342 - 87?
Common core: 13 + 200 + 42 = 255. Same way I'd do it in my head (well, I'd do 213+42).
Old school way: 2 - 7 = 5 (borrow 1 from 4), 3 - 8 = 5 (borrow 1 from 3), 2 - 0 = 2 : 255. If you're doing a math problem in your head....why work backwards?
37 * 12?
37
x12
Common core way: 30 * 10 = 300, 30 * 2 = 60, 7 * 10 = 70, 7 * 2 = 14: 300+60+70+14 = 444. (In my head, I'd do 12*30 + 12*7 = 360 + 84 = 400 + 44.)
Old school way: 2 * 7 = 4 (carry the 1), 2 * 3 + 1 = 7, place a 0, 1 * 7 = 7, 1 * 3 = 3: 74 + 370 = 444. (I had to write in the spoiler above so I could see the math problem to do it in my head that way.)
Not sure about y'all, but to me, it's important to both be able to do the math properly (determine the correct answer) as well as understand why/how you're getting the answer (ie: have good logic/reasoning as to why you came up with your answer).
How do you do a math problem in your head? I think I've almost always used the "common core way" to do math in my head: Break down a "complicated" problem into smaller yet simple problems.
Other than that, I don't know what might be wrong about common core. But I suspect it is the same problem way back in the 60s that we had with "new math". In that case, a greedy bunch of people got together and decided to try to get rich by selling the textbooks etc on something that was obviously flawed.
Now you might say that is just my cynical opinion. But I can prove that:
Quote: ams288I've seen viral images of common core math assignments where the student has to "show their work." The student got the correct answer to the math problem, but they lost credit because they didn't use the correct "common core way" to get to that answer. Which is B.S.
Learning a methodology is just as important as knowing the answer, as it can be useful to look at different problems in different manners.
The problem is testing the student's understanding of the methodology, not the ability to arrive at the correct answer.
Didn't you always have to show your work? It's to show you understand the concepts, not that you can get the answer.
342-87=
342-42=300
and 87-42=45
300-45=255
That said, I always had difficulty in math because I had such an ability to do it in my head. I mean I was multiplying 3 digits by 3 digits in my head when I was 5 years old. I always had issues with being tasked to show my work when I found 346 x 412 (142,552 BTW) was as mundane as doing 6 x 8. That said math started losing me when I got into algebra and completely lost me when I got into stats and calculus. I remember the lesson to this day where I began losing interest in math on an academic level. It was the day where we were multiplying (I think they were called binomials) stuff like ( x + 3) (x + 4). The lesson was called F.O.I.L. standing for First, Outside, Inside, Last. to get the solution. You would do multipication in that order so you would do x * x, x * 4, x * 3, and 3 * 4. To get x squared + 7x + 12. I envision x being something like 7, and I didn't felt it was kind of stupid to make a simple problem like 10 * 11 = 110 and turning it into 49 + 49 + 12 to get the same answer and adding additional steps.
Quote: RS
37 * 12?
37
x12
Common core way: 30 * 10 = 300, 30 * 2 = 60, 7 * 10 = 70, 7 * 2 = 14: 300+60+70+14 = 444. (In my head, I'd do 12*30 + 12*7 = 360 + 84 = 400 + 44.)
How do you do a math problem in your head? I think I've almost always used the "common core way" to do math in my head: Break down a "complicated" problem into smaller yet simple problems.
In my head, for 37*12, I think 37*10 for a quick 370 and add 74 (after a quick 37*2) for 444.
Fortunately for me, my kids are adults and I didn't get exposed to common core. My thinking is that it is awesome for a teacher to be able to explain several ways to solve a problem. Let the kid choose how he wants to solve it. It shouldn't make any difference as long as the kid does the work and gets the right answer.
One dad pretty well summed up the (ill-informed) opposition to 10 squares by flipping out and writing a "common core" check
+444Quote: ukaserexFortunately for me, my kids are adults and I didn't get exposed to common core. My thinking is that it is awesome for a teacher to be able to explain several ways to solve a problem. Let the kid choose how he wants to solve it. It shouldn't make any difference as long as the kid does the work and gets the right answer.
