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Michele's Math, Subtraction
by K. Michele Smith

When I teach subtraction to younger children (below 3rd grade, even some 3rd graders) I teach them to "add backwards" - to be honest, I never did "subtract," except small numbers like 1, 2 or 3.

Basically, it's really logical. Since the human brain is much more adept at going forward than backward (notice that counting forward is easier than counting backwards, and adding is quicker than subtracting), it follows that any calculation that can use "forward" patterns would be easier. Adding is also much more accurate.

I teach to count backwards if you are subtracting 1, 2 or 3, but after that use your addition facts. Number families help children grasp this concept:

8 + 5 = 13
13 - 8 = 5
13 - 5 = 8

Then I help them *see* the subtraction problem as a fill-in-the-blank addition problem. This is pretty advanced stuff, and occasionally confuses younger children if they aren't ready. Watch for reactions - if your student catches on, run with it. If not, slow down and don't push it.

Example: 16 - 8 = ?

I look at it as "8 +  what  equals 16...

The number families above introduce this concept. I like this because, although it takes a little longer, the children learn to look at the relationships between numbers *and* between the different operations, which is going to help them with the rest of math. I always use lots of manipulatives and toys.

I teach addition off the doubles, so that helps too:

18 - 9 = ?

Using the doubles, a child will know that 9 + 9 = 18 and can fill in the blank.

The logic here is as follows:

We check subtraction by adding the answer to the subtrahend to get the minuend (first number), but we don't check adding by subtracting - reason is because adding is *going forward* and is much more natural, easier and accurate. So, why not just think through the check first (since it is more accurate) and skip the backward stuff?

This can be translated to larger problems, where the numbers are over each other:

  386
- 143

To teach children how to "add up" I draw little boxes under each number where the answer goes, one for each digit. Then ask,  what  + 3 equals 6, fill it in and add up. Next column,  what  + 4 equals 8, fill in and add up, and finally  what  + 1 equals 3?

This can also be done when you would normally borrow. Remember that anything you can do in math can be undone, simply do it exactly in reverse.

  832
- 158

In this case, since you can't take 8 and add anything to get 2, you have to add to get to 12: 4+8 = 12. Just like addition right side up, you "put down the 2" (at the top) and carry. Of course, since you are adding up, it follows that you carry DOWN and over to the next number. So the 1 carries over to the  5 .

Now, 5 + 1 (the 1 you carried) is 6; so  what  + 6 equals 13? You fill in the 7, then from the bottom up, 7 + 5 + 1 (carried) = 13, put down the 3 at the top, carry the 1 down and over to the next column.

6 + 1 + 1 carried equals 8, so just put down the 6.

At first this seems really confusing, but if you try to think through a couple of borrowing problems like this, AND assuming the person is really proficient in addition, this is much faster and accurate, and when you think about it, isn't this the "check" you learned to do on a subtraction problem anyway?

Also, I divide by "filling in the blanks" on a multiplication problem.

For more ideas from Michele, check Valder Phonics

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