How do YOU teach long division?

[DarcyM]

I'm not sure why this is so woeful. Well, perhaps it's because my bright son is 7.5, and despite the fact I have paced him, he has done:

Singapore 1a, 1b, CWP 1, 2a, 2b, IP 2b

Horizons Grade 1 book 2, Grade 2 books 1 and 2

several pages of Zaccaro in about 1.5 years.

 

Not to mention dozens of skip counting pages, fill-in-the-blanks 12x12 grids. has his multi and factor facts down cold...

 

I have really tried to slow him down as he has *flown* through all this material. He has reached long division in 3a.

 

About 5 weeks ago he hit a wall. It pulled the rug out from under him. The child who never saw a math problem he couldn't solve was saying things like "This is too hard. I'm not smart" (where do they get stuff like that? it breaks my heart!)

 

I stopped. I spent a month telling him how smart, clever and wonderful he is. Reassuring him that new things can be hard, reviewing factors, playing math games, having fun while cementing math facts. He "rules" at Timez Attack.

 

I'm geared up to try (something) again. What made long division successful in your house? Is 5 weeks a fair break?

 

He will be 8 at the end of May. I will not damage this child's ego, he is a sensitive type A perfectionist. He takes failure very seriously. I don't know whether to proceed or just call it all off until August (The start of 3rd grade). If I don't proceed what do I do with him until then?

 

Thank you for any hand holding you may provide.

 

-Darcy

[Mom2legomaniacs]

Very slowly! I use MCP and love the way it adds to the steps to build up to it nicely.

 

Umm, let's see. Does he understand what division is? Does he understand that multiplication and division work together in a sense?

 

Start with that. Showing the facts with multiplication and division and how they are related. (sorry -- if he knows this already -- I am not familiar with the texts you use)

 

I broke it down into phases. Geesh I am having a hard time explaining myself here.

 

We used graph paper to keep it lined up.

 

SO for 425/5:

 

start with a smaller problem on the side 42/5 and show the remainder

 

reminded of the fact that the 42 represents 420 and there is more to do:

 

then you have 2 as a remainder : which means it is actually 20 (because of above)

 

Another problem on the side: now have 25/5

 

 

Ok, I am going to post this, but it is horribly convoluted. I hope you can get the gist of what I am saying. Feel free to email me and I'll try to do better. We had this issue too and this is part of what got us through it.

[PeterPan]

Well if I could suggest, I think written division is a sort of abstract way of representing something they think of very differently. Try presenting it as repeated subtraction and totally eliminate the discussion of division. Bring it into real life or more interesting situations. (It takes 150 squares to make the quilted pillows I like. I've cut 1370 squares. How many pillows can I make?) Let him think through it, churn on it, and solve it his own way. Division is the shortcut for repeated subtraction, just as multiplication is the shortcut for repeated addition. The way we write it doesn't totally reflect what we're thinking, and I know it took a while to click in my dd's mind, seems to take a while with other kids too. Just stick at it, think of it a lot of different ways, let him churn on the CONCEPT (repeated subtraction, how many of the quantity I can take off) without getting stuck on the notation. Then with my dd I showed it on side two of the abacus using the RS method. Things really started to click at that point, because it gave her a reason why the numbers were written the way they were and showed how they really did match what she was seeing in her mind.

 

Just keep at it!

[Lori in MS]

I assume he can do the simple division 40 divided by 8 etc?

 

Even if he can do that I would start by writing it out in the long division form and have him practice the process with the easy problems. Actually have him multiply 8 X 5 and subtract the 40 so he gets zero. Then I would have him divide larger problems that divide evenly 408 divided by 8 for example having him do all of the steps even though the subraction answers are zero. I would keep doing this until the process becomes automatic. Then do problems like 250 divided by 10 even if he can do the answer in his head, to practice the process. Gradually increase the difficulty but not until he masters the previous level.

[FlockOfSillies]

It helped my dd to see that we were dividing hundreds first, then taking what was left of the hundreds and putting it into the tens column, and so on. She needed to see two leftover hundreds becoming twenty tens, kwim?

[Julie in Austin]

Someone suggested short division to me:

 

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

 

(Really, it is long division but you don't write out all the steps, which sounds like it would be MUCH harder, but for reasons I don't understand was MUCH easier for ds. Go figure.)

