Long Division -- HELP!!!

[SFM]

Holy smokes! I think I take for granted that I have learned this, I thought it wouldn't be that difficult to teach, boy was I wrong. :banghead: This is me right now and probably ds as well. We are in Singapore 3A and we have started the long division, and it's not that he isn't getting it I think it's partly because of all of the process' involved. Division, multiplication, subtraction and combining all of those and remembering when you do each is proving difficult to teach. Especially, he is still not great on his multiplication facts (we are trying he is very right brained and it might just take longer).

 

Any suggestions, tools for helping, wisdom, advise?? :bigear:

[Arcadia]

If he understands multiplication well, let him look at a multiplication chart while doing long division.

You might also want to use graph paper or turn a wide lined paper to get columns so that its easier to put the numbers at the correct column for long division.

[SilverMoon]

I had mine act the problems out with 2x2 Lego bricks several times before we just did it with a pencil. By putting them in stacks of ten, putting a rubber-band around ten of those, and keeping some loose for ones, they could build the number they were supposed to divide. Then they could see how they'd only divided some of the number at a time, why we were setting it aside, and starting over. Lather, rinse, repeat, until it was embedded in their brains well enough they could explain it back to me in their own words.

[dbmamaz]

I found somewhere an example with each step in a different color, so its easy to see what comes next. I was also baffled how difficult it was, and my son LOVES math. But it was mind-bogglingly frustrating for a month or two and then we were almost done.

[taffnus]

You're not the only one. My dd9 is in 4A and we're reviewing long division. She had a great understanding of division going into SM 3 but the process stumped her. Just today she finally said that it's actually getting easy but we have had frustration. Honestly, I didn't push. We went through all the SM pages and I figured it could be a developmental thing. I do still think that.

 

I ran across an easy/fun way to remember the steps and used this from the beginning. It does help a bit. The steps are: Divide, Multiply, Subtract, Whee (bring the next number down), and Repeat. Of course, the "Whee" is what can be made fun.

 

I second the graph paper. That helps keep it all lined up. It may just come down to repetition and maturity. FWIW, dd's end-of-year test scores were still superb, regardless of the shaky understanding of LD. Maybe consider it the "introduction year" and know that it will continue into SM 4. :001_smile:

[TarynB]

So is your DS just having trouble remembering the order of the steps? This doesn't teach the concept of long division, but it really helped my DS remember the steps in order. It is a prepared & detailed graphic that illustrates the steps with a mnemonic device: "Dad, Mom, Sister, Brother, Rover". After he got comfortable with the process, the concept clicked much more easily for him. (Just click "open" after you click the link.)

Edited October 11, 2012 by Kay_ks

[kolamum]

We took a month off with math to focus on division.

 

First, I spent 1 week making sure we had our multiplication facts down pat, we did, but we needed review with our 9's. Once that was accomplished, I took our multiplication programme {Times Alive!} & made division flash cards with the picture clues from the story.

 

We spent two weeks doing those & I pulled out some short/simple division worksheets. I required him to do 10-20 problems a day. Nothing major, nothing more then a few minutes. Just enough to get him comfortable so nothing shocked him.

 

After that, we moved to long division, but only once I was certain confidence was down pat with the short division. It wasn't worth advancing because my fellow would have FrEaKeD out, kwim?

 

Then, I used an idea which was shared on the boards. Basically using visuals to help him remember what he was doing. Keep in mind we were working with NO remainders. ;) You can see the visual here. Basically for something like 9÷3 we had 3 circles drawn on our white board & I had my son divide 9 poker chips evenly amongst them.

 

Once he was super comfortable with things like that we moved forward again to having long division with remainders. It FELT slow, especially at first, but we picked up speed afterwards SO QUICKLY that it was totally worth it. :D

[dmmm]

Dad, Mom, Sister, Brother helped it click for my dd. There are videos on YouTube.

 

Also, doing problems on a white board and drawing the arrows when briging down really helped.

 

Good luck!!

