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pinacolada pinacolada is offline
 
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stupid question on long division
Old 12-10-2007, 03:34 PM
 
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um i forgot how to do long division the way they taught in school for example if you have 1349 divided by 62, i would usually think how many times does 62 go into 134 and go from there but thats not the way students learn it in school right?


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Old 12-10-2007, 05:19 PM
 
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No question is stupid in math in my opinion! What you did sounds fine but I break it up even more to do the estimation part. In the example you gave, I would have the kids try 6 into 13 to get a good estimate. If the number was 68 into 1349, we would use 7 into 13 as an estimate since 68 is closer (rounded) to 70 than to 60. Our book (Harcourt) does teach this estimating strategy but I'm not sure about the other math series.
Hope this helps!
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Old 12-10-2007, 07:11 PM
 
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lol i don't remember that way!!!!!! because if you do 6 into 13 thats 1 with a remainder of 7 it doesnt work because wouldnt teaching the students do that put the 1 above the 3 (in 1346)? ugh is there a website i want to teach it the way they learn in school
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My kids are so weak..
Old 12-11-2007, 02:28 AM
 
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that I have skipped over estimating in dividing. In 5th grade, they came to me not knowing multiplication facts, not knowing fractions at all.... the list goes on. Ugh.

I HAVE to get through material for this year, so I am doing the down and dirty to get them through. I tried to give them the skills to be able to do what the teacher edition wanted and after a month I was 6 weeks behind. Needless to say, I gave up.
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One thing that helps . . .
Old 12-11-2007, 08:26 AM
 
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. . . . is a dot. When students begin working a problem, the first step is to decide where the first digit of the answer will go. In the problem 1349 divided by 62, ask yourself what 62 will go into. You can see that it will go into 134, so put a tiny dot on the line above the 4. This is where you put the first part of the answer. Now you can see that the answer will be a two digit number with possibly a remainder.

Then you go back see how many times 6 goes into 13 to get the estimate, but it goes where the dot is.

I hope this helps.


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Old 12-11-2007, 07:46 PM
 
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6 into 13 is 2 with a remainder of 1.
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oops
Old 12-12-2007, 03:31 PM
 
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you're right 6 x 2 is 12 subtracted from 13 has a remainder of 1 lol i feel stupid and i took was in AP Calc in HS!...thats interesting i've never seen division done that way because its 62, is there a website with an explanation on how to do it that way?
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Partial quotients
Old 12-13-2007, 05:25 PM
 
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I think the most sensible way to teach long division is by teaching partial quotients rather than the traditional algorithm. So if you're teaching 1349 divided by 62, you'd say how many times can you multiply 62 by in your head and not go over 1349. For most of my kids, it would be 20. So they multiply 62 by 20 and get 1240, subtract it from 1349, get 109, then one 62 goes into that with a remainder of 47.
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An old-fashioned way to divide
Old 12-21-2007, 07:48 AM
 
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I've been teaching a very long time. We're using EM and some of the ways they attempt to teach kids end up confusing them PLUS they have too many methods to choose from and master none of them. All of mine learn to long divide like this: (if they can't master it THEN I try another method)

We set the problem up and first discuss that when we say 1349 divided by 62, the 62 goes OUTSIDE the bracket (yep - gotta start small) We proceed one digit at a time - I even cover them as we go)

We ask ourselves - will 62 go into 1 - no- so we put a small X above that place to show that we won't have a 4 digit answer. (My kids don't line things up well so sometimes we turn the notebook paper sideways so they have columns)

Then we move over and ask ourselves if 62 will go into 13 - no - so we put another small x above the 3.

Then we move over and ask ourselves if 62 will go into 134 -yes - so we put a small line above the 4 and the 9 to let us know we will have a 2 digit answer. (and no more!) We also estimate at this point. We ask ourselves how many times a 6 will go into a 13 (or 60 into 134). That would be twice so we put a 2 on the line above the 4 and stick a zero on the line above the 9. Our estimate is 20. This estimate is written at least 1 finger's space above where we will put the answer, NOT right on top of the problem (Heaven knows we wouldn't want to have to rewrite the things)

Now we are ready to solve the problem. We go back to our estimate of 2 and take 2 times 62 to get 124. This goes under the 134 (We do NOT put a zero under that 9. In fact, I even hold a finger over the nine or use a sticky note to cover it for now. 134 divided by 62 looks so much easier, don't you think?) We then subtract 124 from 134 to get 10.

Now we draw an arrow to bring the 9 down so it lines up to make 109. Our established rule is that if we draw an arrow, we have to put a number in the answer. Otherwise, mine forget to put zeroes in.

Now we go thru our steps again. How many times will 6 go into 10 (or 62 into 109) and the answer is 1. The 1 goes in our answer above the 9 which fills our 2-digit answer spaces. We multiply 1 times 62. Put that under 109 and subtract to get 47.

We double check. Is 47 smaller than 62? If so, do we have any more numbers to bring down? If not, are all of our answer spaces filled? If so, we are done. Any remainder is then brought up to the answer. We look up at our original estimate to see if we're close.

Then we check our problem by multiplying which reinforces multiplication skills AND means they never have to miss a division problem. My kids pretty much ace division tests. They can also do huge numbers if we go one digit at a time.

When we divide decimal numbers, we follow the exact same procedure and then move the decimal up. Mine do not generally divide BY a decimal - we just can't get everything in 1 year.

We've had major discussions as teachers on all the whys and whatfors of the process, but when mine need to perform on those tests, they'll nail division. What they miss is the multiplication - go figure.

Hope this is sort of clear, but if you work it thru as I presented it, I think you'll see it. When we do these, I draw student teacher's to go to the board to model and "talk" us thru the process. I also have a large chart on the wall of the steps: determine digits in the answer; estimate; 1. divide, 2. multiply, 3. subtract, 4. bring down the next number - repeat from divide step.

Last edited by jeanmarie; 12-21-2007 at 08:24 AM.. Reason: forgot the remainder
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Just one more thing
Old 12-21-2007, 08:37 AM
 
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JeanMarie's answer is excellent. Adding one little thing: using gridded paper is great for division. The grid printed in pale green works well. It helps keep the digits lined up as they should be.


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Old 12-21-2007, 08:21 PM
 
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Exactly what Jeanmarie said- that is what I do as well.
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division chant
Old 01-20-2008, 02:00 PM
 
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as in Jeanmarie's response....
Dad ...divide
Mom ...multiply
Sister... subtract
Brother ...bring down
and sometimes there's a dog named ...Rover (remainder)
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Dmscb
Old 01-23-2008, 08:04 AM
 
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Does...divide
McDonalds...multiply
Serve....subract
Cheese....check
Burgers...bring down
Ronnie...remainder
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