Carrying and Borrowing

Date: 01/14/98 at 14:18:13
From: Barbara PArnell
Subject: Addition and subtraction

My son has a problem understanding addition and subtraction when he 
has to do regrouping, what I call carrying and borrowing. He can 
borrow a number from the tens or hundreds column but then forgets to 
add it in the total. I have explained it, but maybe I'm doing it 
wrong. Any ideas on how to explain this so that he understands? He is 
in 3rd grade.

Date: 01/15/98 at 09:39:54
From: Doctor Fred
Subject: Re: Addition and subtraction

When I taught this to my son I used money. Get some pennies, dimes, 
and dollar bills. We'll ignore the decimal place involved in the 
money. Since your son is in 3rd grade that shouldn't bother him.  

Consider the problem, 

       58
    + 265
   ------

Put 5 dimes and 8 pennies out on the table to represent 58.
Put 2 dollars, 6 dimes and 5 pennies on the table to represent 265.

He should be comfortable with the idea of adding as putting the two 
quantities, or piles, together.

Have him notice that we have a lot of pennies, 13 to be exact. We can 
trade in 10 of those pennies for a dime. We still have 3 pennies left 
so we write the 3 under the first column of the addition. We now have 
another dime so we put a 1 above the dimes column.

       1
       58
    + 265
    -----
        3

Now let's look at the dimes. We have 12 of them. Again, trade in 10 
dimes for a dollar bill. We'll have 2 dimes left. Put a 2 under the 
second column of the addition. We also have 1 more dollar than before.  
Put a 1 over the "dollars" column.

      11
       58
    + 265
    -----
       23

Now, we have 3 dollar bills so we write the 3 at the bottom and we are 
done.

      11
       58
    + 265
    -----
      323

You can work a lot of examples that way.  

I hope that helps.

-Doctor Fred,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/