Kid starts from left when regrouping in subtraction

[chilliepepper]

WTH? After I-don't-know-how-many-exercises in which my kid has ALWAYS started subtracting in the ones column, determining from there if the tens column needed to be regrouped and so on, BAM. All of a sudden he's subtracting 132-76 and wants to start by regrouping the 100s column.

 

Not that it makes any difference in this particular problem, but I need to tell him the reason that we always start in the ones column when subtracting.

 

While I've been typing this, he's tried to prove me wrong by showing that you can also start from the left when subtracting 360-82 in columns, and get the same answer as when you start from the right.

 

On a good day, I could probably explain this but at the moment I can't. I know it has to do with place value and I probably need to get out some Unifix cubes or something, LOL. Can you help? What we need is a simple example of when it DOESN'T work to start regrouping in another column besides the 1s.

 

Thanks.

[Kiara.I]

Well...you can actually start on any side you like, as long as you make all the trades (regroupings) correctly.  So, does he HAVE TO start on the right?  Or can he go through from the left, figure out any trades to be made, and do it that way?

 

Our curriculum teaches it from the left.   ;)

Edited May 17, 2016 by Kiara.I

[HomeAgain]

We teach from the left.  86-29 would be 86-20-9.  It's easier mentally than the borrow-from-the-left method, though that is faster on paper.

[Syllieann]

Well, he's right in the two problems you showed. Maybe he saw that he would need to regroup all the columns and just started there. My Ds likes to start as far to the left as necessary to set the problem up for simple top to bottom subtraction. Come to think of it, so do I.

[Syllieann]

Oh, so a simple example would be 864-239. If he can do that correctly, I would say he is just figuring out which will need to be grouped rather than blindly regrouping from left to right.

[TX Native]

I taught it from the left. Explaining borrowing and carrying from the right when dealing with a bunch of zeros traded was driving me batty. Our math program teaches an optional way from left to right using negative numbers. So far the method works clearly and consistently for my children. I wish I would have learned subtraction with regrouping this way.

 

I can't demo the way we write it IRL on the keyboard, but imagine the answer below having a 1 in the thousands place, a -1 in the hundreds place, a 1 in the tens place, and a -3 in the ones place. The way to solve this mentally is as written, it just doesn't need to be written out in the expanded form below on paper.

 

2,035

-1,128

---------

1000-100+10-3=907

[ScoutTN]

Khan academy has good videos on subtraction from the left.

Right Start teaches it that way on purpose! 

[kbutton]

Most people start on the right because if you start on the left and regroup something that doesn't need it, then you end up having to carry something or fix your regrouping. It's less likely when you do it from right to left. Does that answer your why question?

 

Miquon teaches left to right or something of that nature. My son does it from the right now, but doing it the other way cemented his understanding. 

[happypamama]

I'm pretty sure that's how my rising sixth grader does it.  That's often how *I* do it myself, and nobody taught me that way; I just do it.  

[chilliepepper]

Most people start on the right because if you start on the left and regroup something that doesn't need it, then you end up having to carry something or fix your regrouping. It's less likely when you do it from right to left. Does that answer your why question?

 

Yes. :) Thank you.

[Ausmumof3]

as long as you look first and regroup correctly it's fine. Singapore does it this way in some problems and sometimes it's more efficient.

 

Not how I was taught but not wrong and if used correctly demonstrates better understanding than just learning and applying a standardised procedure

 

The reason it can be more efficient is you look at all the ones tens etc to see where you need to regroup then do all the regrouping then all the subtracting. If you go from the don't you might regroup 10s then have to regroup 100s to take the 10s.

Edited May 18, 2016 by Ausmumof3

[tm919]

My daughter does it either way, almost interchangeably.... though I think she does right to left more on paper and  left to right more in her head. Not sure why, but I just let it go... since observing this I've realized *I* do left to right when I'm figuring something out without paper too, and always have.

Edited May 18, 2016 by tm919

[El...]

Yes, Dd does that sometimes, too.  It throws me, but she gets the problems right and understands what she is doing.  I think she's a tad faster than I am at looking over the whole question and knowing the plan of attack (and that scares me for future math teaching, but anyhow!). 

 

Edited because I can't spell before the second cup of coffee.

Edited May 18, 2016 by elroisees

[vonbon]

I was taught to ONLY start on the right as a child, for the above-mentioned reasons.  

 

The thing is, now that I'm an adult using math on a daily, practical basis (mileage, bills, ounces, etc.), I use the methods we're exploring in Singapore, which are both algorithm-based and mental-math-based...

 

Example: 852 - 24 =  At this point in life, I've gotten good at estimating, so it's easier / faster for my brain to say 850 - 25 = 825...12 - 4 = 8...828

 

I can't believe how quickly I can do this type of problem now and it is much more efficient and accurate for me.  Prior to figuring this out on my own as an adult, I would literally have to "write" the problem in my head as I would have on paper, start in the right / ones column, "cross out" and borrow from tens in my head, etc.  You know how difficult it is and how long it takes to do that without paper, which I usually don't have when I'm in a real-life situation?!  It's also fraught with opportunities to make mistakes.  

 

i.e., I was mainly taught the subtraction algorithm as a child--always and only starting from the right, vs. truly making use of estimating and mentally playing with the ones/tens/hundreds as groups.  

 

I'm really excited for my kids that they're going to learn it BOTH ways.  I hope to put a large focus on mental math so that these numbers actually mean something to them, vs. just becoming proficient at a paper-based algorithm.  So far, DD and I have totally different ways of processing math ideas.  We almost never take the same "path" to arrive at an answer, though we both obviously get to the same answer if it's correct.

 

I took a workshop last fall on addition and subtraction.  You should have seen the vast number of ways we adults (approx. 10 people) arrived at the same answer for the same problem.  It was almost comical!  There were SO many ways to skin a cat.  It was truly fascinating to see the mental acrobatics people did to get the answer and, if there were 10 people, there were 10 different avenues to the same answer, from differing slightly on one step to differing throughout all of the steps of the problem.  I think we should encourage people to do math in ways that are natural to them.

 

I say, if your DS can arrive at the correct answer in his own way, encourage it!   It truly will serve him in the long run throughout his life, even if it's not the way you would do it.  If we box our kids into stiff rules with math that make no difference (I'm not saying inaccuracy is OK as a whole; we have to use methods that eventually arrive at an accurate answer), I think that = boring and kills the joy of math.