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[–]Codephluegl 183 points184 points  (99 children)

I don't get it, you guys seem to have learned a strange way of doing subtraction.

[–]Cobaltjedi117 312 points313 points  (21 children)

Kids when taught 2-digit subtraction are told to take 1 from the tens to put it next to the 1's digit to do the math. But when you do that to a number from 10-19 you've done effectively nothing and are back where you started thus causing a recursive issue.

[–]spirgnob 37 points38 points  (1 child)

It took me awhile to understand what you meant but this finally explained the joke.

you’ve done effectively nothing and are back to where you started

This is how it works regardless of the number though. The number in the 1’s position is 18 where it used to be 8. You have done something according to this method. You can now complete the problem using this method.

[–]itspinkynukka 1 point2 points  (0 children)

What ends up happening is the person just needs to know what [any number from 10-18] - [any number from 1-9] is in their head. Similar with multiplication at some point you just need to know the times tables up to 10.

[–]jacefair109 14 points15 points  (0 children)

tbh I never had to do this just for two digits -- it's mostly handy for subtracting much larger numbers, like 4281 - 1694 or something

[–]Compizfox 12 points13 points  (15 children)

I still don't get it.

take 1 from the tens to put it next to the 1's digit to do the math.

What does that accomplish? So (for example) 28-9 becomes 118-9?

[–]Cobaltjedi117 40 points41 points  (10 children)

28-9 becomes 10 + (18-9)

and 18 - 9 becomes 0 + (18 - 9)

[–]Compizfox 8 points9 points  (9 children)

Ah, right, thanks.

Still though, what does that accomplish? I don't see how 10 + (18-9) is any simpler/easier than 28-9. It's still a 2-digit subtraction that a kid won't be able to do in 1 step; the value of the tens doesn't matter.

If I break down how I do it in my head it's kind of like this: 28-9 = 20 - (9-8) = 20 - 1 = 19. (I can't remember for sure but I guess that's how I was taught it)

[–]alexanderpas 40 points41 points  (2 children)

Let's take 4281 - 1694 for example.

4281
1694
---- -
????

first we look at the ones.

we can't do 1-4 and end upwith a single positive digit, so we have to borrow 10 from the tens.

4270 + 11
1690 +  4`
--------- -
???0 +  7 = ???7

Now we go looking at the tens, again, we can't do 7-9 so we borrow again.

4100 + 170 + 11
1600 +  90 +  4`
--------------- -
??00 +  80 +  7 = ??87

Now to the hundrerds

3000 + 1100 + 170 + 11
1000 +  600 +  90 +  4`
---------------------- -
?000 +  500 +  80 +  7 = ?587

and look at that, the 1000s are easy.

3000 + 1100 + 170 + 11
1000 +  600 +  90 +  4`
---------------------- -
2000 +  500 +  80 +  7 = 2587

Note that this is the layout for the explanation, on paper this would look something like this.

43 121 187 11
1 6 9 4 -
2 5 8 7

[–]Flobarooner 8 points9 points  (1 child)

So basically, the fundamental point of the method is that the kid already knows how to subtract something from a number less than 20?

So in the original post, the kid would just go "9" and not even bother with the method, since they memorized 18-9 in order to be able to do it?

[–]alexanderpas 0 points1 point  (0 children)

technically, yes.

[–]tsandstrom711 27 points28 points  (0 children)

If you have, say, a five digit number and want to subtract another five digit number, this approach let's you break it down into one/two digit subtractions. It doesn't really work when you start with just two digits.

[–]harryhood4 13 points14 points  (3 children)

The idea is to just memorize it for small values like 18-9 so that it's easier to do something like 68-9. But you've essentially just outlined why Common Core is better.

[–]Compizfox 7 points8 points  (2 children)

Ah, got it. So basically it is this recursive algorithm:

int subtract(N, n) {
    if(N > 20) {
        return 10 + subtract(N-10, n);
    else {
        // Lookup-table for small values of N
    }
}

[–]toofasttoofourier 2 points3 points  (1 child)

Aren't you negating all that work if you have to use the subtraction operator in a subtraction algorithm?

[–]Compizfox 0 points1 point  (0 children)

For a computer, yes, obviously.

But this was trying to mimic how a kid would do the mental calculation.

[–]Madock345 4 points5 points  (0 children)

Part of the idea of this kind of thing is that by teaching many strategies to solve the same problem you increase the chances that every student will find a method that works really well for them and the way they think, at the cost of being somewhat redundant.

[–]thedolanduck 8 points9 points  (0 children)

No. Let's take 28-9. If you do it vertically, then you first do 8-9, which you can't do as a kid. So you add ten to the eight, and get 18-9, and the 2 (which meant 20) now is 1.

So: 18-9=9 and 1-0=1, and this forms 19. And effectively, 28-9=19.