[Jennay]

We just hit long division is SM 3A on Monday. DS#2 just about blew a gasket! He understands division when it doesn't have a remainder and is written horizontally but the vertical way just threw him for a loop. I am going to make the number discs as recommended in the HIG and work through a bunch of problems manually. I think that will help.

[Plateau Mama]

When my son was learning I made him a cheat sheet. It was very simple.

 

1. Divide

2. Multiple

3. Subtract

4. Bring Down

5. Repeat

[Hunter]

I only make problems that are divided by 2. LOOOONG problems all divided by 2. I teach the rhythm of the problem in a sing song voice. I "sing" many problems while the student just watches. Then I coach the student through LOOOONG problems divided by 2, while they "sing" out the steps.

 

If the student is still nervous, I make a board game. And put more of the long problems divided by 2 on cards.

[FO4UR]

Do 1-3 long division problems *together* each and every school day. (Sometimes I scribe while he "teaches" me how to do the problem, and sometimes I talk him through while he works the pencil...eventually, it's just faster if mom stops talking and he just writes.:tongue_smilie: And at that point -he's got it!)

 

Meanwhile, skip ahead in the book and carry on. By the time you finish the book, you'll probably be over the long division slump. Small daily doses of repetition repetition repetition will help it sink in. Keep reviewing in those small daily doses after the slump has past.

 

 

Make *sure* he understands the reasons for all the steps. Work some through with manipulatives. As you talk him through, think about the way you word things. Remind him of place values and how it looked when we used the manips.

 

 

For the multiplication facts, I let him use a "cheat sheet" for most of his math work and just keep working (in small daily doses) at memorizing the facts. My 9yo will memorize and forget if we don't *daily* review mult/div.

[SFM]

So is your DS just having trouble remembering the order of the steps? This doesn't teach the concept of long division, but it really helped my DS remember the steps in order. It is a prepared & detailed graphic that illustrates the steps with a mnemonic device: "Dad, Mom, Sister, Brother, Rover". After he got comfortable with the process, the concept clicked much more easily for him. (Just click "open" after you click the link.)

 

 

Thank you for this, he loves mnemonic devices, he thinks they are a hoot, this might work. Thanks.

[SFM]

I found somewhere an example with each step in a different color, so its easy to see what comes next. I was also baffled how difficult it was, and my son LOVES math. But it was mind-bogglingly frustrating for a month or two and then we were almost done.

 

Great idea, thanks. He is not awesome at math but it is not usually an area of 'struggle' for him. I do this sometimes with words he is struggling to spell, breaking them up into different colors. We also did this when we were borrowing/carrying, it worked also, I didn't think about it this go around. Thanks again.

[SFM]

If he understands multiplication well, let him look at a multiplication chart while doing long division.

You might also want to use graph paper or turn a wide lined paper to get columns so that its easier to put the numbers at the correct column for long division.

 

Great thought. Thanks. I thought about giving him the multiplication chart today, he understands multiplication and has memorized various sets of his 'tables' but he just isn't the best with computation. I just ordered graph paper we are in rural Japan and you don't find the exact things you would in the US. So, thanks for the idea, I will use it.

[SFM]

I had mine act the problems out with 2x2 Lego bricks several times before we just did it with a pencil. By putting them in stacks of ten, putting a rubber-band around ten of those, and keeping some loose for ones, they could build the number they were supposed to divide. Then they could see how they'd only divided some of the number at a time, why we were setting it aside, and starting over. Lather, rinse, repeat, until it was embedded in their brains well enough they could explain it back to me in their own words.

 

Thanks, good tip, he loves legos as well.

 

You're not the only one. My dd9 is in 4A and we're reviewing long division. She had a great understanding of division going into SM 3 but the process stumped her. Just today she finally said that it's actually getting easy but we have had frustration. Honestly, I didn't push. We went through all the SM pages and I figured it could be a developmental thing. I do still think that.

 

I ran across an easy/fun way to remember the steps and used this from the beginning. It does help a bit. The steps are: Divide, Multiply, Subtract, Whee (bring the next number down), and Repeat. Of course, the "Whee" is what can be made fun.

