Now I know why it is called Long Division! How do you teach it?

[kalanamak]

Because it takes a long time to sink in.

 

 

I am getting bored with re-re-reexplaining it. Every day it is like starting from scratch. This is clearly the toughest thing we have faced in math. To make it worse, my son is a good guesser (he got the quotient for 80/3 but not the remainder in about 20 seconds of "3x30 is 90, and 2x2 is" muttering under his breath). He needs to learn the steps, to be more methodical. Anyone have tricks on this? Anyone with a printable sheet of the steps he can keep next to his desk to follow? Should I try moving right up to 1000s to make it harder for him to guess, forcing him to do the steps?

 

Or is it just over and over and over until the nickel drops. Tell me the truth, I can take it.

[HollyDay]

Is this for your 3rd grader? I personally think long division is a very difficult concept to learn. The student must be able to estimate, multiply, and subtract (with carrying or borrowing) while keeping everything lined up nice and neat. And that is just with 1 digit!!!! Throw in multiple digit division and it gets more confusing.

 

Is it possible your dc needs a little extra time to mature into the concept? A conference I attended a few years ago recommended increasing logic and math drills to help the dc mature and develop in the math area. Logic Links were highly recommended as well as MindBenders, Blokus game, Rush Hour game, and chess. The speaker thought these activities helped to develop a logical train of thought and made the multi-step math problems (like long division) easier to accomplish.

[Pam L in Mid Tenn]

I've taught four children long division.

 

The best way:

1. Do a bunch of problems FOR them explaining every single step.

2. Do more problems FOR them letting them tell you the steps.

3. Begin letting them write the problems while you tell them every single step.

4. Continue letting them write the problems while they tell you each step as they are doing it.

5. Do problems silently side by side and compare answers.

6. Give them the problems to do independently.

 

Some kids will need 20 problems in each for #1 to #6.

Some kids will need 100 Problems for each step.

 

Only do about 10 problems per day. Fill in math time with other topics.

[kalanamak]

I've taught four children long division.

 

The best way:

1. Do a bunch of problems FOR them explaining every single step.

2. Do more problems FOR them letting them tell you the steps.

3. Begin letting them write the problems while you tell them every single step.

4. Continue letting them write the problems while they tell you each step as they are doing it.

5. Do problems silently side by side and compare answers.

6. Give them the problems to do independently.

 

Some kids will need 20 problems in each for #1 to #6.

Some kids will need 100 Problems for each step.

 

Only do about 10 problems per day. Fill in math time with other topics.

 

We have worked our way through 1-4, but it isn't sticking. Every new lesson I have to start with 1 and work up to 4 and THEN do his workbook pages. This is all SM 3A, we have been at it 2 weeks. My teeth are getting dry from the forced smile. :D

[Dana]

We started with a single digit divisor and used base-10 blocks to work through a couple of problems. Then I had my son work the problem with the blocks while I showed him how we'd write it with the algorithm, focusing on place value (we're dividing 8 hundreds into 3 groups. Each group has 2 hundreds. We have 2 hundreds left over, so we break them into tens. We had these tens here, so we now have so many tens. Now we're dividing our tens into 3 groups...).

 

It did take a couple of days to sink in... and we had to go back to the base-10 blocks multiple times. If he tried using the algorithm and got a problem wrong, I'd have him show me with the blocks, then write it out. I really think actually manipulating the blocks makes a huge difference in understanding and I doubt my son would have understood without using the blocks.

[Erica in OR]

It does take a lot of repetition to sink in, in our family's experience. I liked the way Saxon 3 dealt with it. The lesson uses play hundred, ten, and one dollar bills to physically split up the money among different groups. So, depending on the problem, we'd say, you have three people that you need to share the money with equally. How many hundred dollar bills can each person have? How many does this "use up" for all the groups? Do you have any left over? What do we do with the left over hundreds so they can be split up (physically change them over for ten dollar bills, etc.). This helped cement the concepts for us and served as a good way to check your answers by counting the money each pile had. Saxon 54 then moves into the checklist/stepwise approach, without the physical backup.

