Long division recommendation for student with ADD...(sorry - got long)

[Heather in VA]

I am currently using Singapore with my 10 year old. It's been going well. She's not up to grade yet and it has taken a while for math to kick in but she's starting to close the gap from her delay. She has her multiplication facts memorized and understands the concept of division in relation to multiplication. She can easily do division problems that are in direct relation to a multiplication problem. i.e. if you ask her 45/5 she knows it's 9 etc. Now we are entering long division. I am anticipating this to be an issue because it highlights a learning issue for her. The steps must be done in order, in organized fashion and the process is multi-step. This can cause issues for her during the learning process. Once she has it down, she'll be fine but I'd like to avoid tears, tantrums and rending of garments (on the part of both of us LOL) during the process. I don't think Singapore is going to be the right program to actually learn the process so I want to take a break from Singapore to learn long division and then go back after she has the process down since the Singapore problems are excellent for her and she loves the word problems. 

 

I am just not sure what to use. Traditional programs have bits and pieces over several years so I'm not sure if they will be the right choice. I know programs like MUS and Right Start are more topical (at least I think so about RS) but I don't know enough about them or if there are other choices. I worry about using manipulatives because I don't want to complicate things but I'm open to it. I'm ok with the price for whatever I need to get this to work. 

 

Recommendations? Ideas? 

 

Thanks

 

[wapiti]

Two possibly useful resources come to mind:  the MM Blue topic book http://www.mathmammoth.com/division_2.php (look at the samples to see what you think) and Lets Play Math's blog post about the cookie factory http://letsplaymath.net/2010/04/12/the-cookie-factory-guide-to-long-division/

[CaitlinC]

No wisdom to impart, but I've been researching the same issue.

 

A couple of things that have caught my attention:

 

JUMP math really breaks things down and works on practicing every little step.  If you look at book 5.1 (http://jumpmath.org/cms/workbook_5) you can get a sense of how they approach long division.

 

There's a little video at the Yale Centre for Dyslexia & Creativity that incorporates some kinaesthetic learning:

http://dyslexia.yale.edu/math.html

 

I will be reading others' responses with interest.

[kbutton]

I am not sure if this is the best way to link to a topic, but this might help. I described what we did to learn long division in this post. My son has trouble with math anxiety, math facts, and procedures that he can't reason his way through.

 

http://forums.welltrainedmind.com/topic/492891-2e-for-those-with-children-who-dont-learn-math-procedurally-what-did-you-do/?hl=long+division&do=findComment&comment=5278420

 

This is what I wrote (in case my link doesn't work), but you should check out some of the suggestions from others in the thread.

 

We did this also. Khan academy has a video about it. We used partial quotient last year (any numbers that could chip away at the total were allowed), and this year, we transitioned to something almost identical to the traditional algorithm. With summer break in between he hardly noticed the transition--I just casually started talking him through it as if it was what we'd done all along. The hated, feared, and intimidating multiplication chart was suddenly fun and friendly also, which helped (I suspect a little vision therapy helped even though his eye issues were minor).

 

What he does now... 8999 divided by 3. He knows that 3 goes into 8 two times, so 3 goes into 8000 at least 2000 times. He writes 2000 on top of the problem, writes 6000 underneath the 8000, and then he subtracts (2999 left). He knows that 3 does not go into 2, so he looks to see how many times it goes into 29. It goes at least 9 times, so it goes into 2999 at least 900 times. He writes 900 on top of the 2000 that's located where we traditionally put the answer, and subtracts 2700 from the 2999. He continues this process until the end. He never has to "bring down" any numbers. It's conceptually sound and deals with all of the numbers the same way the traditional algorithm does. He does have to add his answers on top together, but the place value takes care of itself. For instance, if you end up with a zero for the tens place in the final quotient, it shoes up on its own. Alternatively, you could start by writing the 2000 out on top, and when you put the 900 into the answer, you could erase the zero that's in the hundreds place, and so on, until you have the answer written out without adding all the little answers up.

 

If necessary, you can write the 8999 in place value columns, and you can talk the child through the steps I listed in the last paragraph while crossing out numbers and carrying them to the next column as you go. Kind of like the short division another poster talked about. It's harder to describe though. My son could follow that, but he couldn't really do it. It did help him to see another demonstration even though it didn't become a feasible method for him.

 

Another method that looks really promising is on Education Unboxed. http://www.education...division_1.html

[sbgrace]

This was my son. What worked best here was an idea I got from reading what Hunter added to this thread. She said to just keep dividing really big numbers by 2 to master those steps. We had the steps written out at first, and he did master them with that technique. The only other thing I did was have him draw an arrow to show he's "bringing down" the next number. He would say those steps out loud, too. The 2's technique did the rest. Like your situation, he does know his mult/division facts. But it was important to take one more mental process/distraction out for him.

 

 

Oh, his twin uses a lined notebook paper turned lengthwise to keep things lined up. I've seen graph paper used for the same thing. My ADHD kid doesn't have issues with lining up interestingly! It's tuning in to master the process and also maintaining attention to carry out that process each time.

[AmyontheFarm]

I found an ipad app and made him practice and practice.  We "drilled and killed" it for a week and he was ready to go.  But again, I also made sure he was either dividing by 2 or 5 to make it simpler.

[prairiewindmomma]

I didnt think we'd both survive long division. Writing down the division steps (and showing each step separately in a sample problem) helped. So did turning the paper sideways to line up columns. Eventually he mastered long division as it became automatic enough, but for quite awhile he would lose focus midproblem and not know how to restart. I suspect he still loses focus sometimes, but he now easily knows where to start back again.

