A poorly worded Common Core question is making the rounds, and grammar aside I don’t understand what the question is talking about:
"“Tyler made 36 snowflakes which is a multiple of how triangular snowflakes he made. How many triangular snowflakes could he have made?”
Was there a diagram? 
“Poorly worded Common Core” anything is redundant. I haven’t seen a single genuinely thought-out, well-wrought or even slightly-improved aspect to this clusterfuck.
I don’t understand why, the harder we try to fix education, the more Marx Brothers the results get. I can only conclude that these new curricula and materials are being written by teaching professionals too stupid to actually, you know, teach.
ETA: GQ-quality answer: No, it’s not you; an examination of CC materials shows them to be frighteningly badly written and conceived. There is no possible sensible answer to the question.
I presume that should read “… a multiple of how many triangular snowflakes …” . I hope that’s a transcription error, and the real question isn’t that sloppy.
Given that, “triangular” is just an adjective. Doesn’t matter what it means. Whatever they are, 36 is a multiple of the number of them that Tyler made. So he could have made 1, 2, 3, 4, 6, or 9 of them.
Seems like a reasonable question about factors, if a bit confusingly presented.
What about 12 and 18? Or 36?
I just did a search and can only find statement of this “question” on virulently anti-CC sites (which I have not much problem with) and “patriot” tea-party through radical-right sites that equate CC with the continuing Commie-ish destruction of Our Country (which can get knotted). There’s some discussion in more neutral sites, but all stems from this rather suspect source. Most such cases turn out to be completely invented or grossly distorted.
Until we’ve established that the question (1) genuinely comes from Common Core materials and (2) is correctly and completely stated, this can be nothing but speculation supporting the confusion tactics of the UberPatriot Brigades.
Yep, those too. :o
And, I forgot to address, that, yes, this is what I assume the question is asking. He made some 3-sided snowflakes (okay, something I’ve never heard of), maybe some 4-sided ones. Maybe some normal 6-sided ones. Maybe some 8-sided ones. But the total number of snowflakes he made (36) is a multiple of how many triangular snowflakes he made. So: 1,2,3,4,6,9,12,18,36 as I read it.
Do we have another thread around, perhaps in Great Debates (or perhaps more fittingly in the Pit) on the subject of Common Core in general?
I’ve been sporadically helping my neighbor’s 9th-grade son with his Algebra I (my impression: he’s hopeless) and the textbook, ISTM, is just “teaching to the test” and doing even that very poorly. And its lead author is Larson, a well-established math text author who wrote the very excellent Calculus text that I learned from 30 years ago! Pity that an established excellent math text author should be dragged down to this depth.
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.
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?
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. A lot of students will learn the mathematical techniques that solve problems, but they can’t translate them into real life at all. Word problems can be useful in teaching them to translate back and forth from words to equations. Furthermore, the textbook writers were told that it would be nice if the word problems relied on material from science. So the textbook writers started flipping through books or articles about astronomy. They found mentions of the different temperatures of different colors of stars, so they threw that into the question, despite the fact that they didn’t remotely understand the notion of combining temperatures. The problem is that textbook writers are often hacks who will do whatever the textbook publishers and the state textbook committees tell them, even though the writers don’t understand what they’re doing.
The same thing happened in the question in the OP. The writers were told to teach the idea of the factors of a number and to make up word problems about it so that they could be sure that the students understood the concept and could translate back and forth from equations to words. The writers found somewhere a mention of snowflakes. They decided to use snowflakes as an example. They need to have several different kinds of snowflakes. Maybe or maybe not there are various shapes of snowflakes, but they decided that there are. So the word problem says that a total of 36 snowflakes were made. The problem says that the total number of snowflakes is a multiple of the number of triangular snowflakes. The student is supposed to be able to see that 36 is a multiple of (i.e., has factors of) 1, 2, 3, 4, 6, 9, 12, and 18. (Well, and maybe 36, if your definition says that a number is a multiple of itself or is a factor of itself.)