 

I second the graph paper. That helps keep it all lined up. It may just come down to repetition and maturity. FWIW, dd's end-of-year test scores were still superb, regardless of the shaky understanding of LD. Maybe consider it the "introduction year" and know that it will continue into SM 4. :001_smile:

 

I am glad to know there will be time to continue building on to this skill.

 

We took a month off with math to focus on division.

 

First, I spent 1 week making sure we had our multiplication facts down pat, we did, but we needed review with our 9's. Once that was accomplished, I took our multiplication programme {Times Alive!} & made division flash cards with the picture clues from the story.

 

We spent two weeks doing those & I pulled out some short/simple division worksheets. I required him to do 10-20 problems a day. Nothing major, nothing more then a few minutes. Just enough to get him comfortable so nothing shocked him.

 

After that, we moved to long division, but only once I was certain confidence was down pat with the short division. It wasn't worth advancing because my fellow would have FrEaKeD out, kwim?

 

Then, I used an idea which was shared on the boards. Basically using visuals to help him remember what he was doing. Keep in mind we were working with NO remainders. ;) You can see the visual here. Basically for something like 9÷3 we had 3 circles drawn on our white board & I had my son divide 9 poker chips evenly amongst them.

 

Once he was super comfortable with things like that we moved forward again to having long division with remainders. It FELT slow, especially at first, but we picked up speed afterwards SO QUICKLY that it was totally worth it. :D

 

I think we are reaching the point where we both feel like this :banghead: so, perhaps taking a short break would be worth it in the long run. Thanks. Also, I am going to check out your multiplication facts stuff. I like the poker chips as well, lots of good stuff here, thank you for sharing.

 

Dad, Mom, Sister, Brother helped it click for my dd. There are videos on YouTube.

 

Also, doing problems on a white board and drawing the arrows when briging down really helped.

 

Good luck!!

 

Thank you, I think it will assist him. I will try it out.

 

We just hit long division is SM 3A on Monday. DS#2 just about blew a gasket! He understands division when it doesn't have a remainder and is written horizontally but the vertical way just threw him for a loop. I am going to make the number discs as recommended in the HIG and work through a bunch of problems manually. I think that will help.

 

 

AH, I am not alone, thank you.

 

When my son was learning I made him a cheat sheet. It was very simple.

 

1. Divide

2. Multiple

3. Subtract

4. Bring Down

5. Repeat

 

I made a few other cheat sheets, maybe I could do this one as well. Thank you for your tip.

[SFM]

I only make problems that are divided by 2. LOOOONG problems all divided by 2. I teach the rhythm of the problem in a sing song voice. I "sing" many problems while the student just watches. Then I coach the student through LOOOONG problems divided by 2, while they "sing" out the steps.

 

If the student is still nervous, I make a board game. And put more of the long problems divided by 2 on cards.

 

Great idea and I think it would help boost confidence in his abilities. :)

 

Do 1-3 long division problems *together* each and every school day. (Sometimes I scribe while he "teaches" me how to do the problem, and sometimes I talk him through while he works the pencil...eventually, it's just faster if mom stops talking and he just writes.:tongue_smilie: And at that point -he's got it!)

 

Meanwhile, skip ahead in the book and carry on. By the time you finish the book, you'll probably be over the long division slump. Small daily doses of repetition repetition repetition will help it sink in. Keep reviewing in those small daily doses after the slump has past.

 

 

Make *sure* he understands the reasons for all the steps. Work some through with manipulatives. As you talk him through, think about the way you word things. Remind him of place values and how it looked when we used the manips.

 

 

For the multiplication facts, I let him use a "cheat sheet" for most of his math work and just keep working (in small daily doses) at memorizing the facts. My 9yo will memorize and forget if we don't *daily* review mult/div.

 

Thanks for the tips, I sit and do math with him everyday and I am on standby even if he thinks he can do it. I try to be there to encourage as well. I just started using the whole "you teach me" today and I think he really liked that.

 

Thanks for the advice.

Stephanie

[Arcadia]

I just ordered graph paper we are in rural Japan and you don't find the exact things you would in the US. So, thanks for the idea, I will use it.