 

Erica in OR

[Mandamom]

First step make sure they understand what multiplication and division are.

 

After that I have them use very simple numbers and they are required to show me each step. Problems (in long division form) such as 8/7, 4/3, 9/8 and moving to problems such as 9/2, 10/3, etc. I will also start having them do basic division facts in long division form where, again, they have to show all of the steps (15/3, 24/8).

 

After they are very comfortable I'll start do problems such as 37/5, 46/6 and 34/8.

 

They have to show their work....each and every step and I have found that by now they know the process very very well.

 

After they are comfortable with problems such as 37/5, I introduce the concept of bringing down and work a few with them until they are comfortable.

 

I've had some students move through this process fairly quickly while others take much longer. It works very well.

[Mallory]

We only do short division- I think it makes so much more sense! (Just google it and there are all kinds of sites and videos.) I didn't know about it until I started teaching my boys. They have both gotten through it easy.

 

I think it makes it so much easier to see what you are doing. Kind of like when you subtract by starting with the left side and thinking about what is left, when you do "short division" you can see what those left over hundreds are doing.

[AngieW in Texas]

I bet he'll have an easier time with short division. That's what I resorted to with my girls. They wondered why on earth I tried to teach it the "hard" way instead of the "easy" way.

 

http://www.themathpage.com/arith/divide-whole-numbers.htm

 

[Karenciavo]

Have you tried the game in the HIG? Something fun instead of the same old, same old.

 

I'm going by memory here:

4 sets of cards 0-9 (we made them out of index cards), die

draw 2 or 3 cards, place facing up in order drawn

player rolls

divide # rolled into cards drawn

player with smallest quotient gets point or greatest, or smallest remainder - whatever you choose

[Guest mrsjamiesouth]

Because it takes a long time to sink in.

 

 

I am getting bored with re-re-reexplaining it. Every day it is like starting from scratch. This is clearly the toughest thing we have faced in math. To make it worse, my son is a good guesser (he got the quotient for 80/3 but not the remainder in about 20 seconds of "3x30 is 90, and 2x2 is" muttering under his breath). He needs to learn the steps, to be more methodical. Anyone have tricks on this? Anyone with a printable sheet of the steps he can keep next to his desk to follow? Should I try moving right up to 1000s to make it harder for him to guess, forcing him to do the steps?

 

Or is it just over and over and over until the nickel drops. Tell me the truth, I can take it.

 

 

This is why I changed Math programs with my ds once we hit 4A. We started on long division in 3rd grade with Singapore and he never caught on til the beginning of this year in Saxon 6/5. Finally, he looked at me and said, "OH!! I get it!" :001_huh: Those were wonderful words though.:001_smile:

 

One thing I looked at was his Facts. Does your son know the entire times table immediately? Keep practicing with flash cards. Another thing was Saxon has this little Oval you can draw with the steps to remember:

 

1. Divide

2. Mulitply

3. Subtract

4. Bring Down

 

Instead of writing out the words write out the symbols for him to check while doing long division.

[kalanamak]

Have you tried the game in the HIG? Something fun instead of the same old, same old.

 

I'm going by memory here:

4 sets of cards 0-9 (we made them out of index cards), die

 

 

Yes, we do that, and it is the only game in this section. The HIG actually spends very few pages on it. This has lead me to believe it is repetition rather than some brilliant insight that is required. :)

[kalanamak]

I bet he'll have an easier time with short division. That's what I resorted to with my girls. They wondered why on earth I tried to teach it the "hard" way instead of the "easy" way.

 

 

Well...I've never even heard of short division. I assumed SD was just thinking "30/5 is 6" (see that was short). Short division!

