What Happened to Borrowing and Carrying?
Sunday January 13, 2008
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.
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
Sounds like a Tom Lehrer song to me
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.
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!
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.
Sorry for the delayed response — I don’t check this site that often.
Show me a ‘complicated’ problem that doesn’t work.
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.