 

You can print graph paper here. The website has a PDF of the multiplication chart as well.

http://math.about.com/od/worksheets/a/Graph-paper.htm

[SFM]

You can print graph paper here. The website has a PDF of the multiplication chart as well.

http://math.about.com/od/worksheets/a/Graph-paper.htm

 

WOW, thanks!!!

[Lab1]

After a few problems and my kids still looked like monkeys doing math problems, I remembered the "family" approach from when I was a kid. Wrote it down on a sticky note and they are doing great now.

 

You can turn regular lined paper sideways so it shows columns to keep it organized as well.

[kathy_overman]

You are not alone. I searched the forum yesterday looking for help too.

 

My son enjoyed the You Tube videos, Kahn Academy, and watching me do problems. Also, I decided to sit and walk through each probelm with him. I wanted him to get it in a few days, and he didn't. I told him not to worry, I will do each probelm with him, and this has helped his confidence. I say that, and today will end up being another screaming session! Ha!

 

I put several examples on the white board explaining each step, and I am giving him lots of easy practice with 2 and 3 as divisors. Wow, I never thought this would be so hard!

[SFM]

You are not alone. I searched the forum yesterday looking for help too.

 

My son enjoyed the You Tube videos, Kahn Academy, and watching me do problems. Also, I decided to sit and walk through each probelm with him. I wanted him to get it in a few days, and he didn't. I told him not to worry, I will do each probelm with him, and this has helped his confidence. I say that, and today will end up being another screaming session! Ha!

 

I put several examples on the white board explaining each step, and I am giving him lots of easy practice with 2 and 3 as divisors. Wow, I never thought this would be so hard!

 

 

Thanks for letting me know your story, it's really great to hear that I am not alone. It is so hard and I have been getting a tad frustrated --- ugh, trying to relax.

[Hunter]

 

You can turn regular lined paper sideways so it shows columns to keep it organized as well.

 

Oooh good idea!

[i.love.lucy]

Kahn Academy. My dd did not get long division at all until we watched the video and did it his way. It's different but has opened her eyes to the logic of math more. She is so non-math oriented that she often needs a fresh perspective.

[Dana]

We went slowly at that point as well.

 

First day, we used base 10 blocks. We'd work the problem with the blocks, then we'd redo the problem with the blocks while I wrote the notation for each step. I really liked using the base 10 blocks because you see WHY you go from large to small when all the other operations go from small to large.

 

Second day I had my son write the work after using the blocks.

 

As we kept going, I'd have him use the blocks any time he got a problem incorrect using math notation.

 

I know mnemonics can be helpful, but I've got concerns using them for arithmetic operations. I tend to see where people run into problems with mnemonics though, so that colors my dislike of them. I really liked the base 10 blocks and going from concrete to abstract.

[mama27]

Holy smokes! I think I take for granted that I have learned this, I thought it wouldn't be that difficult to teach, boy was I wrong. :banghead: This is me right now and probably ds as well. We are in Singapore 3A and we have started the long division, and it's not that he isn't getting it I think it's partly because of all of the process' involved. Division, multiplication, subtraction and combining all of those and remembering when you do each is proving difficult to teach. Especially, he is still not great on his multiplication facts (we are trying he is very right brained and it might just take longer).

 

Any suggestions, tools for helping, wisdom, advise?? :bigear:

 

 

I do every long division problem with them until they don't need me to anymore. If the math you're using doesn't have enough practice make some up, 2 or 3 a day, till it's mastered. BTST several times now! lol

[Walking-Iris]

I do every long division problem with them until they don't need me to anymore. If the math you're using doesn't have enough practice make some up, 2 or 3 a day, till it's mastered. BTST several times now! lol

 

:bigear: BTDT as well. My oldest is still struggling with long division. We just hung it up at the end of last year. He has his mult facts down solid so I've been doing short reviews daily with him. Really trying to get the concept between mult and division down solid. He had a light bulb moment yesterday when he realized he could always know the answer to a division problem if he knew that he was dividing with a square number. I'm hoping to slowly build on those concepts and ease him back into long div without remainders. He did relatively okay with that, but WITH remainders caused him to go running for the hills.

