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Topic: subtracting across middle zero
Replies: 14   Last Post: Nov 24, 1997 7:54 AM

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 Chi-Tien Hsu Posts: 144 Registered: 12/6/04
Re: subtracting across middle zero
Posted: Nov 24, 1997 4:29 AM

With all the suggestion on alternative ways of doing substracting
zero across middle zero, I am all in favor of showing them or
letting them invent other algorithm. However, I believe that the
most commonly used algorithm must also to introduced and shown
to be appreciated as one of the best. Isn't it a good test of students
concrete understanding of the place value in base 10 system?

Chi-Tien

-----Original Message-----
From: Joshua Zucker <zucker@Csli.Stanford.EDU>
To: math-teach@forum.swarthmore.edu <math-teach@forum.swarthmore.edu>
Date: Friday, November 21, 1997 1:23 PM
Subject: subtracting across middle zero

>I've taught arithmetic for adults (at community college), but never
>arithmetic for third graders. Still, I have some ideas that I think
>may be equally appropriate for your population.
>
>1) Add enough to both numbers to make the smaller one an even hundred.
>E.g. with 904 - 236, add 64 to both to get 968 - 300 = 668.
>
>2) If they know about negative numbers, 900 - 200 = 700, 4 - 36 is
>negative 32, so the problem becomes 700 - 32. But does that really
>help? I guess this is just like taking 4 away from both numbers to
>make 900 - 232 and then somehow doing that. But maybe taking 32 away
>from 100 is easier than taking 36 from 104?
>
>3) Use some manipulatives (maybe, whatever you call those things, with
>a square to represent 100 that's the same area as 10 sticks
>representing 10) and show them how if you want to take away 236, you
>need to replace the 100 with ten 10s, and then replace one of the 10s
>with ten 1s, and relate that physical manifestation to the symbolic
>(numeric) one.
>
>And, despite feeling that I should have better judgment than to do this,
>I find myself unable to resist suggesting Karl Casper's solution
>to this problem, by analog to his suggested method for solving
>polynomial equations, which is that the kids should learn how to type
>9 0 4 - 2 3 6 = on their calculator, and the middle zero therefore
>doesn't make it any more difficult than any other subtraction problem
>with any number of digits.
>
>--Joshua Zucker
>
>

Date Subject Author
11/21/97 Mara
11/21/97 Ron Ferguson
11/21/97 Cathy Liebars
11/23/97 David and Gail Englert
11/23/97 Gerald Von Korff
11/21/97 Lou Talman