 

Okay. Why long division taught rather than this? I'm going to give it a go tomorrow, but I can almost bet my son will do better with this. At least, we can go along and do it one way and then the other. He "gets it" after examples. It just isn't sticking day to day. It MAY be that he finds division real work, and is "limping" on purpose. I'm catching his eyes drifting out the window more these days, and he has even yawned during math recently.

[Sweetbeebie]

It helped my daughter a lot to put the times sign by divisor so she would remember the number on top the "house" is the missing # in a multiplication problem. I even wrote it out that way on the side a couple of times to help visualize it. As for bringing down the zero's.... I told her that if the question didn't specify rounded to the nearest place value that you place the decimal to show the whole # and add zero's until you get zero or the same # to infinity:) Hope that makes since....

[Nakia]

Thanks for this thread! My oldest has caught onto every math concept pretty easily, but my middle is not as mathy. Short division, which I have never heard of, will probably come in very handy with her!!

[MerryAtHope]

Here's another way to do division that is easier for some kids to grasp. Let's say you want to do 850/15. Maybe your child has no idea where to start with this. You can set up the problem this way:

....._____

15/850....l

..............l

..............l

 

(pretend those "l's" are a straight line down.)

 

So...maybe we can't guess right off how many 15's are in 850. Does it look like there's at least 10? Ok, let's take 10 out.

....._____

15/850....l

...-150.... l..10

....700.....l

 

Hm. It sure seems like there are a lot of 15's in there. Maybe we could take 20 out this time.

....._____

15/850....l

...-150.... l..10

....700.....l

...-300.... l..20

...-400.... l

 

Well, I'm sure there are at least 20 more, let's go with that again.

....._____

15/850....l

...-150.... l..10

....700.....l

...-300.... l..20

....400.... l

...-300.... l..20

....100.... l

 

Ok, I see from what I tried before that I can't get 10 more 15's out of this, but I could do 5 more.

....._____

15/850....l

...-150.... l..10

....700.....l

...-300.... l..20

....400.... l

...-300.... l..20

....100.... l

...-..75.... l...5

...-..25.... l..

 

Oh, there's one more 15 in there...

....._____

15/850....l

...-150.... l..10

....700.....l

...-300.... l..20

....400.... l

...-300.... l..20

....100.... l

...-..75.... l...5

......25.... l..

...-..15.... l...1

......10

 

Ok, so now I can add what's in the column to the right of the line--10 + 20 + 20 + 5 + 1, and I see that there are 56 15's in 850, with a remainder of 10. This is more concrete (and for some kids less stressful) than trying to have to make the right guess in the tens column, not putting a number in the hundreds column by mistake, making the wrong guess & having to start over, etc... I learned this method from Tom Clark, author of Video Text.

 

You can also demonstrate this with Base 10 blocks if you have them.

 

One more thing that is sometimes helpful--stop and take a break for a week or so, and try the concept again later. I often find this "unblocks" my kids on a particular issue. Sometimes we do review during this time, or fun math games, play with manipulatives etc... If your son is still struggling with multiplication or subtraction, that can slow him down in this process, so you could focus on fun ways to practice those facts if that's the case, then try division again.

 

HTH some! Merry :-)

[wapiti]

If you're looking for additional/alternative demonstrations, my kids really enjoyed this:

 

http://letsplaymath.net/2010/04/12/the-cookie-factory-guide-to-long-division/

 

Then we made cookies, of course :)

[Janice in NJ]

Takes about a week of explaining and re-explaining. Reviewing the steps. Making sure they follow the steps neatly.

 

We used the "I show you, we do it together but I lead, we do it together but you lead, you show me, and then you do it on your own" method.

 

Worked with all three kids - and they are ALL very different learners.

 

Then they practice for about a year until they can do it quickly and neatly without thinking - a problem a day. Then I STILL slip in about one problem a week for a couple more years. :001_smile:

 

There are a lot of life-lessons imbedded in long division. Lot of opportunities to demonstrate neatness, patience, diligence, and focused-attention.