 

I'm thinking that only after he has a strong memory of division facts as the inverse of his mult facts then I'll ease him back into long div.

 

But remainders? That was our primary struggle.

[justLisa]

We got stuck a bit in SM long division, and I went to the MM section. It breaks it down in increments. Further than SM IMO. It helped here.

[Mallory]

My right brained child learned this much quicker when we did short division. I think it makes much more sense then long division. I also let him fill out a multiplication table if he needs it.

 

You'll have to do you're own search (my dial up is way to slow for me to watch or recommend videos) but I know Khan has short division lessons.

[ChicoryChick]

When my son was learning I made him a cheat sheet. It was very simple.

 

1. Divide

2. Multiple

3. Subtract

4. Bring Down

5. Repeat

 

I teach this also. For my VSL, I also finds that using lined paper sideways so the columns line up helps. She also found that making a multiplicatiin chart of the divisor helps. She then puts "T" over the number being multiplied to remember that number goes on top and and a "B" over the product to show that the answer goes below to be subtracted.

[Spy Car]

Long division is one of those curious challenges in early math where children need to develop both an ability to work a multi-step algorithm in a procedural fashion and need to (hopefully) understand what they are doing.

 

My feeling is it is important for the parent/teacher and/or the student to keep talking though both the procedural steps AND discuss what is happening as each procedure takes place to ensure understanding.

 

We recently mastered long division (with a single digit divisor). My son is pretty math adept, but it took some time. Part of the problem IMO was the "fear factor"—as stories of the horrors of the dreaded "long division" circulate among children—and part of it is the mix of multi-part steps and conceptual awareness.

 

Making sure my son understood the reasoning of the algorithm was the key IMO. One day—and it happened recently—he just got it and declared that long division was easy and fun. Quite a reversal.

 

Bill

 

ETA: the comments by previous posters about making sure numbers line up in their "place" are well taken. Understanding place value is essential in long division and not allowing sloppiness in writing out the algorithm helps keep the place value clear.

[SonshineLearner]

We did short division... It's easier and works out the same, I think... I showed him "long" and then we did "short". For some it works out well to show them what you are actually doing. I'll try for an example. Ok, so we have 121 divided by 5. That's like 121 race cars to divide fairly into 5 groups. Hmmmm... How will we do that? Ok, well, that means you have 1-100, 2-10's, & 1-1. How should we figure that out? Hmmmm..... well, lets do this with pennies.... and then you represent all of the groups... and then you continue... We do a lot of this in real life. I mean... if you just explain it all on paper, then you can show them WHY it makes sense and go from there...

[simplyme99]

These are all great ideas!! My DD is having a difficult time with division as well, and I don't understand why!!

 

What is the difference between long and short division? :confused:

[Mommy22alyns]

I do every long division problem with them until they don't need me to anymore. If the math you're using doesn't have enough practice make some up, 2 or 3 a day, till it's mastered. BTST several times now! lol

 

:iagree: It's super easy to find extra long division problems online. I printed Becca a couple of extra pages and have her do 5 if we're good on time. We've also done a lot on the white board and used different colors for each step.

[FO4UR]

:bigear: BTDT as well. My oldest is still struggling with long division. We just hung it up at the end of last year. He has his mult facts down solid so I've been doing short reviews daily with him. Really trying to get the concept between mult and division down solid. He had a light bulb moment yesterday when he realized he could always know the answer to a division problem if he knew that he was dividing with a square number. I'm hoping to slowly build on those concepts and ease him back into long div without remainders. He did relatively okay with that, but WITH remainders caused him to go running for the hills.

I'm thinking that only after he has a strong memory of division facts as the inverse of his mult facts then I'll ease him back into long div.

 

But remainders? That was our primary struggle.

