely, so third graders are seeing it for the first time. I’m not a fan. Grade 2 focuses on length, time, and money. No weight/mass either, also a grade 3 thing. Again, not a fan. You’re exactly right about the “multicultural” names component–which is, as demonstrated here in this thread, often misunderstood. One of my current writing/editing projects requires me to fill out an ethnic-slash-gender tracking document for each lesson…the publisher gives us specific quotas from particular cultures (Middle Eastern, South Asian, African American, Caucasian, etc.). Something like 45% of the names and faces are supposed to be “Caucasian.” So, I actually \*have \*to include a bunch of Johns and Marys, or more likely Sophias and Katies and Bradens and Jonathans, along with Seemas and Abduls and Juans and Takeyukis. [Yes, what constitutes “Caucasian” is open to question. However, _we have a list to choose from_, so we don’t really have to make the call.] ---
**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 20, 2017, 11:49am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/139 "2017-02-20T11:49:19Z")
> [@yearofglad](#): > > I agree - as someone who writes assessments for a living, multi-culturalism is something that is DESIRABLE But you have to be careful [which cultures you use](http://www.snopes.com/humor/question/mathtest.asp). ---
**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 20, 2017, 11:55am UTC](https://boards.straightdope.com/t/third-grade-math-question/779477/140 "2017-02-20T11:55:20Z")
> [@Ulf\_the\_Unwashed](#): > > Second grade CC actually leaves out volume/capacity measurements entirely, so third graders are seeing it for the first time. I’m not a fan. Grade 2 focuses on length, time, and money. No weight/mass either, also a grade 3 thing. Again, not a fan. Oops–thanks for the correction. I really should know more about the lower-grade curriculum. > [@Darren\_Garrison](#): > > But you have to be careful [which cultures you use](http://www.snopes.com/humor/question/mathtest.asp). The underlying point here is, even when folks are asked to acknowledge nonwhite students, there are teachers who turn it into another opportunity to make minority students feel shitty about themselves. But I suppose that’s another discussion :). [Previous page](https://boards.straightdope.com/t/third-grade-math-question/779477.md?page=6) [Next page](https://boards.straightdope.com/t/third-grade-math-question/779477.md?page=8)