# wtf is a "triangular snowflake"? **URL:** \ **Category:** Factual Questions\ **Created:** [January 18, 2014, 7:07pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161 "2014-01-18T19:07:23Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [January 19, 2014, 5:55pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/21 "2014-01-19T17:55:17Z")
Actually, Twoflower, that’s a different county. The question from the OP is from Carroll County, as you can see in the worksheet. The link you’ve given is to something from Cecil County. The statement in your link is basically correct anyway. ---
**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:** [January 19, 2014, 5:59pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/22 "2014-01-19T17:59:41Z")
> [@Maserschmidt](#): > > And finally, here is the actual worksheet: > > [Google Search](http://webcache.googleusercontent.com/search?q=cache:sQNOm035nvkJ:www.carrollk12.org/Assets/file/ElemMath/CountyBenchmarks/JB.4.2014.doc%20&cd=2&hl=en&ct=clnk&gl=us) > > It appears to have been put together by a teacher who wanted to give kids a chance to practice over the winter holiday for a benchmark assessment. I don’t see anything to indicate that it’s anything other than the work of an incompetent teacher (as opposed to the Common Core illuminati), but it’s possible, given that it’s in Maryland, that Obama wrote it himself. Yeah, it appears a couple words are cut off there, as mentioned. But is it not also possible that “triangular snowflakes” was discussed in this particular class? I see there’s links above to various shapes of snowflakes, so it’s not inconceivable that there was a science class and perhaps even an art project that dealt with these triangular snowflakes, so the kids might even know what the question is talking about. If the worksheet is real, then I’d surmise this is a pretty good possibility. I somehow doubt the teacher making the worksheet pulled the term “triangular snowflake” completely out of the blue. At any rate, no knowledge of what a triangular snowflake is required to solve the problem. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [January 20, 2014, 2:08am UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/23 "2014-01-20T02:08:31Z")
> [@Wendell\_Wagner](#): > > Senegoid, does the textbook say that it’s designed for the Common Core? Why do you assume that it is? As Amateur Barbarian pointed out, let’s make sure the examples we’re discussing are actually from the Common Core before we blame them on it. I didn’t read the introduction, but I did notice that throughout the book, there are collections of problems marked as being example Common Core questions. The text itself struck me as sort of a cook-book approach, with no depth to it – just a few sample problems worked out step-by-step. It struck me as being shallow and superficial, and the many Common Core examples suggested to me that it’s just “teaching to the Common Core test”. > [@](#): > > The problems with the question in the OP certainly predate the Common Core. Richard Feynman in one of his books gave an example from a 1964 arithmetic book in California which sounds rather similar. There was a question in the book that went something like this (although I’m reconstructing from memory and the details are definitely not correct): Stars of different colors have different temperatures. Red ones have temperatures of 4000 degrees, yellow ones of 5000 degrees, blue ones of 6000 degrees, and green ones of 7000 degrees. If you put together two red stars, one yellow one, three blue ones, and five green ones, what temperature will the result be? That came from _Surely You’re Joking, Mr. Feynman_, chapter “Judging Books By Their Cover” (where he notes that one of the publishers submitted a text that was literally all blank pages, with only the cover to show). You’ve sort of done just what this thread is complaining of, by mis-stating the problem that Feynman stated . . . > [@](#): > > Now, even if those temperatures are correct, you can’t add together temperatures and have them say anything about the temperature of the resulting thing, so this is simply a bad example of whatever they’re trying to teach. So why was such a question written? It was because the textbook writers were told that they had to come up with word problem questions for every idea they introduced. Coming up with word problems isn’t that bad in itself. The problem simply asked the student to find the sum of all those temperature numbers, although worded somewhat badly like “find the total temperature of those stars” or some such. Feynman’s complaint was that the problem was unrealistic, something that made no sense to compute In Real Life (although he immediately shot down his own argument by granting that the computation was relevant if you were asked to compute the _average_ temperature). But **Wendell Wagner** ’s defense here is more to the point: Most Real-Life problems are actually more complicated than you would throw at a grade-schooler, so you have to develop some over-simplified, and hence unrealistic, problems to practice with. Hey, it’s just practice with word problems! It doesn’t really have to be a _realio-trulio_ problem. For those, we have PhD’s to work on them! ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [January 20, 2014, 2:31am UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/24 "2014-01-20T02:31:01Z")
> [@Senegoid](#): > > The problem simply asked the student to find the sum of all those temperature numbers, although worded somewhat badly like “find the total temperature of those stars” or some such. I took it to mean what’s the _average_ temperature of that collection of stars, which would be 6000 degrees. (Completely ignoring actual astrophysics) ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [January 20, 2014, 3:53am UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/25 "2014-01-20T03:53:01Z")