 

 

This is where the old Strayer-Upton book shines. All of the long division work divides evenly for a long while. (The child is getting the rhythm of the process and solidifying x facts through this.) Interspersed are practice problems like 12/5= 2r2 and 30/7= 4r2 ....so the child is working with small and easy-to-see numbers to work out those pesky remainders. By the time we met remainders in a long division problem, it was a non-issue.

 

 

 

(I have been Strayer-Upton as systematic review, and Singapore for my main curric.)

[Walking-Iris]

This is where the old Strayer-Upton book shines. All of the long division work divides evenly for a long while. (The child is getting the rhythm of the process and solidifying x facts through this.) Interspersed are practice problems like 12/5= 2r2 and 30/7= 4r2 ....so the child is working with small and easy-to-see numbers to work out those pesky remainders. By the time we met remainders in a long division problem, it was a non-issue.

 

 

 

(I have been Strayer-Upton as systematic review, and Singapore for my main curric.)

 

That's a very good idea. I don't have Strayer Upton books, but I think I will linger over division longer than (maybe) usual to give him time to really understand what he is doing.

[mammajen]

I found the "family" method of long division online. It was a great pneumonic (?) device that helped my ds remember the process. It is:

Dad - divide

Mom - multiply

Sister - subtract

Brother - bring down

Rover - remainder or repeat (depending on outcome)

 

HTH,

Jennifer

[CatholicMom]

I think this is one of those skills where a lot of kids hit the road block. I still remember my 4th grade self being confused, discouraged, and really struggling with long division and it was because I didn't know my math facts. I had always struggled with math facts and just did not memorize them easily. So it really hit the fan with me with long division for the exact reasons you're saying... all those operations come into play with every. single. long division problem. If each operation is still a chore for the child, they can practically lose sight of what they are even going for in solving the division problem and it becomes an incredible struggle.

 

I know this only addresses the "how do you get them to solve the problem" question and not "how do you get them to understand what they're doing" issue. But, for a lot of kids, solving problems repeatedly (once they know their math facts) and applying those skills in real life will eventually produce that lightbulb moment when they realize why this operation makes sense.

 

Anyhoo, in my non-expert opinion, I would not continue with long division until your child has addition & multiplication facts memorized. Once that is not a distraction and a struggle (not to mention tedious), they can focus on the task at hand.

[Walking-Iris]

I think this is one of those skills where a lot of kids hit the road block. I still remember my 4th grade self being confused, discouraged, and really struggling with long division and it was because I didn't know my math facts. I had always struggled with math facts and just did not memorize them easily. So it really hit the fan with me with long division for the exact reasons you're saying... all those operations come into play with every. single. long division problem. If each operation is still a chore for the child, they can practically lose sight of what they are even going for in solving the division problem and it becomes an incredible struggle.

 

I know this only addresses the "how do you get them to solve the problem" question and not "how do you get them to understand what they're doing" issue. But, for a lot of kids, solving problems repeatedly (once they know their math facts) and applying those skills in real life will eventually produce that lightbulb moment when they realize why this operation makes sense.

 

Anyhoo, in my non-expert opinion, I would not continue with long division until your child has addition & multiplication facts memorized. Once that is not a distraction and a struggle (not to mention tedious), they can focus on the task at hand.

 

:iagree: I think if a child still has to look at a cheat sheet for multiplication facts then maybe they shouldn't really do too much division. In our case my ds has those facts down, but the relationship between division and mult wasn't solid and imo there's no reason to push forward without a basic foundation set. This is a big reason why I homeschool. I was one of those kids who could have benefited with more time for math than a typical ps is going to allow. I was metaphorically slapped on the hand for trying to figure out multiplication instead of just memorizing the facts. I have memories of teachers saying "no" and looking mad or disappointed when I tried to repeat add or draw arrays on my paper or to stop and think "2 7's is 14 so 4 7's should be..."--nope. I was always stopped in my act of thinking and reprimanded because I wasn't spitting out the answer in their arbitrary time limit to prove that I've memorized the answer. This was around 3rd grade age.

 

As you can imagine it followed me throughout school until I was old enough to figure some things out for myself. I vowed to keep my kids on an individualized developmental schedule for math as opposed to a grade/age schedule for that reason.