 

When I converse with most people about math, I've found that most I-hate-math people trace the onset of their loathing back to 4th grade long division. I decided early on that we were NOT going to die on that hill. I faced that one with full armor on!

 

We made it over the top. :001_smile:

 

Peace,

Janice

 

Enjoy your little people

Enjoy your journey

[Paintedlady]

My ds, who is a year or two ahead in math, struggled with long division for a while. We just kept at it and over time with practice he finally cemented it. Probably took him a a couple weeks or so to really get it.

 

I also tutor a 6th grade public school boy in math and last year when we started he was always confused about division. Again, lots of practice has helped but he still occasionally forgets a step.

 

You'll get there. :grouphug:

[Closeacademy]

My older dd has a book that we made of math notebooking pages. It has helps for various math problems including a page on long division. Since Rod and Staff keeps throwing long division at her, I just tell her to follow the steps on the page.

 

We've been working with long division now for 3 years and she is finally starting to get good at it. I think they need lots of practice with long division even if it is only 1 or 2 problems a day for a few years.

 

:001_smile:

[Paintedlady]

If you're looking for additional/alternative demonstrations, my kids really enjoyed this:

 

http://letsplaymath.net/2010/04/12/the-cookie-factory-guide-to-long-division/

 

Then we made cookies, of course :)

 

Love this! :D

[ABQmom]

I just have a tip that we learned from MUS. Mr. Demme tells the kids to turn their notebook paper sideways so that the lines on the paper form columns. They then put a number in each column. I can't really explain that well without showing you. Mmmm... maybe I'll have to blog this tip sometime. Anyway, with one number in each column, they can line up their numbers better and have a visual way to keep them lined up as they divide.

 

He has them do multiplying 2 or more digits by 2 or more digits this same way.

[katilac]

Short division!

 

Okay. Why long division taught rather than this?

 

Part of it is simply inertia, I'm sure. My other guess would be that many 3rd graders would have trouble neatly inserting the remainder and then keeping track of the 'new' problem. That could cause a lot of wrong answers.

 

Many kids at this age are still writing fairly big and not so neat - - their short division is not going to look nearly as neat as the ones on the computer, lol! I can see that causing problems.

 

The example I looked at did not have the student crossing out numbers that had already been used; they are just adding in the remainder. I can definitely see some kids having trouble with that. In long division, you are moving to a new line for each part of the problem, so each time, you are only looking at the 'active' part of the problem.

 

 

The latter problem can be solved by having the student cross out the part of the dividend that has been 'used' already. I would also consider having them write out the problems with extra space between the numbers; I know many 3rd graders who would have trouble neatly inserting a remainder between the numbers of their problem.

[Crimson Wife]

Singapore 3A is IMHO *HORRIBLE* at teaching long division. I *STRONGLY* recommend having him work through the single-topic "blue" Math Mammoth worktext Division 2. Maria Miller does a fantastic job walking the student through long division incrementally. It's inexpensive and you can download it instantly.

[mama27]

Because it takes a long time to sink in.

 

 

I am getting bored with re-re-reexplaining it. Every day it is like starting from scratch. This is clearly the toughest thing we have faced in math. To make it worse, my son is a good guesser (he got the quotient for 80/3 but not the remainder in about 20 seconds of "3x30 is 90, and 2x2 is" muttering under his breath). He needs to learn the steps, to be more methodical. Anyone have tricks on this? Anyone with a printable sheet of the steps he can keep next to his desk to follow? Should I try moving right up to 1000s to make it harder for him to guess, forcing him to do the steps?

 

Or is it just over and over and over until the nickel drops. Tell me the truth, I can take it.

 

With one of my dd's I would do 3 problems every day of long division until she got it. With her, telling her each step, before she asked, until she started saying " I know." Or started just doing it before i could tell her.

It stuck eventually.

[katilac]

Singapore 3A is IMHO *HORRIBLE* at teaching long division. I *STRONGLY* recommend having him work through the single-topic "blue" Math Mammoth worktext Division 2. Maria Miller does a fantastic job walking the student through long division incrementally. It's inexpensive and you can download it instantly.

