Longer DivisionDate: 09/27/2002 at 14:12:17 From: LaDonne Subject: Helping my elementary school daughter understand the concept of division My daughter is not grasping how to do division. She is in the 5th grade. They are working on long division with remainders. I get frustrated because I show her over and over again and she IS NOT understanding how to divide. Please suggest something that I can do to help her comprehend. Thanks. Date: 09/27/2002 at 16:29:47 From: Doctor Ian Subject: Re: Helping my elementary school daughter understand the concept of division Hi LaDonne, The thing about long division is that it's designed to be efficient. But you're not _required_ to be efficient about division! And sometimes it's much easier to see what's going on when you're not. For example, suppose I want to divide 3466 by 41. In long division, I start this way: ______ 41 ) 3466 Hmmmm. 41 doesn't go into 3, or 34, but it goes into 346. How many times? At this point, you start guessing - is it 8? Is it 9? Frankly, in most cases, it's a pain. In long division we have to get each choice 'right' because the algorithm is set up so that we can keep going from left to right, without having to go back. But what if we don't mind coming back? Then we can do something like this: 41 * 10 is 410, so 41 goes into 3466 at least 10 times. 3466 - 410 10 times ----- 3056 Wow. It goes in a _lot_ more than 10 times! Will it go in 50 times? 100 times would be 4100, so 50 times would be half that, or 2050. 3466 - 410 10 times ------ 3056 - 2050 50 times ------ 1006 Okay, it will go at least 20 more times. 3466 - 410 10 times ------ 3056 - 2050 50 times ------ 1006 - 820 20 times ------ 186 I can just keep subtracting now: 3466 - 410 10 times ------ 3056 - 2050 50 times ------ 1006 - 820 20 times ------ 186 - 41 1 time ------ 145 - 41 1 time ------ 104 - 82 2 times ------ 22 remainder Now I just count up the number of times I subtracted groups of 41: 10 + 50 + 20 + 1 + 1 + 2 = 84 so the answer is 84 remainder 22. So what's the difference between long division and what I did here (which we might call 'longer division')? What's different is that I didn't force myself to get an '8' in the tens column on the first try! Instead, I broke it into 3 separate tries: 10, 50, and 20. Other than that, it's the same thing. Suppose I had guessed 80 the first time, and 4 the second time. This is what would have happened: 3466 - 3280 80 times ------ 186 - 164 4 times ------ 22 remainder Does this look familiar? It's just long division with the numbers in different places. 84 ______ 3466 ) 3466 - 3280 80 times 328 ------ --- 186 <==> 186 - 164 4 times 164 ------ --- 22 remainder 22 There are two nice things about starting with 'longer division'. The first is that it's easy to understand - it's just grouping and subtraction, and everything is right there out in the open. The second nice thing about it is that as you get better at guessing, it more or less turns into long division naturally... but you take that step on your own schedule, not when someone else thinks you should. Let me know if this helps. If not, we can try to think of something else that will. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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