To teach that only one method is "correct" is foolishness. Not all minds think alike, and what 'clicks' for one may not click for the other. Who does it benefit to teach and test only one methodology? This is what turns students off to math.
As to the OP, for me, 37*12 breaks down to 360 + 84 in my head, which gets added as 36 + 8 = 44, then concatenate the last 4 to the end to get 444. If the second number was in the 90's, I would have added 100 and subtracted the proper units' digit. I find that different numbers get treated differently by my brain.
Quote: MoscaI'd do 342-87 as 342-100+13.
On second thought -- I would have done it that way as well.
Quote: ams288I've seen viral images of common core math assignments where the student has to "show their work." The student got the correct answer to the math problem, but they lost credit because they didn't use the correct "common core way" to get to that answer. Which is B.S.
*What school did you go to, where all you had to do was fill in the correct answer and you didn't have to "show your work"? I lost plenty of points in lower/middle/high school because I didn't always show my work. Teachers usually said something like, "You don't have to show your work for something that is obvious." I took it to mean, "If I can quickly and accurately do it in my head, showing my work isn't necessary." I had to complain to my teachers a couple times because I wouldn't think 12*13 is something I'd have to show my work for....usually got the points added back to my grade. One teacher suspected me of cheating saying I had to show my work because there's no way it was immediately obvious. I said it was obvious. Teacher asked me another similar question, quickly did it in my head....boom - no more suspicion of cheating, and I don't think the teacher was too worried about me showing my work on not-so-obvious problems (or at least, parts of the problem).
I'm kinda surprised to see more people (at least IMO) support common core math than disagree with it. Perhaps I've seen too many posts and articles on Facebook and whatnot. Theory: Because this is a more math-oriented forum and thus more math-savvy people exist here....I'd say common core is more likely to be supported by those who understand math, and may be more likely to be disagreed with by those who don't quite understand / dislike math. Yay? Nay?
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My child wrote 5x3=15. The "correct" answer was 3x5=15. I wanted to punch someone, especially since the class had already covered the commutative property. Marking correct answers wrong is not the sort of lesson kids should be learning.
That said, the real problem isn't that kids are learning the Common Core math philosophy, it's that their parents didn't learn it. What we have is two or more prior generations having learned a rigid, algorithmic approach to arithmetic calculations based on rote memorization and unyielding steps. That means many parents are often not able to help their kids learn the new techniques. The entire philosophy behind Common Core is antithetical to that rigid approach, it's about teaching kids to correctly intuit their way to the right answer using whatever path their minds find most comprehensible. I get the philosophy, it's just harder to implement in practice because nobody's used to it yet.
Quote: MathExtremist...Part of the problem is that the teachers never learned it (as kids) and the textbooks aren't always entirely clear as to how to interpret the problems, so there are lots of teacher misinterpretations...
Almost every example of "bad" common core I have seen my friends complaining about with their kids' homework comes back to this. The teacher doesn't understand it and is using crappy materials, so they end up marking answers wrong when the kid actually understands it just fine. People are complaining about common core but what they should be complaining about is incompetent teachers. Anyone who doesn't realize 5x3=15 is the same as 3x5=15 has no business teaching math.
Quote: MathExtremistThat said, the real problem isn't that kids are learning the Common Core math philosophy, it's that their parents didn't learn it.
New approaches can be mystifying.
I distinctly remember being fresh out of college and asked to help with some homework, kid was maybe in the 8th grade. She was attending a Christian private school and asked me to help by giving me her textbook. I opened it up to where she wanted and IIRC it was on a page about geometry. I swear to you I couldn't understand a word of it. It was all complete gibberish to me. I think I went through the book generally and, same thing, gibberish. It was embarrassing. I wound up questioning myself.
I still think about that once in a while.
These days, I have to guess that they picked up these textbooks really cheap because nobody wanted them. It can't imagine there being a good excuse for making it so hard. If my current thinking is true, what a shame, since my experience with students going to such schools [or being home-schooled] - they can be very good in English and related subjects, impressively good, but likely hurting pretty bad in math and science.
As you can see, I am inclined to sympathize with those questioning the common core changes.