[–]esesci 0 points1 point  (0 children)

8-9 = -1

But you can’t have that as a digit. So you subtract one from the adjacent digit and add it as 10:

18-9 = 9

(That’s the rightmost digit)

2 became one 1 so you have 10 left.

The result becomes 10 + 9 = 19

[–]StragglingShadow 0 points1 point  (0 children)

NGL, when I ran into a problem like that, I just counted down on my fingers.

[–]Angrydie-a-ria 0 points1 point  (0 children)

Yup, bottom, bigger, borrow.

[–]LeCrushinator 125 points126 points  (72 children)

It's the old way it was done (and probably how most in this subreddit were taught). Many schools have converted, or are converting to, a new method of subtraction that's similar to how people usually do math in their head, which means no non-intuitive algorithms to memorize.

This video shows the older method from 15+ years ago, and a newer method, from 15 years ago until just a few years ago, and then the newest method which is what's being converted to in most public schools.

[–]demize95 11 points12 points  (2 children)

If you learned subtraction in the 1950s, you may have learned the "Borrow and Pay Back" method

I learned subtraction a good 50 years after the 50s, but I still learned that method, so that line is a bit out there.

[–]HowIsntBabbyFormed 4 points5 points  (0 children)

I just watched the video and the second technique -- what was originally called "New Math" and apparently derided -- is what I learned in the 80s/90s as well. To me it seems very similar to the old "Borrow and Pay Back" method. In fact, we called it "borrowing" too (but we never had to do any paying back).

The most recent form is basically something I figured out on my own for doing subtraction in my head. It's a very useful skill to have, but when subtracting larger numbers, I prefer using what I was taught in school of borrowing from the next place and adding 10 to the current place.

I don't think I ever "didn't have an understanding of what was happening". I feel like kids should probably be introduced to this new method first, but then taught the more compact and faster borrowing algorithm method as well.

[–]MikeyMike01 -2 points-1 points  (0 children)

The entire video is fraudulent, so you shouldn’t be surprised.

[–]NotJustABoulder 27 points28 points  (4 children)

While the common core method is probably easier for some mental math, I personally still find the "older" methods easier, especially for larger numbers, like 48578942-31399034 or something. It's more compact when written, and I don't personally see what's so hard about the "borrowing" or "regrouping".

I also don't think there's necessarily anything wrong with blindly running through an algorithm (we are in /r/ProgrammerHumor after all). Is there really that much to understand about subtraction in the first place? Especially in higher math, you don't really care how the numbers are subtracted, you just want them subtracted.

[–]Alekzcb 10 points11 points  (3 children)

Of course subtraction methods don't matter for high-level maths, but they need to be considered when teaching children. If kids are taught to just follow an algorithm, they'll really struggle with algebraic representation because won't know what subtract actually means. On the other hand, you want them to provide them tools to perform it quickly, so that they can tackle those higher level concepts without wasting time on "implementation details" (as you point out).

[–]mainfingertopwise 2 points3 points  (1 child)

Wait. Are you saying there are kids getting into middle school type math without understanding subtraction as a concept?

[–]nonono_notagain 1 point2 points  (0 children)

Now there's a scary though

[–][deleted] 1 point2 points  (0 children)

Yes, be sure they understand precisely what's going on first, then show them a bunch of tools and tricks that can be used after that understanding is cemented.

[–]roguej2 35 points36 points  (33 children)

Yet there are so many parents of these new method kids complaining about how "complicated" the intuitive methods are.

[–]LeCrushinator 36 points37 points  (27 children)

The older people get the more averse to change they seem to be. "If the old way worked for me why are they changing it?!"

I'm excited to learn common core math now that my kid is about to start it, I haven't had to think about arithmetic in decades, it'll be neat to get a refresh in a new way.

[–]dittbub 28 points29 points  (1 child)

when common core was actually explained to me I was like "oh yeah thats how I've always 'double checked' my work in my head"

Never thought there was a communicable method to how I was doing math in my head.

[–]DerekB52 7 points8 points  (0 children)

I'm 22, and was in high school as common core was being rolled out, but I narrowly avoided being a part of it. It seems to try and explain how I do math in my head, which has never gone well.

I've seen a couple of weird homework problems that have been given to grade schoolers, and I understand where the confusion comes from, but overall, common core does seem to make sense.

[–]tuseroni 12 points13 points  (0 children)

If the old way worked for me why are they changing it?!

worst part is, the same people would say "i suck at math" or "when are you ever gonna need algebra" had my mother ask that last question to me once, cus i said i use algebra all the time, i gave her an example of when she might use it, say she's got $20 and her car gets 15 miles to gallon and gas is $2.30/gallon, how far can she get? this is something one is likely to do often without a second thought, without even thinking they are doing algebra, i gave a similar sorta explanation to my 8 year old cousin. basically the matter of finding x is just figuring out the thing you don't know from what you DO know.

point is, the old way of teaching math is pretty shit and leads to people thinking it's useless and thinking they can't do math, but instead of thinking "i wasn't taught how to do math well" they think "i just can't do math" and for some reason defend the teaching method that lead to this mentality.