[ArwenA]

I sat DD down at our "math lab" and we did every long division problem she had using manipulative's until she could do them no trouble. Her favourite thing to use was chocolate chips. She would put them in groups and then move them around to do her division. The bonus was that she could eat them when she was done. We didn't do that everyday.;)

[Pretty in Pink]

once my ds had a firm grasp on multiplication and simple division facts i introduced long division.

 

i used a blank index card. on the top half i worked a long division problem. on the bottom half i wrote these four steps:

 

divide.

 

multiply.

 

subtract.

 

bring down.

 

my ds kept this in his notebook and put it out daily on the table next to his book until he got the hang of it. worked like a charm. now he has the steps memorized so if he's got a reallllly long division problem and gets confused, i'll hear him talking to himself "now where was i? divide...multiply...subtract..."

[TrixieB]

once my ds had a firm grasp on multiplication and simple division facts i introduced long division.

 

i used a blank index card. on the top half i worked a long division problem. on the bottom half i wrote these four steps:

 

divide.

 

multiply.

 

subtract.

 

bring down.

 

my ds kept this in his notebook and put it out daily on the table next to his book until he got the hang of it. worked like a charm. now he has the steps memorized so if he's got a reallllly long division problem and gets confused, i'll hear him talking to himself "now where was i? divide...multiply...subtract..."

I did something similar for my dd. Saxon 5/4 has a handy flow-chart diagram; I borrowed the book and copied the diagram onto an index card so she had a handy reference.

[ELaurie]

Click on "Sample lesson" - I think long division is one of the options you can view. If so, he goes through his method step by step.

 

HTH!

[TCoppock]

After pulling my hair out trying to teach DS long division I came up with a silly way to help him remember. I told him we look at the first number like it is the first day of mom cooking dinner, we divide it, and subtract what we have from the total. On day two we don't have enough to divide that same meal so we have to add something else so we bring the next number down. We then divide the combined food and subtract from that to know what we have left. We do this until we get to the last day and have nothing more to add. The remainder gets placed on the side or back in the fridge. This seemed to click in his mind so he remembered the steps.

[Suzanne in ABQ]

I used Base-10 blocks, too. We did it that way for a very long time before introducing the algorithm. When it got boring, I made it into a game. Using construction paper, I cut out about 5 "boats" (just flat paper, shaped like a boat -- no sides or anything. I also made a "dock" out of brown paper, and a bunch of little men (like stick figures, but with their long legs folded opposite each other so they would stand up). One of the little men had a hat, he was the loading boss. The others had big muscles.

 

Anyway, I laid out two boats on some blue paper (water) next to the brown paper dock. I placed the "cargo" boxes (Base-10 blocks) on the dock (hundreds, tens, and ones). Then, I told ds that "These 246 boxes needed to be loaded evenly on two ships. You are this little loading boss. You must decide how many boxes go on each ship, and tell these other little men to load them."

 

Then, we'd go through the steps, first loading the hundreds, then the tens, then the ones.

 

When he got the hang of that, I'd add another boat, or I'd make it so that we had to break up a hundred or a ten into smaller units. He liked pretending the little burly men were carrying those hundred-flat boxes all by themselves.

 

Eventually (after a few days of this), I started writing down the steps in the algorithm as we did them.

 

After what seemed like forever, it clicked. We no longer needed the manipulatives, and he could do the algorithm by itself. He loves long division now (go figure). He actually gets excited when he's doing a word problem and realizes he needs to do long division! "Oh! Long division! Okay!"

 

This might not exactly work for your son, but it just illustrates how creative we can be if we think outside the box. :o) FWIW, my dd figured out long division in about a week. It took this ds about two months. But, he got it! He's flying through 4A now.

[nmoira]

My oldest didn't hit a wall with long division conceptually, but rather with showing her work: She could do it in her head and got mixed up going backward to show the steps. I considered doing short division instead, but stuck with Singapore and it worked itself out. We did every problem on a whiteboard; I wrote, she talked. I'd write down every step, even if she just gave me the remainders at each step. After a while I started to look confused and say, "Hmmmm, I can't quite follow... I think you're right but what do I write here?... you're ahead of me... I can't write that fast." Eventually she was telling her slow mama each step and was able to show all the work herself, every time.

[Lori D.]

My math struggler's long division journey was a series of repeating this cycle: a.) introduce long division in a new way; b.) gently persist until it was clear he wasn't getting it; c.) put it away for a few months; d.) go back to step a.)

 

We tried at the beginning of 4th grade (over 9-1/2yo) with Saxon.

