Long Division

Gurp.

This is a big, difficult question.

Alas, nine times out of ten, or even more, asking some questions in a little depth shows that the student is shaky and lacking confidence in basic number sense and meaning of the operations. This is disguised in the child with a good memory and a bad teacher by rote memorization of procedures or recipes.

This rote memorization of procedures very often breaks down exactly where you are, with long division and fractions. The system is too long and complicated with too many apparently unrelated steps, and there are too many previous rote-memorized recipes in the mental space, taking up time and causing confusion of which one to use.

If you are lucky and this is not the case, if your daughter has a pretty good grasp of the base ten system and of addition and subtraction and multiplication *and* of what they all mean, then all that is needed is a little practice with a concrete model - some abacus or base-10 blocks or squared paper cut into rows of ten and blocks of 100; show for example first how many 8’s go into 500: 60 X 8 = 480, leaving 20 over, 2 X 8 = 16 leaving 4 over, so the answer is 62 with remainder 4 or (much better)
62 4/8
then how many 12’s go into 280: 12 X 20 = 240 leaving 40 over, 12 X 3 = 36 leaving 4 over, so 12 goes into 280
20 + 3 or 23 times, leaving 4 remainder or (better)
23 4/12 as the answer. (This is much easier to show than to type or say, which is why you get out the materials and work it out and show it!)

Once you see that you are asking how many hundreds times and how much left over, how many tens times and how much left over, how many ones times and how much left over, then the standard algorithm (set of rules and procedures) will make sense.

On the other hand, if your daughter has been subjected to the usual just-do-this-memorize-it-and-don’t-ask questions approach, and the “pick this number up here and move it over to here” way of thinking about math,. you have a long haul in front of you. You can continue memorization and drill her an hour a night until she fails algebra — you can guess that this isn’t my recommendation, but many people do this. Or, you can go back and try to help her understand what numbers are about, how the base tens (ones, tens, hundreds, thousands,… and decimals . . ) work and what they mean, and what addition and subtraction and multiplication are and why they are used and how they work.

I second Victoria’s suggestions for developing the concepts. Here’s something that has helped my son with cranking through the algorithm. Let’s say the problem is
____
17 | 698

He’s not going to know for sure how many groups of 17 are in 69. Let’s try 3, and since that’s in the ten’s place it’s really 30, so he writes
____
17 | 698
- 510 17x30
–—
188

Oops- we can obviously get another 10 groups of 17 out of 188. So now he writes.
____
17 | 698
- 510 17x30
–—
188
- 170 17x10
––-
18

The next step is easy.

____
17 | 698
- 510 17x30
–—
188
- 170 17x10
––-
18
- 17 17x1
––—
1

The result is 30+10+1 = 41 with a remainder of 1. This helps him keep track of his work and if he isn’t on target with the first attempt, it’s easy to correct and move on. I hope this makes sense. I found this method on a post on the Math Forum- you might search there under long division if you want to find more info.

Jean

I tutored an adult student for a while who had problems with long division. She had apparently been taught a system something like what you are advising. When I showed her the standard algorithm, she just repeated, over and over and over again for weeks, that she never realized how easy it could be, that in school she had just been taught to chip away and chip away at the number and it took forever. So yes, this kind of system works as a temporary stage, but do try to get past it and into something more efficient before passing people on.

Thanks so much guys!
>

You’re right- this is supposed to be just an intermediate step, not the final product. Thanks for pointing that out since I forgot to mention it in my post.

Jean

If your child is dividing with single digits do the following:

1. Have her create the steps for division by allowing her to choose a word that she can remeber in order to do the steps for division. Look at the eaxample below.

1. D- Donnie McClurkin
2. M- Martin Luther King
3. S- Shirley Caesar
4. B-Benjamin Banneker
5. R-Rosa Parks

Please tell your daughter that D stands for divide.
M stands for multiply.
S stands for subtract.
B stands for bring down.
R stands for remainder .

You can place the letter of the term by the math problem as she solves this problem. If memorization of times tables is a problem, email me and I will help you with that too. Please email me so that I will know that you tried this strategy. My students have did well with this method.

If your child is dividing with single digits do the following:

1. Have her create the steps for division by allowing her to choose a word that she can remeber in order to do the steps for division. Look at the eaxample below.

1. D- Donnie McClurkin
2. M- Martin Luther King
3. S- Shirley Caesar
4. B-Benjamin Banneker
5. R-Rosa Parks

Please tell your daughter that D stands for divide.
M stands for multiply.
S stands for subtract.
B stands for bring down.
R stands for remainder .

You can place the letter of the term by the math problem as she solves this problem. If memorization of times tables is a problem, email me and I will help you with that too. Please email me so that I will know that you tried this strategy. My students have did well with this method.

Joanne wrote:
>
> Does any one have any tips on teaching long division (single
> and double digit). My daughter (garde 6) has a test this
> week on it and she is having trouble grasping it.

An easier step guide is:

D - Dad
M- Mom
S- Sister
B- Brother

Hope this helps
Brenda

I was looking for additional tips for teaching this to my fourth graders when I came across your DMSB… We use it too, but with a little different meaning - Does McDonalds Sell Burgers? The kids seem to remember this easily. Alas… some are still struggling with the concept. We will keep plugging away though!