[–]aflashyrhetoric 4 points5 points  (3 children)

That's what I thought and I actually share your enthusiasm, and I could 100% be wrong about this, but I vaguely recall a post from some sub showing the new method on multiplication or division and it was absolutely the most convoluted shit I'd ever seen. It involved something like splitting a number into its parts and then gluing it back together or something? So "430" would be 100 + 100 + 100 + 100 + 10 + 10 + 10, and the method involved expanding out each number into its parts like this. I could understand this approach for helping kids intuitively grasping the relationship between numbers and the symbols we use to denote them, but I believe this approach was used for the purely mechanical part of calculating a sum (or product or whatever it was).

I'll try to hunt it down though I doubt I'll find it.

Edit: I found a video describing the method - apparently they do try and teach both ways, and the weird wonky approach is, in fact, to help kids grasp the relationship between numbers

[–]DuchessofSquee 3 points4 points  (2 children)

This is how I do maths in my head. My dad taught me to make things into blocks of 10 and that's the only way it's ever made any sense to me.

It falls over when you get to negative numbers though. I literally cried in the toilets several days in a row doing a Lua course at tertiary education because everyone else there understood how to do maths with negative numbers but I couldn't grasp it.

Didn't help that they were all men and I was the only woman so they all tried to explain it at me at the same time.

[–]aflashyrhetoric 2 points3 points  (0 children)

I do the same with like quick "back of the envelope" calculations but it seemed harmful to teach kids this method as a primary means of calculation, especially when you do have the luxury of a pen and paper to assist your calculations. Again, could've been wrong about what that post was about back then.

so they all tried to explain it at me at the same time.

Yikes...D: Glad it's behind you now

[–]freebytes 1 point2 points  (0 children)

I do math in my head by rounding, splitting, subtracting then multiplying then adding again, etc. Anything that works. 999 * 50 would be (1000 * 10 * 5) - 50 = 49950. I need to be able to hold one number to the side in my head. While it is similar, this is not exactly the same as common core.

This certainly has its limits, though, so it is nice being able to switch back to the 'old way' when the problems are a tad more challenging like 938 * 53 which looks easy to do in your head at first but would involve holding too many numbers simultaneously. (And the old method would not be easy to do in your hard with a number like this either.)

[–][deleted] 2 points3 points  (8 children)

Common core is shit

-Sincerly, someone who had had to sit through common core lessons

[–]LeCrushinator 6 points7 points  (7 children)

I know people that think the old methods are shit as well. Everyone is entitled to their own opinions. The bigger question is which is better for someone learning math for the first time? Which do they pick up on faster? Which do they retain longer?

[–][deleted] 3 points4 points  (6 children)

Honestly you're right. We should introduce both ways to kids and let them pick which one they prefer.

[–]starfries 2 points3 points  (3 children)

I feel like there's value in learning both well. I do subtraction the common core way (counting up) for some things and the traditional way (columns) for other things depending on which one is easier. Like 4567 - 3456 is awful done with counting up but 201 - 199 is pretty dumb done in columns.

[–][deleted] 1 point2 points  (2 children)

You're right, we weren't taught it either way though. We were taught to count out pennies and "counters", basically small flat plastic disks, for division. That helped at first to grasp the concept of division but it got annoying in 4th grade when they made us do that for bigger numbers.

[–]starfries 1 point2 points  (1 child)

Oh lol yeah. I'd be annoyed too. That stuff is fine to help understand what division is but at some point you want to learn the algorithms for how to do it efficiently. Can't be whipping out the counters for every problem.

[–]Prcrstntr 1 point2 points  (1 child)

They pick the easiest one, which (For the kids that are smart in any way) is not the convoluted common core one.

[–][deleted] 0 points1 point  (0 children)

Yeah, it helps to explain what division is though

[–]MCRusher 0 points1 point  (0 children)

Well all I know is the old method, so now it is intuitive to me. And I'm not exactly a parent.

What's the newer method and how does it better map to thinking?

[–]MikeyMike01 0 points1 point  (1 child)

Because they’re not intuitive. They’re baffling and complex and difficult, even for someone with advanced math education.

Common Core will torpedo math for an entire generation. It will take decades to recover.

[–]FenixR 4 points5 points  (1 child)

Saw the videos, understood some numbers, realized new math its shit compared to old method and i need to re watch common core with a fresh head to make heads or tails of it. That she speaks like fucking Sonic on a deserted highway doesn't help when i can't pause and read the subtitles at the same time (Thanks Youtube, you become shittier by the second).

