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Date: 08/17/98 at 21:50:25
From: maria ralston
Subject: Learning family facts to 12

I have trouble doing all the addition and subtraction problems that
still make me count on my fingers. I lose track of what I am counting
if I get distracted. I have not memorized all of them yet. I need help
so I won't be slow in math in my 3rd grade. I was in a mixed classroom
last year and I got to be a second grader. My mom taught me a little
bit of math before I went to school. I love to read and write, but I
want to be as good as that in math too.
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Date: 08/18/98 at 12:56:49
From: Doctor Peterson
Subject: Re: Learning family facts to 12

Hi, Maria. I think you can see why it's good to learn those facts, so
you don't need to count. The lucky thing is that you don't really need
to learn any facts past 9 + 9 (though learning facts through 12 is
useful), because you add bigger numbers one digit at a time. Wouldn't
it be awful if you had to calculate 1485 + 9385 by counting on your
fingers? Even centipedes would have trouble.

One thing that I think might help you both with learning the facts and
with working out the facts you haven't learned yet, is to find ways to
avoid having to count too far.

For example, suppose I don't know 8 + 9 yet. The hard way would be to
count nine past 8:

8; 9, 10, 11, 12, 13, 14, 15, 16, 17
1   2   3   4   5   6   7   8   9

An easier way is to switch the numbers so you start with the bigger
number, 9, and add 8 to it:

9; 10, 11, 12, 13, 14, 15, 16, 17
1   2   3   4   5   6   7   8

An even easier way is to notice that 9 is very close to 10, so you can
add 10 (that's easy, right? 8 + 10 = 18) and count backwards:

18; 17
1

This means 8 + 9 is one less than 8 + 10.

You can do the same sort of thing with any other facts that you know.
If you know 5 + 5 but not 5 + 7, then you can just notice that 7 is 2
more than 5, so 5 + 7 is 2 more than 5 + 5.

Another trick that helps a lot is to know all the combinations that
add to 10. If you don't know those, work on them first, because they
are the most useful facts to know.

Here's another way to do 8 + 9. Since I know that 8 + 2 = 10, and 9 is
7 more than 2, then 8 + 9 = 8 + 2 + 7 = 10 + 7 = 17.

-------8------- --------9--------
O O O O O O O O X X X X X X X X X
-2- ------7------
-------8------- -2-
---------10-------- ------7------

Once you've used these tricks for a while, you should have enough
experience to have learned most of the facts, since you learn them best
just by using them. Most of us seem to have a few facts that we never
quite learn, so these tricks are still useful even when you're grown.
know the numbers better - when numbers are close friends whose habits
and personality you know well, math becomes fun.

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