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A Different Way to Subtract
by Gail Englert

A response to the question:

Could you explain this subtraction method that is different than what is normally taught?

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My daughter is in third grade and is being taught a different way to subtract than I was taught in school. They are calling it "nicks way". The way I learned was, if you were given the problem (34-18) you would borrow from the tens column and do 14 - 8 then do 2-1 and get 16. They don't seem to borrow from the tens column, they borrow from some imaginary place and then remember to give back at the end. My daughter has not be able to explain this to me so I can help her, and I have not had the chance to meet with the teacher yet. If you are familiar with this method could you explain this to me.

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I will bet the class is calling it "Nick's way" because a child named Nick, in her classroom, figured it out. I often name a "discovery" after a student, to help my fifth graders feel ownership.

As for subtraction methods, this is called compensation, and what it does is help the child who is having trouble with regrouping solve the problem without the need to regroup (that is what we did when we "borrowed" from another number). Here is what you do:

Suppose the problem is 34 - 28.

There are actually many problems that will give us the same answer as
      34 - 28, for example,
      33 - 27
      32 - 26
      31 - 25
      30 - 24
      29 - 23     Ah ha!   Look at that one.   It is different from all the
other ones on the list. The one's place in the second number is smaller than
that in the first number.  Let's keep going

      28 - 22     So, here is another one that does that
      27 - 21     and another...
      26 - 20     and another...
      25 - 19    oops!   This one has the one's place in the second number
larger than the one's place in the first number.

So, why is that such a big deal? Well, if the second number has a larger digit in the ones' place than the first number does, there is a need to "regroup" or "borrow" from the tens place to solve the problem. If you can find a different problem that will give you the same answer without regrouping, that could be an easier problem, right?

So, lets' look at what happens when we find these "other" problems:

      34 - 28
      33 - 27   We took "one" away from each number.
      32 - 26   We took "two" away from each number.
      31 - 25   We took "three" away from each number.   See what is happening?
      30 - 24
      29 - 23   Here is the first one that we don't have to regroup.
      28 - 22
      27 - 21
      26 - 20
      25 - 19

And, actually, we could have gone in the other direction.

      35 - 29
      36 - 30    
      
there is a good choice, and we can get it by just adding 2 to each number...

So, a strategy you could show your daughter is that if she is working on a subtraction problem, she may want to shift both numbers to amounts that don't require her to regroup.

Whatever method she feels most comfortable using should rest with her, though, at first. Remember, the method you prefer is one you have used for a long time. It will seem like the "easiest" and "least confusing" method to you, because it is very familiar. But in truth, all these methods we have used our whole lives were, at some point, not very comfortable for us to work with, just like the ones your daughter is showing you now. The best approach to take is to make sure your daughter realizes there are many different ways to solve a problem, and the way that makes the most sense, and works every time, is the one she should choose. At some point it will also be important to add efficiency to that list of criteria, but the beginning stages are not the time to worry about that. Get the number sense in place first, then move toward being efficient.

-Gail, for the T2T service

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