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
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