Q&A #4824

A different way to subtract than normally taught

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From: Gail (for Teacher2Teacher Service)
Date: Oct 08, 2000 at 14:04:42
Subject: Re:A different way to subtract than normally taught

Jeanne gave you some great strategies for subtracting that are similar, but
not exactly like the decomposition method we were taught.  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, here is another, that is similar to what Jeanne
showed you.   It 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
that 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

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 seems 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 Teacher2Teacher service

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