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Working Up to Counting Up

```Date: 09/25/2003 at 23:10:22
From: Jane
Subject: explaining how to make change

My adult daughter was in LD classes. She works at a register all day
now and wants to learn how to make change by counting up. She has been
able to cover up for the fact that she does not know how but is
petrified someone will find out she can't. I do not know how to
explain it to her.
```

```
Date: 10/14/2003 at 11:47:06
From: Doctor Ian
Subject: Re: explaining how to make change

Hi Jane,

As with anything else in math, the key is going to be to take it

One way to approach it might be to help her see that counting up is
one of many possible ways to do subtraction:

Subtracting Decimals With Borrowing
http://mathforum.org/library/drmath/view/58892.html

Another way would be to get her to start concentrating on how to break
a single problem into multiple problems.  For example, if someone
gives me a \$10 bill for something that costs \$7.33, I need to

1. Get to the nearest multiple of 5 cents.
(In this case, add 2 cents, which gets me to \$7.35.)

2. Get to the nearest multiple of 25 cents.
(In this case, add 15 cents, which gets me to \$7.50.)

3. Add enough quarters to get to the nearest dollar.
(In this case, add two quarters, which gets me to \$8.)

Now I just need to get from \$8 to \$10, which I do in the same kind of
way, but using bills instead of coins.

One value of breaking it down this way it that it can make the process
seem less intimidating.  Each step is manageable, and if all the steps
are manageable, then so is the whole problem, right?

Another value of breaking it down this way is that she can practice
the steps individually, until each one becomes second nature.  For
example, just have her work on step 1 (getting to the nearest multiple
of 5 cents) until she can do it without thinking about it.  Then move
to step 2, and eventually to step 3.

If she thinks that this is going to be too hard, it might be helpful
to get her to think of other things that she's learned in the past,
which seemed difficult at first but which now seem pretty easy.
Sometimes being confident that you'll be able to learn something is
half the battle in actually learning it.

or anything else.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
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