We tried halfway through 4th grade (age 10) with Cuisenaire Rod books about Division

We tried again at the end of 4th grade (age 10-1/2) with something else

We tried at the beginning of 5th grade (over 10-1/2yo) with Math-U-See (old Intermediate).

 

Finally -- success! Why? I don't know. Probably a combination of finally finding the math that clicks for this math struggler -- but more likely, his brain finally matured into being able to grasp this tough math concept. Let's face it, long division requires a lot of steps, and requires a firm grasp on both multiplication AND subtraction, AND it requires being able to keep track of the steps in the right order, AND in keeping this long column of numbers lined up. WHEW! That's a lot for a young, developing brain to keep track of!

 

Just want to encourage you -- he *will* get it, when his brain is ready to click with it. And your son is quite young yet. (Note how old my math struggler was before he "got" long division!!) Perhaps put your spine math away for a few weeks and have fun with something else -- manipulatives and an accompaning booklet, perhaps, like geoboards and a geoboard booklet on geometry, or pattern blocks and a booklet on simple fractions with pattern blocks...

 

Encouragement and empathy! BEST of luck! Warmest regards, Lori D.

[Lori D.]

I didn't read your original post very carefully, and see now that you *have* taken a break. The idea that comes to mind at the moment is Miquon. It is discovery-based, gentle, and comes at the math from a different perspective. Many of the concepts covered in Miquon easily go up through 4th grade math, so you may find it a useful series as a supplement or as something to go to if some other math topic gets tough. Sounds like your son would definitely skip the first workbooks, and work from the Green, Yellow and Purple level workbooks.

 

Miquon is extremely easy to use as a supplement or a break from your spine math, and I *love* the way it really helps kids find math connections and think mathematically. : ) My math-minded son loved it; he also loved Singapore. (Even my math struggler son did the best with Miquon of all the math programs we tried from 1st-5th grade.)

 

Take a look at this webpage for the scope and sequence of which math topics are covered in which workbooks (click on the link that says "Scope and Sequence": http://www.keypress.com/x6252.xml

 

And you can see some sample pages of the workbooks at http://www.christianbook.com

 

 

BEST of luck Darcy! Warmly, Lori D.

[Kathie in VA]

Darcy,

 

I totally agree with OhElizabeth. Teaching division as reverse multiplication just didn't make any sense to my kids. However introducing problems that required repeated subtraction quickly lead to the questions of "Is there a faster way?" And wow when you look at the repeated subtraction and notice how many TIMES the same number is subtracted and notice that multiplication will get you to that final answer faster you are on your way to wanting long division. The steps also will then make sense.

 

Good luck!

[fishnoises]

I have only used Saxon and even though they have trouble being careful, they understand the concept. (Using food and dividing it up really helps! Kids love to make sure everything is 'fair'.)

[Laura in STL]

We used play money as a manipulative for long division. It works similarly to the base ten blocks in that you can see the left over hundreds exchanged for tens and tens for ones. We had to work on this skill more than any other up to this point. My ds was also 7.5 when we hit long division(he just turned 8 this week.) I think its a complicated process for younger kids and takes a lot of practice. Especially for those perfectionist types. I have a sensitive type-A guy, too. Good luck!

[AngieW in Texas]

I don't. I teach short division instead. It's a lot easier to learn.

 

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

[DarcyM]

I love all these ideas! Thank you all so much! I can't picture how to do it with base ten blocks, but I totally get the kitchen and boat analogies. He loves Narnia and Star Wars, so I'm thinking we might form armies or planets, and maybe pull in another love of his - Legos.

 

I also think explaining it as repeat subtraction is brilliant. I never thought of it that way (I am NOT math-minded, naturally, but like I can follow a recipe, I can follow an logarithm). But I can't wait to show him that. Brilliant! Thank you.

 

Lastly, when it's time to finally put pencil to paper - I love the idea of short division. Why don't we all do it that way? After reading that, I know I'll never do long division again. Is there a reason why kids have to write it all out the long way? The answer is the same regardless.

 

Thank you all. I feel... well... a glimmer of hope. Like we can do this and come out still feeling smart and whole. ;)

[claire up north]

Here are some suggestions:

 

1. Use graph paper. I found some with pretty big boxes, but before that I made do with the regular graph paper. This worked really, really, really well and was the single biggest improvement in our attempts to beat the long division monster.

 

2. Require child to use arrows to bring down the next number. This keeps them on track visually with what they have already done. Eliminating mistakes due to sloppy work is a huge help.