 

I totally forgot until I saw your post, but you're right: the Singapore long division section is horrible. I used something different to teach both my kids; can't remember what, but likely Saxon or just any book we had floating around. After reviewing the Singapore section, I almost forgot how to do long division myself :D.

[Penelope]

Singapore 3A is IMHO *HORRIBLE* at teaching long division. I *STRONGLY* recommend having him work through the single-topic "blue" Math Mammoth worktext Division 2. Maria Miller does a fantastic job walking the student through long division incrementally. It's inexpensive and you can download it instantly.

 

ITA. I thought it was just me thinking that. I have been so happy with Singapore than all of a sudden the algorithm is just thrown at them and I'm wondering where the "Singapore way" of teaching went during this section. I also agree that continuing a few problems per week of working on it, after moving on, is a good idea. I don't think this is a topic where you can just do it for a couple of weeks and then move on, especially in 3rd grade (and why 3rd grade, anyway, I'm wondering. I remember this in 4th grade, and I still did algebra 1 in 8th, so I'm wondering why it was moved down a year).

[kalanamak]

Singapore 3A is IMHO *HORRIBLE* at teaching long division. I *STRONGLY* recommend having him work through the single-topic "blue" Math Mammoth worktext Division 2. Maria Miller does a fantastic job walking the student through long division incrementally. It's inexpensive and you can download it instantly.

 

I never think of SM as teaching my child. I think of it as teaching ME, and then I work with what clicks with this kid. Interestingly, I got MM division 2 a couple months ago, in prep, and I read it through.

 

I decided I was having an attention problem with kiddo. This was the most steps we've faced in math, and, like most humans, he likes things easy, and rushes to an answer. So, yesterday I put away the books, got out my large grid graph paper (which I use when I really want to show the columns), our play coins (dimes and pennies...money makes him pay attention) and a wet-erase pen. I then wrote ON his desk (which was designed for shock value...it worked) 1-5 and set out 10 dimes and 5 pennies. I had him "divide" these equally while I worked the problem on the paper, in nice big numerals. He kept seeing the 2 dimes in each area and the 2 above the 5 on the paper. Then I added another dime and we "broke it down" into pennies and divided it up. He saw that 1 under the 6-5, and saw it become part of 15.

 

I did this until he was getting smooth and bored. I repeated today. After a couple of very smooth runs, I opened up SM and started doing our workbook. After 2 problems he decided to DO THIS in his HEAD, and did the rest of his problems IN HIS HEAD. (He loves doing math in his head...he feels like he is getting out of work.)

 

The two salient points were: I got his attention.

I got him to do it in a clumsy, boring way until he was sick of it and was willing to attend to the process.

 

When we got to the story problems, his focus paid off. He caught onto the logic of problems faster than ever because he was "pumped". I pointed this out to him, and, at the end of it, I hope THAT lesson sticks more than anything. He was so pumped, he got out his hotdots and did multiplication cards so "he could do it better next time". :svengo:A whole hour of math!

 

Thank you ladies....one more 8 year old who didn't get his neck ringed today. :)

[Kennic]

We used manipulatives a lot with my son. Which is what I think the HIG said to do. We used the MUS blocks I had. I showed all the steps with the blocks first. Put hundreds into groups, rename the remainder and so on. We did that for a while. Then I showed how what he did with the blocks related to the written problem (which I also remember was in the HIG, I think). I never made him worry about writing all the stuff under the dividend if he did not need it; that is all sort of notes to be sure you get the right remainder. He was always free to pull out the blocks and do the problem that way when he did the workbook, and he did do that quite a bit at first. Then he started not using them. He had very little problem with division after that, though initially he used the blocks a lot and worked out the problems that way. I think doing the problems concretely really helped him understand it in a basic way that he never forgot. Not just memorizing steps.