Long division help!

[camracrazy]

Arghhh!

My dd has trouble with long division and multiplying anything that has two numbers on the top and bottom (ex. 56 x 23). Every day we work on these kind of problems, it is like starting with a fresh slate. She doesn't seem to retain any of the information! After I help her with two or three problems she may be able to do a few on her own, but not always. I am so frustrated! I hope someone has some tips for helping her retain this info so we can move on to other things.

[Kyamo]

Have you tried doing the multiplication problem as the two problems 56x20 and 56x3, so that she understands why the steps work?  Understanding why can help remember the process.  

For long division, try writing DMS at the top of the page (stands for Divide, Multiply, Subtract).  These three steps are repeated over and over to perform long division, the acronym can help to keep the steps straight so she can do them more independently.  

Other than that I would just be patient and keep helping her each day.  Is she getting frustrated too?

[moominmamma]

For multi-digit multiplication (assuming she understands the distributive property that this algorithm uses and is just getting muddled up by all the different digits) try working on a whiteboard with coloured markers, or on a paper with pencil crayons. Write the top number in black, and the bottom number according to whatever place-value colours you'd like to use: maybe blue for the 1's digit, red for the 10's digit, green for the 100's digit. Then, as you multiply the blue digit through, do all the figuring in blue. Then switch to a red pen and doing all the figuring for the 10's digit. And so on. That way the patterns of where the numbers come from: 

  421
 x 43
 1263
16840
18103

I think that may help her tease apart the sense of the algorithm as she does it. If she's holding the red pen, she's less likely to accidentally multiply the 3x2 rather than the 4x2. I gave an example without regrouping because the regrouped numbers are impossible to show using basic HTML, but the different-colored pen approach works especially well for that. If you've had multiple digits to regroup and lots of little numbers sketched in next to the various digits, the pen you're holding is the clue to which one is the important one for this pass through the problem.

Doing the work on a grid (eg. using graph paper) can also be helpful, so that the different place values stay nicely lined up in their boxes and therefore in their columns.

Long division would be incredibly confusing and frustrating for a kid who was still having trouble with multiplication. I think that I would deal with the multiplication troubles first.

Miranda

[chaoticzenmom]

ah, we had this problem not that long ago.  A friend showed me a trick for understanding long division..

437/3

Make three cups and divide 437 into ones, tens and hundreds

0000         000        0000000

cup 1-0

cup 2-0

cup 3-0

1st do the hundreds (three goes into four 1 time with one (hundred) left over.  Take that one from the hundred and break t down into tens

hundreds   tens                                  Ones

                   000 (0000000000)            0000000

Break those tens down by putting them into the 3 cups.  See what you have leftover and break those down into ones and put them into the ones section

hundreds     tens           Ones

                                      0000000 (0000000000)

Now break those ones down and put them into the correct cups.  What you have left is your remainder.

You can also just circle groups of 3 instead of putting them into the cups.

After you do this model, then do the problem, matching each step up with the model.

My son finally understood it when l presented t this way.

[camracrazy]

I think the different color idea might work. One problem she has is not lining up the numbers correctly.

She was doing fine in multiplication until long division started confusing her. When she gets nervous about one thing sometimes it floods into other things that she CAN do. I am hoping that once she can get a handle on long division she will go back to doing her multiplication better.

I'm not sure if the cups would confuse her more or not, but it's definately an idea.

Thanks!

[moominmamma]

If you think the cups might be confusing you could give her four dollar bills, four dimes and seven pennies and ask her to divide that money evenly into three piles. Tell her you're the banker and you can make change any time she needs it. Write 

    ____

3 ) 447 on a piece of paper.

If she's like most people she'll start by distributing the dollars. One dollar in each of the three piles. She'll have one dollar left over and she'll want to make change -- give her ten dimes for it, which will give her a total of fourteen dimes. Add the following to the paper:

   _1____

3 ) 4 ₁4 7

Say "One dollar in each pile: that's part of the answer, so that goes on top. One dollar left over, regrouped into dimes: now you have fourteen dimes. Which coins are you going to share out next?" Now she'll probably distribute the dimes, four in each pile, with two left over. She'll want to change the leftovers into pennies. Take her two dimes, give her twenty pennies and add the following:

   _1 4___

3 ) 4 ₁4 ₂7

Remind her that four is part of the answer, and that the two remainder dimes have been regropued as pennies, making twenty-seven. At which point she can distribute the twenty-seven pennies, nine to a pile with no leftovers:

   _1 4 9 _

3 ) 4 ₁4 ₂7

Sometimes working with money, because it's familiar and interesting, makes more sense to kids than other symbols. Showing how what she naturally does to divvy up some money is recorded on paper as she goes through the process may be helpful. When doing problems without money/manipulatives, you can remind her "Remember how you always started with the dollar bills? So on paper you should always start with the biggest place value too." 

Tucking the remainders in as above is what was called "short division" when I grew up. It works well up to a divisor of 10. It makes more sense to my kids because the idea of regrouping by tucking in a subscript or superscript numeral beside another is familiar to them from addition, subtraction and multiplication. We only moved to long division with its odd x's and separate bits of multiplication and subtraction after they were absolutely bombproof in their short division work. My kids were pretty young when they learned this, so we hung for a long time with short division -- 6 or 8 months or so. The added complexity of long division makes it that much harder to see exactly what each step is accomplishing. 

Miranda