The problems predate the Common Core by a long time. The problem is that the textbooks are written by hacks who are trying to slavishly follow the instructions of publishers and textbook committees and the organizations who lobby the committees. Everybody has an agenda, often a political one of the right or the left, and no one is really trying to create a great textbook. Everyone is trying to avoid getting fired from their jobs, so they follow instructions no matter what. Their job isn’t producing a great textbook; rather, it’s following the instructions they’re given.
I have no experience with Common Core, so I’ll ask. Coming into the question cold, and knowing that real snowflakes have six-fold symmetry, the question seems really bizarre. Could this have been one of a series of questions, where the idea of Tyler making paper snowflakes with different numbers of sides was introduced earlier? Then the only issue would be the missing word “many” (which might not have been missing from the original text).
A little Google searching found some textbooks that included discussion of fractals that were either square snowflakes or triangle snowflakes.
ETA: and here, a little more searching found me even more:
And finally, here is the actual worksheet:
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.
Also, a couple of the websites I found made fun of the notion of “reasonable estimate” instead of a calculation. That’s actually a great practice intended to give kids the chance to check their answers; but hey, in the good old days we just churned through the calculation and assumed it was right at the end. It was good enough for us!
It only gets worse.
Tomorrow’s question: How long is a piece of string?
What’s the point of your joke about the length of a string? There’s no string mentioned in the worksheet that Maserschmidt links to, so I presume that you’re trying to make some obscure joke. In any case, note that several of the questions in that worksheet have things missing. Apparently, when the file was converted to html from whatever it was before, things couldn’t be converted and thus dropped off. Possibly this wasn’t a final form of the worksheet but needed to be finished before it was released, which would mean that it’s a preliminary form of the worksheet that somebody inside released outside without permission. It appears to be impossible to access the part of the Carroll County website where this is stored for parents to access, since you need the password. All of the things in this worksheet strike me as being reasonable topics for a child at that level to study, although some of the questions could be better phrased.
I don’t think it’s all that obscure a joke. Monday’s question will be “How high is up?”
These things only need about ten seconds of consideration, plus a few moments of Googling (1) who says so and (2) where to determine their validity. Going on endlessly about its “meaning” without checking to see that it is or isn’t essentially bullshit to begin with is… so Oughts.
Any chance that this is some garbled reference to the Koch snowflake, a fractal generated by repeatedly adding triangles to a triangular starting form? It’s the only context in which I can conceive of a connection between triangles and snowflakes…
I think Kenm’s joke is pointless. What he’s doing is the typical “Hey, I’ve found something here that’s a little strange. So what I’ll do is wildly exaggerate it. Then if people accept my exaggeration they will henceforth quote my ridiculous exaggeration instead of the original thing which was only slightly off. If they question my exaggeration, I’ll accuse them of not getting the joke. So I win either way. Either I will cause people to not understand that the original item was only slightly off, or I will make anyone who disagrees with me look like a jerk.”
Perhaps in the back of someone’s mind was the Koch snowflake, but if so it was only an unconscious memory perhaps. You can understand what the question-maker is saying without worrying about the Koch snowflake. The question from the OP is oddly framed and could be better written, but it’s not inherently ridiculous.
Other than that one question being a bit wonky, I don’t see any problem with that worksheet at all. Seems like a perfectly reasonably set of “practical math” review questions.
I also found the following, which would appear to be from the school district in question:
[QUOTE=Cecil County Public Schools]
The Common Core is not a curriculum. The new standards do not tell our teachers what or how to teach; they simply outline the skills that all students should master. CCPS teachers have worked with our central office to write our own curriculum, using Common Core standards as a guide. The Common Core effort was launched through a partnership of the Council of Chief State School Officers and the National Governors Association working together with parents, teachers, school administrators, and educators from across the country. The federal government was not involved in writing these standards.
[/QUOTE]
I don’t see any grounds at all to somehow blame triangular snowflakes on the evil Common Corps Curriculum.
Not to defend the author(s) of the worksheet, but literal triangular snowflakes are quite real (scroll about two thirds of the way down for pictures and discussion). It is a myth that all snowflakes are hexagonal. There are several non-hexagonal forms (as well as several types of hexagonal ones). (I do not know how Tyler managed to make any, however.)
Or he could click the link upthread… 