# Long Division Teaching Technique Help!

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

1. ### Research_ParentCohort

Joined:
Jul 29, 2006
Messages:
649
0

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:

3. ### AliceaccMultitudinous

Joined:
Apr 12, 2006
Messages:
27,534
6

May 6, 2007

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

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

Joined:
Dec 7, 2005
Messages:
354
0

May 6, 2007

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. ### teachingmomof4Groupie

Joined:
Aug 25, 2006
Messages:
1,304
0

May 6, 2007

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_ParentCohort

Joined:
Jul 29, 2006
Messages:
649
0

May 6, 2007

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. ### teachingmomof4Groupie

Joined:
Aug 25, 2006
Messages:
1,304
0

May 6, 2007

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

Joined:
Oct 21, 2006
Messages:
374
0

May 8, 2007

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

yes I'm bored

9. ### TeacherGroupieModerator

Joined:
May 13, 2005
Messages:
29,807
1,171

May 8, 2007

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_ParentCohort

Joined:
Jul 29, 2006
Messages:
649
0

May 8, 2007

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. ### AmersCohort

Joined:
May 4, 2007
Messages:
695
0

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!

Joined:
Oct 21, 2006
Messages:
374
0

May 8, 2007

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!!!

13. ### AliceaccMultitudinous

Joined:
Apr 12, 2006
Messages:
27,534
6

May 8, 2007

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. ### TeacherGroupieModerator

Joined:
May 13, 2005
Messages:
29,807
1,171

May 8, 2007

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. ### MrsCMultitudinous

Joined:
Aug 8, 2005
Messages:
14,070
1,886

May 8, 2007

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

Joined:
Oct 21, 2006
Messages:
374
0

May 8, 2007

I cheated by spacing with periods which I coloured white.

ie

..............22 --- black
..............22 --- grey
..............22 --- white

Joined:
Oct 21, 2006
Messages:
374
0

May 8, 2007

And you should see what I can do with Photoshop and a spare hour...

Joined:
Oct 21, 2006
Messages:
374
0

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.

Joined:
Oct 21, 2006
Messages:
374
0

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. ### oasisRookie

Joined:
May 8, 2007
Messages:
8
0

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.

Joined:
Oct 21, 2006
Messages:
374
0

May 10, 2007

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

22. ### oasisRookie

Joined:
May 8, 2007
Messages:
8
0

May 10, 2007

I could do without the sixth graders........

Joined:
Nov 1, 2005
Messages:
88