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?
-----Original Message----- From: Joshua Zucker <zucker@Csli.Stanford.EDU> To: firstname.lastname@example.org <email@example.com> 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 > >