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Deb Russell

What Happened to Borrowing and Carrying?

By January 13, 2008

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Yes, when I went to school, we borrowed and we carried when referring to adding and subtracting. However, today the term that is most often used is 'Regrouping' Why? Well, this term really does make sense when you analyze it:
Adding:
Let's take a simple addition question like 34 + 17. We line them up vertically and then say 7 + 4 is 11, so 'carry' the 1 and put is over the 3. Ahhhh, carry the one. It isn't really a 1, it is a group of ten, so it's somewhat misleading. We have really regrouped the 1's into a group of 10 and we put a 1 in the 10's column, the 1 represents a group of ten.
Subtracting:
Let's take the same question 34 - 17 and line the numbers up vertically. We then say, you can't take 7 away from 4 so let's borrow 1 and make it 14. Again, we are actually taking a group of 10. The term borrowing also suggests that we pay it back. So, once again we regroup by taking 1 ten from the tens column and our 4 becomes 14.

The very best way to support young learners with this concept is to use counters, preferably base 10 manipulatives. Another good way to support these concepts are to use money and let dimes and pennies become the counters.
See also:Addition and Subtraction Worksheets

Comments

January 15, 2008 at 3:37 am
(1) Michael says:

Sounds like a Tom Lehrer song to me

January 20, 2008 at 10:52 am
(2) Noreen says:

I look forward to using the dimes and pennies as manipulatives. My SPED students have difficulty generalizing from the concrete manipulative to the formulaic presentation of subtraction. I have created a social story for subtraction that trains the student’s eye to recognize the top number and a simple yes/no dichotomy to determine whether this is a regrouping/borrowing situation.

January 21, 2008 at 3:38 pm
(3) Mary Alice Hatchett says:

Why ‘carry’ at all? With 34+17, most young children (if they haven’t been told that they must start with the ‘ones’ place would start with the ‘tens’ place) 30+10=40; 4+7=11;40+11=51. Most young children would do this in their heads & not need to write down anything.
Now for the subtraction:34-17;34-20 is easy=14, but I subtracted 3 too many, so add them back in 14+3=17. Many 2nd graders and on up would recognize 34 as double 17 & would use that information to say the answer of 17.
I think we spend way too much of our instructional time with ‘regrouping’ instead of asking children to think about how our numbers work together! A typical problem I see children doing is 10-7; and they cross out the one (in the 10s place) and write a small 1 next to the zero (in the ones place). What good has that done? It tells me that they are just following a procedure and not thinking about the numbers!

July 17, 2009 at 11:00 am
(4) R. May says:

Sorry Mary Alice but my child is doing this ‘new’ math you described and it’s horrid! Sure she understands numbers but a simple addition problem done the way you describe takes many steps all over the paper. It’s take her too long to do a simple problem.

It doesn’t work once you get to more complicated problems. How on earth can you do long division until you learn what borrowing and carrying (or regrouping) is. Or algebra. It’s fine as a supplement to increase underatnding on mathematics but should not be taught as the way to do things.

October 5, 2009 at 1:48 am
(5) Mary Alice says:

Sorry for the delayed response — I don’t check this site that often.

Show me a ‘complicated’ problem that doesn’t work.

October 10, 2009 at 3:54 pm
(6) Doc Ramsay says:

Well . . . what bothers me in my selfishness . . . is the implication that the way the boomers and pre-boomers were taught was somehow wrong. I (a pre-boomer) am more comfortable with, and can do all sorts of math much better than most of the people who were raised by the re-group etcetera (Yeah Tom Lehrer) method; (By-the-way I was average not exceptional.) and that’s with or without a calculator.

June 22, 2010 at 11:20 am
(7) Julie says:

I am home schooling my child and we use ABEKA, which is using the “regrouping” method. So far she is confused with the steps of having to regroup her numbers before she just does the problem. Even she asked me, “Why can’t I just borrow this from the tens place without all that other stuff we do?”

I had no good reason. I never did this “regrouping” and I am an excellent math student. I just think it is an additional step that doesn’t add any value to learning.

I like the suggestion that it be used to help students who are confused anyway, but they aren’t then just let that go! Boo to regrouping!

September 13, 2011 at 4:37 pm
(8) Jeri says:

Regrouping is a mess along with sticks and circles, the jumping method and mountain math.
My son was very interested in numbers and money at an early age so he was taught at home the old way (borrowing/carrying). He’s now in 3rd grade where his class is learning addition and subtraction of multiple digit numbers but he’s getting D’s and F’s because he does it the “old way” rather than drawing sticks and circles and counting them. As long as he shows his work and gets the right answer then it shouldn’t matter if he understands any of the new concepts. When he has tried to use them he’s gotten very frustrated because it’s too much busy work.
In my opinion children will learn different ways, for some these new methods are good but the old way should be shown as well – it’s worked for many generations, let’s not make our children feel dumber than they are by simplifying a basic concept.

September 27, 2011 at 8:09 pm
(9) Jeanne Tunks says:

A colleague posed this question that was raised in a mathematics methods course at our university. Can someone address it? Thank you.

Is there a name for subtraction with regrouping strategy when students are taught to “borrow” from the highest place rather than “borrowing” from the next place over?

And, is this method more or less effective than traditional “borrowing” method? Some of my students are seeing the “borrow from the highest place” method in their observation classrooms.

September 27, 2011 at 8:11 pm
(10) Jeanne Tunks says:

This question came up in a university math methods course. Can you address this one?