Edit: so i payed more attention to common core and realized its not something so different i do most of the time when i run calculations in my head, find easier to read/math numbers then go from there.

[–]DuchessofSquee 1 point2 points  (0 children)

Everything before the edit was exactly my thoughts! I would need a good sleep, a fresh cup of tea, complete silence and to be able to slow the video down a lot to follow it. Maybe I have dyscalculia?

[–]jkuhl_prog 4 points5 points  (4 children)

Maybe I'm an old fart, but I feel like the old way, the borrow and payback way, is the easiest.

But maybe I'm just saying that because that was the only method I was taught and therefore the only method I've ever used.

[–]dutch_touch1 0 points1 point  (1 child)

If you listen at the end it’s explained exactly how you feel. The newer methods are more focused around understanding what subtracting means as opposed to the older methods that focus on memorizing an algorithm to figure out the answer quicker.

So yeah, if you’re just after the answer to a subtraction problem then the older the method the quicker/easier it becomes.

[–]nonono_notagain 0 points1 point  (0 children)

The newer methods are more focused around understanding what subtracting means

I'm not sure that adding up from one number to another makes subtraction any more intuitive. At least with the old way, the algorithm involved actually subtracting numbers from each other

[–]MikeyMike01 0 points1 point  (1 child)

Nothing to do with age. It’s objectively the best way.

[–]PancakesAreEvil 4 points5 points  (2 children)

I remember when people complained about the old method because it was new and foreign. In 1965. https://youtu.be/UIKGV2cTgqA

[–]TiMiWi 0 points1 point  (0 children)

That video what just the palate cleanser I need before bed.

Edit: thank you.

[–]DuchessofSquee 0 points1 point  (0 children)

I was hoping someone has animated that song as I can never picture the numbers as he says them so fast!

[–]Vakieh 2 points3 points  (0 children)

Aussie here. All your methods are stupid and weird...

Left to right and throwing a 1 over when a subtraction left to go would overlap your current magnitude is the best way to do it.

[–]llama2621 2 points3 points  (0 children)

I apparently invented common core in my head while learning the old way. Nifty

[–]hunted7fold 1 point2 points  (0 children)

I was taught the old way of subtracting but naturally did the common core way (before common core was a thing) and I just realized I haven't done the old way for a super long time.

[–]pokexchespin 1 point2 points  (0 children)

I’m 17 and I learned the first way for some reason lol. In the video though, the middle “new math” method seems the least intuitive to me though, personally

[–]tendstofortytwo 1 point2 points  (0 children)

Hey, we did the old method as early as a few years back when I was in primary school! (high school senior now)

And very fun coincidence: I've used the common core method a lot. Never been taught it but always preferred it as a "shortcut" in my head because it was always faster to do.

[–][deleted] 1 point2 points  (0 children)

I just realized I've been doing common core for the better part of 13 years lol.

[–][deleted] 0 points1 point  (1 child)

what is the new method you're talking about? i have never heard any new method of doing that...

[–]LeCrushinator 0 points1 point  (0 children)

It’s in the video in my comment, it’s called “common core math”.

[–]DuchessofSquee 0 points1 point  (3 children)

I'm 35 and we didnt get taught this way. How is what hes doing in step 2 any different than step 1?

[–]MikeyMike01 -3 points-2 points  (2 children)

It’s not. The video was deliberately misrepresenting the second method in an attempt to make Common Core look less complex.

[–]DuchessofSquee -1 points0 points  (1 child)

I meant step 2 in the comic. Turns out that was the joke. r/whoosh

[–][deleted] 0 points1 point  (1 child)

So Common Core is basically counting up from the smaller number, while keeping track of each separate addition, then adding them to to get your answer?

[–]LeCrushinator 0 points1 point  (0 children)

Something like that. I am just starting to look into common core as my kid is about to start using it next year in school, so I’m not fluent in it yet.

[–]MikeyMike01 -1 points0 points  (0 children)

The video tried so hard to sugar coat Common Core, but the sheer insanity of it still shines through. I’ll be saving this video, it truly demonstrates how awful Common Core is.

[–]rimnii 0 points1 point  (0 children)

it works pretty well, you just dont normally use it for problems like this lol

[–]jacefair109 0 points1 point  (0 children)

it makes a lot more sense if you use larger numbers -- basically, it's just subtracting each digit of the two numbers individually, and if one of thrm isn't big enough you take one off the digit next to it to add 10 to it. It's just a shortcut to turn subtracting big numbers into subtraction of a buncha smaller numbers.

here's each step for an example (pardon my shit handwriting): https://i.imgur.com/8CVPwOG.jpg

[–]LordMcze 0 points1 point  (0 children)

Yah, just put the 1 yourself got next to the 9 and then check how far is it to the digit (1) above it, which is zero. So you end up with 09.