Long Division Teaching Technique Help!

Discussion in 'Elementary Education Archives' started by Research_Parent, May 6, 2007.

  1. Research_Parent

    Research_Parent Cohort

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    May 6, 2007

    I am seeking some help or suggestions on ways to help 3rd/4th graders understand how to do long division with multiple digits. The students have successfully worked with standard multiplication and division facts (1 to 15) and dividing by up to 15 but are now beyond that stage.

    Example: 5393 divided by 22.

    I have always thought long division at this stage is mainly a trial and error of what to try. Is there a better way to help students get to the answer quicker?

    For example, I suggest starting with 1, 10, and 5 times the number and then work from there. Any other ideas on how to approach this?

    :thanks:
     
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  3. Aliceacc

    Aliceacc Multitudinous

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    I've always done it by estimation: take the 1st 2 digits of the dividend, divided by the divisor; quotient is your starting place.

    So, in your example, 5393/22

    53/22 is 2, so that's the first digit of your quotient.
     
  4. michelb366

    michelb366 Comrade

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    The first thing mine do is find out where the answer will go. Does 22 go into 5? no...53? yes. The answer will start above the 3. Then they round the divisor and begin dividing. 53 divided by 20 is about 2 and so on. The only trick is making sure they multiply by the divisor, not the rounded number.

    I'm surprised you are doing double digit division with 3rd graders!
     
  5. teachingmomof4

    teachingmomof4 Groupie

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    My son showed me how to do it but it is a bit hard to explain. If you google "forgiving method" it will show you how to do it. It is really simple once you understand it.
     
  6. Research_Parent

    Research_Parent Cohort

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    Here's what I found explaining the forgiving method...

    Solving division problems using the "forgiving" method

    I'd never heard of the forgiving method, and couldn't find references
    to it in our archives. From a reference that I found in a discussion
    group on the net, I gather that it's about piecing together whatever
    multiplication facts you are comfortable with to solve the problem at
    hand.

    Suppose you want to know how many 6's there are in 100. You
    can remember that 7*6=42, so you write down the 7 as part of your
    answer, then take the 42 away from 100 and have 58 left.

    Next step: you might say the same thing. There's another 42 in
    there, so there's another 7 sixes. Write down another 7 under the
    first one, and subtract 42 from 58.

    Now you've got 16 left, and you know you can squeeze 2 sixes out of 16, but not 3. So you write down the 2 under your 7's and add them up: 7+7+2=16.

    You've pulled 16 sixes out of 100 (with 4 left over that wasn't enough to make another 6). You did it in groups of 7, 7 and 2, but someone else might have done 5 and 5 and 5 and 1, and the "standard" method would have been to do 10 + 6. The method is forgiving in the sense that your partial guesses don't have to be anything in particular, as long as you don't overshoot.

    - Doctor Mitteldorf, The Math Forum

    Any other ideas?
     
  7. teachingmomof4

    teachingmomof4 Groupie

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    That's exactly it. It is pretty easy to do.
     
  8. h2omane

    h2omane Comrade

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    May 8, 2007

    I felt like doing your math question
    .................245.6 R8
    ...........22]5393
    ...............44
    .................99
    .................88
    .................113
    .................100
    ...................130
    ...................122
    ......................8

    :D
    yes I'm bored
     
  9. TeacherGroupie

    TeacherGroupie Moderator

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    Nice job getting long division to work on the forum, h20mane. (I have a pretty good idea what you had to go through. You must have been very bored indeed!)

    Um, meaning no disrespect, however, there are some glitches in the math. Last time I checked, 22 * 5 wasn't 100, it was 110. And I think one reports EITHER an integer result with a remainder OR a decimal result (or fraction result), but not both.
     
  10. Research_Parent

    Research_Parent Cohort

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    So now I have 3 techiques for helping students do double digit long division:
    1) creating a baseline...1x, 5x, 10x
    2) estimation...53/22 ~ 53/20
    3) forgiving method...use known multiplication facts

    Yes, there really are 3rd graders doing double digit long division with the remainders and the 4th graders take it out to 2 decimal places and stop.