[Sara Mac]

I would highly doubt that any of my kids could actually write out a long division problem as "long division". With my eldest, she struggled with the steps - divide this, times that, subtract that ..... Far too confusing. So after showing her long division I then showed her the way I learnt which is short division. It's exactly the same process but you don't write down all the steps. To be honest I've never, ever found a problem that *requires* being written out the long way.

 

http://www.wikihow.com/Do-Short-Division

[jmarchman]

We are in the middle of long division with my 11yo ADHD son.  He really struggled with the concept, too, at first.  We use MUS Delta, and I found the manipulatives very helpful.  He is doing very well after working with the manipulatives for a couple weeks.

 

Basically, we worked with the MUS Decimal street and the base ten blocks.  I have the decimal street poster covered in contact paper so that we can use dry erase markers on it.  We built the dividend with the blocks, and then drew a division bracket around the blocks in dry erase.  For the divisor, we used paper cups.  We talked in terms of cookies (the dividend) and the people receiving the cookies (the divisor).  The cups we very helpful in getting the idea that they were really receiving something.  It was much less abstract.  And we worked the problems out right there on the poster.  The people (the cups, the divisor) visits the *first house* on the street for cookies, whatever ever that is, the hundreds house, or the tens...divides what they have if you can, or if not, combines with the next house.  

 

He's no longer using the manipulatives.  He gives them up as soon as he can, because they are a pain once he gets it--- so they never become a crutch.

 

HTH,

Jennifer

[Tress]

Two possibly useful resources come to mind:  the MM Blue topic book http://www.mathmammoth.com/division_2.php (look at the samples to see what you think) and Lets Play Math's blog post about the cookie factory http://letsplaymath.net/2010/04/12/the-cookie-factory-guide-to-long-division/

 

I have no experience with MM, but what Let's Play Math calls the 'cookie factory' is what I have been doing.

(We always do math with cookies, somehow that makes it easier.)

 

You talk about dividing large number of cookies. You could do this one by one (kids tend to want to start with the 'ones') but that is an aweful lot of work :), so you show them that dividing the 'big boxes of 100 cookies' first is a much better idea. Then you divide the 'smaller boxes of 10 cookies' and then the normal cookies. At first you make sure that every number divides neatly, use manipulatives and *you* write everything down, untill your child can talk you through the problem. Then you let your child write it down.

 

When that is going okay, you start with numbers that don't divide neatly, so after giving away the boxes with 100 cookies you have still several left. Those boxes can be opened and than you have boxes of 10. Those you add to the boxes with 10 cookies you alreay had. You divide those etcetc. You are writing things down, talking about what you are doing. When your child can talk you through the problem, you can let her practice writing it down.

 

Those steps *may* take days, but I wouldn't go anywhere near writing down things or memorizing algorithms until your childs understands what she is doing.

 

[sbgrace]

I would highly doubt that any of my kids could actually write out a long division problem as "long division". With my eldest, she struggled with the steps - divide this, times that, subtract that ..... Far too confusing. So after showing her long division I then showed her the way I learnt which is short division. It's exactly the same process but you don't write down all the steps. To be honest I've never, ever found a problem that *requires* being written out the long way.

 

http://www.wikihow.com/Do-Short-Division

 

I like this! I had never seen it before. I just played around with it with my attention issues kid. Actually, for him, I think writing down the steps takes some of the working memory demands out of it. It may just be that he's really internalized/become comfortable with the long division way he finally mastered.  But I think my other son might really take to this. And, for him, it would take away the need to have the guides to line up his work.

[Ravin]

For the steps, we made a poster. It's on the wall as a reminder.

[laundrycrisis]

I have a similar 10 yo.  I will suggest two alternatives to traditional long division (aka wading through mud).

 

1.  Double division.  It's an adaptation of partial quotients that is less random.  This is very useful for a student who does not have good recall of the multiplication facts.  All you have to be able to do it is double numbers, subtract, and add.

 

http://www.doubledivision.org/

 

 

 

2.  Partial quotients.  This is what our son uses now that he has all the multiplication facts down. 

 

I haven't found a tutorial on partial quotients that I like very much - because I always think my own way of using it is much better. There are a bunch of them online though. 

 

My own favorite way to use partial quotients - if the dividend is at least 10x the divisor, I always start by subtracting off multiples of 10 (of the divisor).  First, I have him make a table of the multiples of 10 of the divisor.  10 - add a 0.  20 - double the 10.  30 - add the 10 and 20 together.  20 - double the 40.  50 - multiply by 5, add a 0.   Etc.  Pick the multiple of 10 that didn't go over the dividend. Subtract it off, write down the factor that was used.  Repeat until you have a remainder that is no longer 10x greater than the dividend.  Then start using factors that are 1-9 (same table, but ignoring those last 0s).  This gets us very quickly to a final remainder (that is less than the divisor), and the final answer.  He can solve problems that look really hard very quickly, usually in only 2-3 steps.  If the dividend is 100x the divisor, you make the first table with multiples of 100, etc.  It's fantastic - simple, easy, little room for multiplication mistakes, and he doesn't get lost.  Great for us ADD folks. 

[EKS]

Teach short division first.

 

Actually, not exactly first.  Try to teach long division for a day or two.  Then when it's not going well, introduce short division.  Your student will be relieved.  After she gets good at short division, have her try it with two digit divisors.  You can do it, but at a certain point it becomes obvious to the student that the long division algorithm is more efficient.