No, the problem did not say that the student was to compute the average temperature. It said to compute the total of all the temperatures. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [January 20, 2014, 7:26am UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/26 "2014-01-20T07:26:08Z")
> [@Wendell\_Wagner](#): > > No, the problem did not say that the student was to compute the average temperature. It said to compute the total of all the temperatures. Right, but . . . Feynman mangled his own argument. His argument was that this was an utterly useless thing to ask the student to compute – but then contradicted himself by suggesting that it would be useful to compute after all, if it were part of a larger problem asking the student to compute the average temperature. (But the problem as given in the book, as reported by Feynman, didn’t ask for the average.) _Your_ argument, however, is really the right one, I think: That hey, it’s just a simplified problem for the grade-school student to practice. Feynman was trying to argue that word problems should be realistic problems, which seems kind of pointless for the grade-school audience in a case like this. ---
**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:** [January 20, 2014, 8:50am UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/27 "2014-01-20T08:50:19Z")
> [@Senegoid](#): > > Feynman was trying to argue that word problems should be realistic problems, which seems kind of pointless for the grade-school audience in a case like this. I don’t know. It seems a reasonable complaint to me. I guess it depends on what grade I was in when I got that question, but I suspect I would have been tripped up by it, or at least got myself second guessing what the question is looking for exactly. I mean, if the question were written as Jack has a tray of ice cubes at 25F. What is the total temperature of a group of three of these ice cubes? I mean, I guess I would probably end up with 75F, but that’s a pretty stupid question. Part of me might think it’s a trick question, looking for the 25F answer. Same with the stars. Much better to write a realistic question. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [January 20, 2014, 2:33pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/28 "2014-01-20T14:33:47Z")
> [@Wendell\_Wagner](#): > > No, the problem did not say that the student was to compute the average temperature. It said to compute the total of all the temperatures. “Total of all the temperatures” is a meaningless phrase. Temperature isn’t an additive quantity like calories are. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [January 20, 2014, 3:06pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/29 "2014-01-20T15:06:44Z")
That was exactly my point and Feynman’s point. It asked for the sum of the temperatures, which makes no sense for temperatures. The writers of that 1964 textbook thought that since they had looked up the temperatures of various colors of stars in some astronomy book they had thrown a scientific reference into their textbook. They didn’t comprehend that you need to actually understand the scientific reference before you put it in your textbook. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [January 20, 2014, 3:25pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/30 "2014-01-20T15:25:06Z")
You mean they went through all that rigmarole just to ask what’s the sum of (4000x2) +(5000x1) +(6000x3) + (7000x5)? :smack: Apparently I hadn’t realized just how dumbed down the question was expected to be taken as. Sort of like the old joke about math: “Does one plus one equal two?” Kindergartener: “yes” Math PhD: “Give me a precise definition of ‘one’, ‘plus’, ‘equal’, and ‘two’, and I’ll tell you”. ---
**Author:** ![Amateur\_Barbarian](https://avatars.discourse-cdn.com/v4/letter/a/59ef9b/32.png) [@Amateur\_Barbarian](https://boards.straightdope.com/u/Amateur_Barbarian)\ **Post date:** [January 20, 2014, 3:27pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/31 "2014-01-20T15:27:14Z")
> [@Lumpy](#): > > You mean they went through all that rigmarole just to ask what’s the sum of (4000x2) +(5000x1) +(6000x3) + (7000x5)? > :smack: It was, IIRC, about a fourth or fifth grade textbook. The word problem would have been just as useful and far less misleading if it were the weights of colored balls. Feynman’s objection was to throwing in a bogus pseudo-scientific aspect that served no useful purpose and would certainly mislead some students down the road. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [January 20, 2014, 4:08pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/32 "2014-01-20T16:08:55Z")
The problem wasn’t dumbing down the question. The problem was a chain of individuals or companies or committees who thought they did their part by passing on instructions or information without feeling any necessity to check if what they said or what the people who followed the instructions did made any sense. Someone who was an expert on what a fourth-grader should be learning about arithmetic prepared a list of things which included the fact that they should be able to add a list of perhaps half a dozen numbers, each of which was in the thousands or so, and each of which had been multiplied by a small number. They also said that the student should be able to figure out from a word problem what the set of numbers to be added and multiplied were. The list was given to the publisher, who handed it to one of their regular textbook writers and told them to write a fourth-grade arithmetic book. The publisher had been told by someone else, perhaps a state textbook committee, that it would be good to include problems which referred to scientific matters, so the publisher handed some elementary