I need a succint way of explaining long division

[LG Gone Wild]

with emphasis on place value for moms who want to help their kids struggling with long division.

 

I have the Professor B book but his method takes several days. I would like to put his explaination in a two paragraph e-mail.

 

Any takers?

[klmama]

Sorry, I don't have an easy way of explaining it. I did find, however, that my dc understood long division better once they had mastered short division. There are fewer writing steps, so it's easier to remember. If you don't know how short division works, take a look here: http://www.themathpage.com/arith/divide-whole-numbers.htm

[Blueridge]

Years ago one of my daughters used Oak Meadow. They taught a little tune (you could just make up your own) for long division that had the words: divide...multiply...subtract...bring down. You just repeated those words until you ran out of numbers in the problem. Maybe that will make some sense, and maybe not. :D It will get easier once that 'light bulb' goes off.

Ginger

[LG Gone Wild]

instead of A going into B or if that doesn't work, BC, subtract, bring down D.

[Frontier Mom]

Not sure if this will help but what I do:

 

Daddy-divide

Mother-multiply

Sister-subtract

Brother-bring down

 

Also, I print out free graph paper online. I use colored pencils and use one for each of the above. I also use a red one to "mark" each place above the number where the next quotient numeral will go.

 

For instance, I would say 217 / 7. First, write out on gragh paper. With a red colored pencil, I would question student as to where the first number of the quotient will go. Over the 2, can 7 go into 2? No, but can you divide 7 into 21? Yes, then first red dot goes above the "1" in 217.

 

Then, using a different color pencil, say blue, I have them do Daddy, Mother, Sister, Brother. Divide 7 into 21, multiply 7 by 3, subtract 21 from 21, bring down next number.

 

For the next sequence of dividing the 7 into 7, I have them use a different color pencil, say green. This just helps with lining things up and seeing how each step works.

 

I'm not sure if this is what you need but just a way it makes it visual for my dc's.

[ELaurie]

My first suggestion is to click the link to Professor B math in my signature line, to see whether the sample CD for level 2 contains a succinct explanation.

 

Our anti-virus software prevents me from accessing the sample CD's on his website :glare:

 

Here's how I do it with ds 9:

 

Let's say the problem is 366 divided by 6. I would begin by saying "The first number in the dividend is in the hundreds column, so we begin by asking if we can subtract 100 sixes from the divisor." Ds 9 responds by explaining that we cannot, because 100 sixes is 600. Ds 9 would then write a small x above the hundreds column.

 

Next I would point out that the second number is in the tens column, and suggest that we proceed by estimating how many tens of sixes we can subtract from 366. Using his knowledge of multiplication, ds 9 is able to estimate that we can subtract 6 tens x 6, or 360 from 366.

 

After subtracting 360 from 366, ds 9 would see that there is a remainder of 6. From there he can readily complete the problem.

 

If the answer were less obvious, for example, 588 divided by 7, and he was uncertain how many tens of seven he could subtract from 588, I would suggest that he try a variety of options as he estimates what the answer might be. As I walked him through the process, he would assess that 1 ten x 7 would be 70, 2 tens x 7 would be 140 and so on until he came to 8 tens x 70 which would be 560.

 

The phrase "tens of seven" in this example is somewhat awkward, but it is the phrase Professor B uses in the CD to preserve an understanding of place value.

 

If ds 9 were dividing a number like 480 by a two digit divisor such as 24 I would follow a similar line of reasoning with him. Again, I would point out that the first number is in the hundreds column and ask if we could subtract even one hundred 24s from the divisor. Of course, he would say no, because 100 x 24 would be 2400. After he placed an x above the hundreds column, I would ask if he could subtract ten 24s from 480 and so on as in the example above.

 

Clear as mud?:tongue_smilie:

 

ETA: If the phrase "tens of sixes" seems too awkward, one can also ask "Can we subtract ten sixes from the divisor? What about twenty sixes?" and so on. The same pattern would hold for hundreds; ask, " Can we subtract 100 sixes?" and so on.

Edited March 27, 2009 by ELaurie

[PiCO]

My older dd had trouble wrapping her head around long division. I am not one who is willing to have a child memorize an algorithm instead of actually learning what's going on. Here's a website explaining why it's not the best idea to merely teach the method without understanding the math. (I have no problem with teaching an algorithm after the child understands what's going on. Can't use base 10 blocks forever.)

 

What helped dd's light bulb turn on was explaining division as the opposite of multiplication. Multiplication is repeated addition; division is repeated subtraction. We did long division problems subtracting multiples dd knew, and just adding similar place values together to get the answer.

 

As someone else said, teaching short division was helpful- it's the reverse of multiplying by a one-digit number.

 

[ELaurie]

:iagree:I taught ds 9 to do division problems as repeated subtraction problems first as well.

Edited March 27, 2009 by ELaurie

[Perry]

This may not be what you're looking for, but my son only began to understand long division after we worked on partial quotient division first. Once he got good at that, we transitioned to long division and the place value just made sense.

[PiCO]

This may not be what you're looking for, but my son only began to understand long division after we worked on partial quotient division first. Once he got good at that, we transitioned to long division and the place value just made sense.

 

YES! This is exactly what I did. I didn't know it had an official name- thanks!

[LG Gone Wild]

Some of those websites were too wild but nice to know about. I went to ProfB's site and he has long division explained on his CD sample. I found it funny.

[ELaurie]

in the form of a teaching story that will be readily recalled by students practicing long division.

[Laura Corin]

Here's one version.

 

Laura

[Guest Jack201]

You can find a good long division calculator on www.dol88.com

 

 

Step by step mode for better understanding.

All operations capable (addition, substraction, multiplication, division)

 

User manual available on the web site.

 

 

Enjoy !

[unsinkable]

Food for thought:

 

 

Let's start with the underlying fact. Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not. Multiplication of natural numbers certainly gives the same result as repeated addition, but that does not make it the same. Riding my bicycle gets me to my office in about the same time as taking my car, but the two processes are very different. Telling students falsehoods on the assumption that they can be corrected later is rarely a good idea. And telling them that multiplication is repeated addition definitely requires undoing later.

 

How much later? As soon as the child progresses from whole-number multiplication to multiplication by fractions (or arbitrary real numbers). At that point, you have to tell a different story.

 

"Oh, so multiplication of fractions is a DIFFERENT kind of multiplication, is it?" a bright kid will say, wondering how many more times you are going to switch the rules. No wonder so many people end up thinking mathematics is just a bunch of arbitrary, illogical rules that cannot be figured out but simply have to be learned - only for them to have the rug pulled from under them when the rule they just learned is replaced by some other (seemingly) arbitrary, illogical rule.

 

http://www.maa.org/devlin/devlin_06_08.html

 

http://www.maa.org/devlin/devlin_0708_08.html

[LaxMom]

This may not be what you're looking for, but my son only began to understand long division after we worked on partial quotient division first. Once he got good at that, we transitioned to long division and the place value just made sense.

 

Yes, that's what our math curriculum does, too. Maria has great explanations on her site, homeschoolmath.net. If you scroll about 1/2 way down the page, there is a link to "Long division and why it works" (among others) that may be helpful.