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Q&A #1733


Long division

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From: Gail (for Teacher2Teacher Service)
Date: Jul 08, 1999 at 06:48:28
Subject: Re: Long division

I agree with Suzanne that there are different methods. I have found that some elementary students do just fine with the traditional method, but some need a little help going from the concrete step to that abstract algorithm. I ask my students to think about what they think the answer should be. For example, if the problem is 478 divided by 4, about how many groups of 4 do you think there are in 400? How many in 500? The answer to the problem should be somewhere between those two amounts. Using base ten blocks, and making groups of four (which is tedious), or four equal groups, using the blocks, is one way to make this hands on. Students can arrange the blocks to find that the quotient is somewhere between the number of groups in 400 and the number of groups in 500. Then, I like to start with an alternate algorithm for division, rather that the traditional method. I have found that the transfer to the traditional is very smooth, and this alternate method gives students who are still struggling to learn the multiplication facts, a chance to be successful, even if they only know the 1's, 2's, 5's and 10's. You might consider an alternate algorithm: It is easier for them because they do not have to have the prefect factor each time, just one that will work. They can continue finding factors and dividing until they have a remainder that is smaller than the divisor (in this case, 7). When they have found all the factors, they just add them up (not the 7, but the other one each time). That is their quotient, and what is left is the remainder, which can be put in fraction form (in this case, 2 out of 7, or 2/7) , or they can place a decimal, and add zeroes to continue dividing. Besides the help this gives a student, it treats the dividend (in this case, 478) as a whole amount, instead of looking at 4 hundreds, then 48 tens, as the traditional algorithm does. ____ 7 /478 7 X 10 - 70 _____ 408 7 X 10 -70 ____ 338 7 X 10 -70 ____ 268 7 X 10 -70 ____ 198 7 X 10 -70 ____ 128 7 X 10 -70 ___ 58 7 X 2 -14 ___ 44 7 X 2 -14 ___ 30 7 X 2 -14 ____ 16 7 X 2 -14 ___ 2 10 + 10 + 10 + 10 + 10 + 10 + 2 + 2 + 2 + 2= 68 See, this student was able to finish the problem without using any of the facts except 7 X 10 and 7 X 2. This could be of great assistance to someone who understood why we needed to divide, but did not have the facts mastered yet. I try to move my students to try larger "chunks" once we have that first step mastered. ____ 7 /478 7 X 30 -210 _____ 268 7 X 30 -210 ____ 58 7 X 5 -35 ____ 23 7 X 3 -21 ____ 2 30 + 30 + 5 + 3 = 68 Then we have a challenge to try to find the one "best chunk" for each place value. In the next example, there is one "chunk" for the tens, and one for the ones. (There is no hundreds chunk, because 7 X 100 would be more than 478). _____ 7 /478 7 X 60 -420 _____ 58 7 X 8 -56 ____ 2 60 + 8 = 68 You will probably notice that that is very similar to the traditional algorithm. It is just a small nudge away for most students, at that point. :-) -Gail, for the Teacher2Teacher service

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