Is there a name for subtraction with regrouping strategy when students are taught to “borrow” from the highest place rather than “borrowing” from the next place over?

And, is this method more or less effective than traditional “borrowing” method? Some of my students are seeing the “borrow from the highest place” method in their observation classrooms.

July 17, 2012 at 11:12 am
(11) Ben says:

I feel like this discussion about which method is better is not really relevant when both methods (all methods) are relevant. Depending on the student which ever method works for them is fine as long as they demonstrate an understanding, as well as the correct answer. I feel like the idea that all students are different and therefore learn differently has been lost in this discussion. This is especially the case with students with special needs, in particularly those with working memory issues.

“.. Now for the subtraction:34-17;34-20 is easy=14, but I subtracted 3 too many, so add them back in 14+3=17. Many 2nd graders and on up would recognize 34 as double 17 & would use that information to say the answer of 17…”

This method of doing subtraction is fantastic way of doing subtraction though it should be noted that this is actually quite a difficult concept for some children to understand as it requires an extra step (adding the 3 back on). This is more or a less a computation method and this also goes for the addition method mentioned.

The new ‘regroup’ method tends to be more easily understandable when teaching it to students that it constantly relates to the place values. ie: 12+9
T U
1 2
+ 9

October 18, 2012 at 9:52 am
(12) Chris says:

This is like grammar nazis for math (and yes, I realize I just proved Goodwin’s Law). Just because we’re carrying a “one” that is really a ten, hundred, thousand, etc (and do we need to draw a million sticks if we get that high…) doesn’t mean we have to rename what we do merely for the sake of proper semantics. I think if the student understands the places (100s, 10s, 1s) then “carrying” makes perfect sense.

November 1, 2012 at 5:10 pm
(13) Kathy Bickel says:

I respectfully disagree with your comment about carrying. You are carrying the 10 over and noting it with the number one. Call it what you want to but it is still the same. I think the mistake is that people thought they were ‘carrying the one’. I actually had a 1st grade teacher tell me when she was young she didn’t know why she was carrying. The problem isn’t the term used, it is with how the term is taught.

February 20, 2013 at 8:20 am
(14) DWR says:

I disagree. The one carried is placed in the relevant column, thus it can be interpreted in context as ‘ten’, ‘hundred’ etc. the other digits in the column are similarly represented. It would be inconsistent to mark the carry over ad anything other than a single digit.

March 27, 2013 at 9:32 pm
(15) mathguy says:

“carrying” and “borrowing” aren’t really describing what is really being accomplished with the actual QUANTITIES and while these terms might be familar to us, they mask the mathematics and focus thonking on the moving of digits In column addition, a two digit sum in a column requires REGROUPING that column sum into a group of tens and the remaining ones. The group of tens is added to the next column to the left because that column has a value 10 times larger. Conversely, we really don’t “borrow” when we subtract (a student once asked me if it ever gives it back!), we “ungroup” the value in that column into ones so there will be “enough” ones to subtract from.

January 20, 2014 at 11:01 am
(16) Mike says:

My son came home from school and was a little confused about regrouping. I explained the process using borrowing and carrying terminology and he understood it much better. Learning comes from association of what they understand and so I break down the equation into steps:

1. Is the bottom right number larger or smaller than the top?
Larger – borrow; smaller just subtract the right column
2. Cross out what number? And the number becomes what number?
3. The borrowed “1″ goes in front of what number?
4. Now (the new top number) minus (the bottom number) is?
5. Subtract the numbers in the left column

March 3, 2014 at 6:03 pm
(17) Ray says:

“regrouping” – seriously??

Sorry, but the children need to develop an understanding of the essential tools of addition and subtraction. Simply because there may be an easier way to add/subtract small numbers doesn’t justify not teaching a tool that can be applied to larger number sets easily, different numbering systems (base 10 isn’t the only one), and for complex algebraic equations. Focusing on a simplistic way to perform a limited set of problems by calling it “regrouping” is shortsided.

March 5, 2014 at 2:17 am
(18) Pete says:

I admit to not knowing all of the details of “regrouping”, but I am curious as to how this translates to more advanced mathematics. Can a proponent of regrouping please explain how to complete the following?

(4x^2 + 3xy – y^2) – (x^2 + y^2)

The real advantage of the “former” method is that it could directly lead to a method for the above, but for the life of me I can’t think of how it would work with regrouping.

May 19, 2014 at 9:18 pm
(19) Dave says:

Pete, “regrouping” is just a different name for borrowing and carrying. It doesn’t refer to a different procedure. As for your example, regrouping does not apply to addition and subtraction of polynomials (except where it may be used to add or subtract the coefficients).

May 21, 2014 at 11:08 am
(20) Dillon says:

I think at this stage of the game they should leave the math terms alone. Teachers are already burdened with too many children now they have the burden of teaching our children something WE never learned. My wife and I just adopted an 8 year old we’ve had the privilege of parenting since she was 6 (first grade). I tried to help her with her math and she kept correcting me when I say borrow, she would say re-group. However, whenever she would take a math test or have to work independently, she got them all wrong. After their testing and seeing that we weren’t able to teach her, the teachers are too bogged down to teach we enrolled her in a private tutor program. She came home after the first tutor session, I asked how it went. She says with excitement, “I can’t believe how easy it is, it’s called borrowing. I got it now.” : ! Really!!!!! Isn’t that what I showed her last year?? LOL Go back to the terms we all grew up on, please.

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