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### What Number Am I?

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Date: 02/04/2002 at 09:50:27
From: Dorothy
Subject: What Number Am I?

I am the mother of a first grader. This is a question that was in her
Math workbook as part of her homework.

What number am I?  If you double me and take away 4 you get 8.

I had to think back to my algebra.  This is the solution I gave her:

2x -  4 = 8
2x = 12
x = 6

I can't understand why this type of problem appeared in a 1st grade
Math book. Could you help me with a way to explain this to a
6-year-old? Is there a more appropriate way to solve this problem for
her?

Thank you.
Dorothy
```

```
Date: 02/04/2002 at 12:39:58
From: Doctor Peterson
Subject: Re: What Number Am I?

Hi, Dorothy.

It can be an interesting challenge, once you know algebra, to find a
way to solve a problem like this without using algebra. It's
instructive, however; you learn that the kind of reasoning people had
to use before algebra is not all that different, it just takes more
thought.

The best way to do this, probably, is "working backward," which is
really what you're doing in your solution; we just have to avoid the

We started with some number, doubled it, and subtracted 4. The result
was 8. What did we have BEFORE the last step when we subtracted 4?
Well, if we add that 4 back on to the 8, we get 12, and if you
subtract 4 from 12 you get 8.

So now we know that when we double our number, we get 12. What number
can we multiply by 2 to get 12? Again, we can undo this operation,
reversing the multiplication by dividing. Divide 12 by 2 and we get 6;
6 times 2 is 12, minus 4 is 8. So the number we started with was 6.

You could even do this with manipulatives. Put down 8 counters, add 4
more to show what you had before subtracting, and then split it into
two piles to show what you had to double. Depending on the level the
child is at, you can do some pretty sophisticated things without
getting into the abstract symbolism they are not ready for.

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

```
Date: 02/06/2002 at 13:04:01
From: Dorothy
Subject: What Number Am I?

Doctor Peterson,

I showed my daughter the method with the counters. That is, I put
down 8 counters, added 4 more, and then split it into 2 piles of
6 counters. As this was a visual method, it was very effective for
her.

Dorothy
```
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