    Thank you for your tips, techniques, and ideas. I like having more than one approach to work from.
     
  11. Amers

    Amers Cohort

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    May 8, 2007

    Something I've seen done is the "Does Mcdonald's Sell Cheese Burgers" method. It's for students who have trouble remembering the steps in long division. Basically, it's DMSCB, which stands for: 1. Divide 2. Multiply 3. Subtract 4. Check your answer 5. Bring down.
    If your kids have trouble remembering the steps of long division, this might help!
     
  12. h2omane

    h2omane Comrade

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    YES YES I'm glad you caught that. After colouring it up I noticed the error and wanted to see if any one else caught it.

    GOOd JOB!!!

    :D
     
  13. Aliceacc

    Aliceacc Multitudinous

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    Forget the math.... how on earth did you get it do display so well???

    For my own classwork I use Mathtype, but I had no idea that we could post something like that here!

    Bravo!!
     
  14. TeacherGroupie

    TeacherGroupie Moderator

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    Alice, go back to his first post with that and use Reply w/Quote instead of quick reply - in fact, he did this so elegantly that I completely forgot to be astonished till I saw what amounted to the code that it required.

    (The trick is partly judicious use of periods or something of the kind and the text color "white". And I promise you he will have sweated over it.)
     
  15. MrsC

    MrsC Multitudinous

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    Yikes--h2omane--you really were bored! I could never do that!
     
  16. h2omane

    h2omane Comrade

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    I cheated by spacing with periods which I coloured white.

    ie


    ..............22 --- black
    ..............22 --- grey
    ..............22 --- white
     
  17. h2omane

    h2omane Comrade

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    May 8, 2007

    And you should see what I can do with Photoshop and a spare hour... :)
     
  18. h2omane

    h2omane Comrade

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    May 8, 2007

    .....X....X...XXXX.....XXX...X......X...XXX....XX....XXXX
    .....X.X.X...X....X.....X.......X.....X...X.......X..X......X
    .....X..XX...X....X.....XXX....X.X.X....XXX...XXXX.....X
    .....X....X...X....X.........X....X...X....X......X.....X....X
    .....X....X...XXXX.....XXX.....X..X.....XXX..X......X...X

    this was done in about 12 minutes. Did I mention that I'm an ART MAJOR. :D
     
  19. h2omane

    h2omane Comrade

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    May 8, 2007

    Here is the corrected question with red dots instead of white ones...

    .................245.6
    ...........22]5393
    ...............44
    .................99
    .................88
    .................113
    .................110
    ....................30
    ....................22
    ......................8

    Does anyone want to give me a challenging problem to solve?

    hee hee
     
  20. oasis

    oasis Rookie

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    May 9, 2007

    From a Constructivist perspective (Piaget, Vygotsky, etc), you need to start with concrete materials and establish a strong CONCEPTUAL understanding (I recommend Base-10 blocks and/or Cuisenaire rods). I also recommend reading John Van de Walle, who offers "invented strategies" that are easier than the traditional algorithm for children to understand. Basically, our argument is that kids need to first understand the CONCEPTthat division is nothing more than equal grouping, even with larger numbers. Once they completely understand that concept, you can guide them to inventing strategies for solving problems, rather than forcing them to memorize the steps to the abstract traditional algorithm, a systme that only confuses them.
     
  21. h2omane

    h2omane Comrade

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    May 10, 2007


    4th 5th 6th grade combo... Ouch, but those are the 3 grades that are my favourite :D
     
  22. oasis

    oasis Rookie

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    May 10, 2007



    I could do without the sixth graders........:)
     
  23. Teacher-AK

    Teacher-AK Rookie

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    May 10, 2007

    Another way to look at it is with compatible numbers (or basic facts). The closest basic fact to 22 and 53 are 20 and 40 and the answer is 2. My 4th and 5th graders find this method very helpful.
     

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