Quote: Gabes22I think the root in most common core math arguments are the same complaints that have been said about our schools since I was a kid. Instead of propping up kids who are excellent and proficient at math, it insteads brings those exemplarery kids back towards the mean. 3 x 5 or 5 x 3 isn't a problem that should require work to show yet common core makes you do so. It's like driving to Las Vegas from Los Angeles by going through San Francisco
I was going to say this. Math classes that are required to graduate (Algebra 2, right?) were so damn boring. They have to cater to the lowest common denominator. Looking back, this was my biggest frustration, my teachers would always talk about things at the stupidest, most basic level, and I'd just be sitting there bored out of my mind. In Junior high, it got better when I was able to take math two grades above me. However, it showed me how much more I could have learned if I was put into a special science class as well... which didn't happen until High School. I'm sure I wasn't unique with this.
Most of the issues I've seen relating to Common Core involve extremely stupid questions being marked wrong for not doing it a longer, more drawn out, way. I have no problem teaching children mental math, which it seems like what this is trying to move them towards, but we need to use some common sense.
I have no practical experience with Common Core, I graduated high school 10 years ago.
First, they are not introducing one new method. They are introducing EVERY method. I tried to help my granddaughter with her work and it was utterly depressing. You have to solve the same problem in five different ways! This means the actual answer is irrelevant (you got the answer the first try) but the method. So kids are being asked to learn five different methods.
Remember how hard it was to learn something in school (any subject you may have found difficult?) Now imagine if you had to learn that difficult subject in five different ways. And you don't get graded if you find the method that suits you best, that you find easiest. You have to learn every method and get them all right or you are getting the question wrong.
In the 3rd grade, my granddaughter would have six to eight pages a night of math, four to five of reading. I mean, her homework sometimes took 3-4 hours to complete. So many parents are upset at this aspect too as they have to divert so much time to helping their kids and half the work looks foreign.
There are dozens of examples of common core math. You should see them and ask how it simplifies things.
Here is a good example of simple math turned common core.
http://sanders6thgrade.blogspot.com/2012/06/common-core-math-training.html
Scroll down to day four!!!
Quote: darkozHere is a good example of simple math turned common core.
http://sanders6thgrade.blogspot.com/2012/06/common-core-math-training.html
Scroll down to day four!!!
I would venture to say even someone like the Wizard gets a headache looking at that stuff. Sure, those who excelled in math before would excel with common core math too, once they learned the ropes.
But I sympathize with the parents etc who have to help.
And, yes, I suspect but won't try to prove that there are elements of "new math" afoot here, selling screwy ideas.
Quote: beachbumbabsI had ignored the common core question until this thread. Graduated 30+ years ago, no more math classes. So, thanks, RS! This closely resembles how I do math in my head, much more so than relying on rote memorization of tables. That's very cool that they figured out a better way to learn it intuitively.
As little as I support kids being required to learn common core, (not at all) the Wizard can attest that I am one of the better people he has ever seen with respect to mental math (he said so, anyway) and common core very closely resembles my mental approach.
Quote: ukaserexQuote: RS
37 * 12?
37
x12
Common core way: 30 * 10 = 300, 30 * 2 = 60, 7 * 10 = 70, 7 * 2 = 14: 300+60+70+14 = 444. (In my head, I'd do 12*30 + 12*7 = 360 + 84 = 400 + 44.)
How do you do a math problem in your head? I think I've almost always used the "common core way" to do math in my head: Break down a "complicated" problem into smaller yet simple problems.
In my head, for 37*12, I think 37*10 for a quick 370 and add 74 (after a quick 37*2) for 444.
Fortunately for me, my kids are adults and I didn't get exposed to common core. My thinking is that it is awesome for a teacher to be able to explain several ways to solve a problem. Let the kid choose how he wants to solve it. It shouldn't make any difference as long as the kid does the work and gets the right answer.
I do math very quickly in my head. Always have, in school it was hard for me to show my math but I could get correct answers easily.
For 37x12 I do 37x10+37+37 instead of multiplying them
Quote: GWAE
I do math very quickly in my head. Always have, in school it was hard for me to show my math but I could get correct answers easily.
For 37x12 I do 37x10+37+37 instead of multiplying them
Mine would be:
(37 * 10) + (37 * 2)
370 + 74
444