textbooks, including one on astronomy, to the writer. The textbook writer knew a lot about writing textbooks, but their scientific knowledge wasn’t very good. They flipped through the science textbooks they had been given. The astronomy one talked about the various temperatures of stars. They put this into the word problem that they needed to write. They didn’t realize that temperatures can’t be usefully added in this way. When they were finished with the textbook, they handed the manuscript to the publisher. An editor at the publisher read the textbook rather quickly. They didn’t exactly understand the point of the question either, but it did what the instructions said, which was to create a word problem that showed a particular level of difficulty of addition and multiplication while referring to scientific matters. The publisher handed the textbook to the state textbook committee, who read through it even faster than the editor. Everybody did exactly what they were told and nobody cared whether the instructions made any sense. They all knew that following instructions would probably mean that you kept your job, while pointing out that the instructions didn’t make sense might well get you fired. ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [January 20, 2014, 4:26pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/33 "2014-01-20T16:26:19Z")
If you arrange three hexagons together, you’ll get something “triangleish.” Just sayin’. ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [January 20, 2014, 7:29pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/34 "2014-01-20T19:29:12Z")
Am I the only one that made paper snowflakes as a kid by folding a piece of paper into a triangle and snipping off the edges? ---
**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:** [January 20, 2014, 10:57pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/35 "2014-01-20T22:57:46Z")
> [@Chessic\_Sense](#): > > Am I the only one that made paper snowflakes as a kid by folding a piece of paper into a triangle and snipping off the edges? If you started off by folding it in half so you end up with a 6-pointed snowflake, then I’m pretty sure you just described the standard way of making paper snowflakes. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 20, 2014, 11:33pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/36 "2014-01-20T23:33:42Z")
> [@Maserschmidt](#): > > And finally, here is the actual worksheet: > > [Google Search](http://webcache.googleusercontent.com/search?q=cache:sQNOm035nvkJ:www.carrollk12.org/Assets/file/ElemMath/CountyBenchmarks/JB.4.2014.doc%20&cd=2&hl=en&ct=clnk&gl=us) Hmmmm. When I click on your link, I get an HTML version of the calendar, generated by Google. When I downloaded the .DOC file that it was generated from, it has a completely different question in place of the triangular snowflake question (though as far as I can see all the other questions are the same). ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [January 21, 2014, 12:09am UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/37 "2014-01-21T00:09:33Z")
> [@Thudlow\_Boink](#): > > Hmmmm. > > When I click on your link, I get an HTML version of the calendar, generated by Google. When I downloaded the .DOC file that it was generated from, it has a completely different question in place of the triangular snowflake question (though as far as I can see all the other questions are the same). The new question is “Find all of the factor pairs of 36.”, which is pretty much the same, just without the snowflake and grammar problems. Presumably the teacher changed the problem after it went viral, but google hasn’t re-translated the document. ETA: Or maybe the kids were confused too, and it was reworked for that reason. Since Google still has the old version, so conceivably, the controversy could have begun after the change was already made. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [January 21, 2014, 3:30am UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/38 "2014-01-21T03:30:18Z")
If I may threadshit a little bit, this whole thread, about a badly-written test question that may or may not have been reported accurately in the press, reminds me of [_The Pineapple and the Hare_](http://www.npr.org/blogs/thetwo-way/2012/04/20/151044647/the-pineapple-and-the-hare-can-you-answer-two-bizarre-state-exam-questions) – the cute little fable that got mangled and published as a grade-school reading comprehension test problem. Even Ken Jennings, the _Jeopardy_ champion, reported that he couldn’t make head or tail of it. But we all learned that pineapples have no sleeves! 😃 ---
**Author:** ![Kenm](https://avatars.discourse-cdn.com/v4/letter/k/bc79bd/32.png) [@Kenm](https://boards.straightdope.com/u/Kenm)\ **Post date:** [January 21, 2014, 3:33pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/39 "2014-01-21T15:33:49Z")
America is doomed. That is all. ---
**Author:** ![Keeve](https://avatars.discourse-cdn.com/v4/letter/k/f07891/32.png) [@Keeve](https://boards.straightdope.com/u/Keeve)\ **Post date:** [January 21, 2014, 3:54pm UTC](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161/40 "2014-01-21T15:54:07Z")
> [@Maserschmidt](#): > > And finally, here is the actual worksheet: > > [Google Search](http://webcache.googleusercontent.com/search?q=cache:sQNOm035nvkJ:www.carrollk12.org/Assets/file/ElemMath/CountyBenchmarks/JB.4.2014.doc%20&cd=2&hl=en&ct=clnk&gl=us) > > Tyler made 36 total snowflakes which is a multiple of how triangular snowflakes he made. How many triangular snowflakes could he have made? Everyone else is asking what “triangular snowflakes” are. I want to know what a “total snowflake” is. [Previous page](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161.md?page=1) [Next page](https://boards.straightdope.com/t/wtf-is-a-triangular-snowflake/679161.md?page=3)