What Number Am I?

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 
symbols and use words instead.

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, 

Thank you for your suggestions!

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