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The following article has been circulating which includes a video that demonstrations a Common Core math problem: "This Common Core Math Problem Is So Absurdly Difficult It Stumps College Students and Teachers" via Independent Journal Review. In the video, the following steps are taken to solve the math problem "32 - 12 = ?" (summary from Slashdot):

To solve 32 - 12 = ? you do the following:

12 + 3 = 15

15 + 5 = 20

20 + 10 = 30

30 + 2 = 32

Then 3 + 5 = 8, 8 + 10 = 18, 18 + 2 = 20. Therefore 32 - 12 = 20.

Is this an accurate depiction of how math is being taught or is it being grossly exaggerated and is an instruction technique of more limited use like base ten blocks.

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Am I missing something? Where do the numbers come from in those 4 sums? –  Jamiec May 22 at 14:54
This is a valid technique for subtraction. I believe cashiers do this all the time, even though they just collect the coins as they go instead of summing their steps afterwards. –  Jens May 22 at 15:00
@Jens - What is the technique? How does one go from the problem (32 - 12) to the 4 sums following? –  Jamiec May 22 at 15:01
@Jamiec: They are imagining something like counting back change. To figure out the difference I start from 12 and add 3 to get 15, add 5 to get 20, 10 to get 30 and add 2 to get 32 (where we started). The sum of the bits we added is 3+5+10+2=20 (the difference). This is not how I would have written this, but it is a working algorithm for subtraction. Many of these "Here's a bad common core question" posts seem to involve working algorithms that are unlike the "usual" system. I conclude that the idea is to offer a lot of methods and hope each student learns at least one. –  dmckee May 22 at 15:36
Aside from the obvious extra steps, it seems a little tautological to me anyway -- at each step, you kind of implicitly have to do subtraction anyway (when the sum gets to 30, how do you know it's 2 you have to add to it to get 32? You could say you 'count up' to 32, but you also kind of had to know earlier then that it was okay to add 10 to 20). –  YungHummmma May 22 at 16:36
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1 Answer 1

up vote 21 down vote accepted

This is one of four algorithms for subtraction listed here (p. 2). In that document, it is called "Adding Up", or the "Cashier's Algorithm".

It is not always the best algorithm to use, but it's one option. It's particularly useful when the total returned doesn't really matter, but rather only that the correct total was in fact returned. (Said another way, using this algorithm, it would be possible to return the correct amount without having to actually know how much you returned.)

How does this relate to the Common Core? The Common Core standard for Grade 2 operations and algebraic thinking includes "Fluently add and subtract within 20 using mental strategies.", and this is a valid mental strategy. Common Core doesn't prescribe this strategy though, and it doesn't prescribe this problem.

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The standard you linked is talking about adding single digit numbers. I think the more related one might be Use place value understanding and properties of operations to perform multi-digit arithmetic, since it deals with rounding to nearby numbers and multi-digit operations. –  Geobits May 22 at 19:52
This being a third-grade skill goes a long way to explaining why my first-grader gets so bored in math class, though. –  Geobits May 22 at 19:52
@Geobits I think the standard I linked to is about adding and substracting "within 20". But I think you're right, this problem is also related to some other standards like the one you link to. This one, also: Add and subtract within 1000, using [...] the relationship between addition and subtraction. –  Articuno May 22 at 19:58
Interesting: I've never seen the cashier's method used to add up to a non-round number. In particular, if I gave a cashier $22 to pay for a $12 item, I would be upset to get $3 + $5 + $2 in change rather than a $10 note. –  Oddthinking May 22 at 19:58
@Articuno Ah, I was under the assumption it meant the sum was within 20. There's a similar entry for "multiplication within 100" that then says they should know the products of two one-digit numbers. Either way, lots of them seem to overlap now that I look a bit closer. –  Geobits May 22 at 20:02
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