 

3. Put the book away! For my child, just seeing those pre-printed long division problems was enough to drive him nuts. We had much better success with a technique I learned when teaching my kids to read. We used a plain piece of paper--or even better, a white board--and did one problem at a time. Keep it to just two or 3 problems a day--there's no need to overwhelm the child with 10 problems a day.

 

4. Also, another technique I used was to quickly progress. Doing a million problems of one digit into 3 digits is BORING:bored:! So we would do one or two easy ones, and then I would act like we were done. But then I would say, "You wanna see something cool?" And then I would show him a single digit into a 14 digit number. (I would then usually have to solve a single digit into a 30 digit number that he wrote for me!)

 

On another day, I might show him a 2 digit number into a 6 digit number (easy numbers to minimize frustration). Often I peeked in his math book to get some pre-printed problems so that I knew they would come out even and not introduce repeating decimals or something!

 

On another day, I might show him how to do a few shortcuts when dividing by 10 or 100.

 

5. While we were focusing on long division, I did not require any other math. No need to torture the child, and for my kiddo, more math would certainly have qualified as torture!

 

6.We have now progressed into "really hard" long division problems. I scratch most of them out of his book and do not require them. About once a week I make him do one, but I don't go nuts. He knows how to do it, but he still doesn't like it. I can hardly blame him! If I am working on a project that requires more than one or two long-division calculations, I go for the calculator, thank you very much! :001_smile:

[Nestof3]

Wow -- great ideas ladies. I just printed this out to use when we get to this math!

[Nancy in MI]

Long division seems to be one of those places. Fractions is another. That's where we are right now!;)

 

Division is really only repeated subtraction. Someone on this board a while back suggested doing a long division problem as repeated subtraction. I did that with my math-challenged ds and it clicked for him.

 

I did this first with simpler problems and the MUS blocks. Then I showed him how it's written on paper. Then we worked up to harder problems.

 

For example, 256 divided by 4. Subtract 4 from 25 over and over. How many times were we able to do that? 6. How many did we have left over? 1. Now, we have 16. Subtract 4 over and over. How many times can we do it? 4. How many are left over? None. We were able to subtract 4 64 times from 256. So 256 divided by 4 is 64 with no remainder.

 

 

This really clicked for him. I wish I knew who on this board should get the credit for that idea!

 

:001_smile:

Nancy

 

PS. One reason I think this method clicked for him was it showed the reason "why" for the steps. I could have just shown him the steps and had him memorize them, but I wanted him to understand why he was doing those steps. It took longer, but in the long run it was better because once he got it he *got it*. I think you are very wise to stop and not move on until he gets this. That's one of the many blessings of homeschooing, isn't it? Good job, Mom!

[Guest Jack]

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

 

 

Step by step mode for better understanding.

 

All other operations included.

 

User manual directly on the website

[dragons in the flower bed]

I think it can end up being a wall because it's the first math that requires running through a multi-step process. Borrowing and carrying is a process, but an intuitive one if you understand place value. With long division, it's hard to see why you do what you do next. I had my eight-year-old do a long division problem with manipulatives (place value blocks, tens and ones) so we could get a sense of why it works. That was fun, and helped a little, but the, "Wait, why does that work?" question kept resurfacing because it's just hard to see it as you're doing it. So in the end, I asked the child to think of it like a neat math trick. Pretend it's never going to make sense, and memorize the process. I wrote the steps in the process on the chalkboard and gave the child two problems to do everyday. I sat nearby and watched while the kiddo worked through those two problems. As soon as a mistake began, I caught it and said, "Woops, you need to look at step __ again." I also emphasized that this is tricky, that most kids have a hard time with this, and that it's no big deal for us to practice it, "slow and steady," for as long as we need to do so. We treated it like memory work.

 

If you need to keep him feeling successful and learning other things in math while you're practicing long division, you could do some LivingMath.net books and activities the bulk of your math class time and do only two division problems a day.

[Dana]

Lastly, when it's time to finally put pencil to paper - I love the idea of short division. Why don't we all do it that way? After reading that, I know I'll never do long division again. Is there a reason why kids have to write it all out the long way? The answer is the same regardless.

 

 

The algorithm for long division can be generalized for polynomials. That won't work well with "short division".

 

In algebra, you'll see things like (x^2 - 5x +2) / (3x +4).

Understanding long division :auto: with numbers will make this much easier to do.

And this becomes essential if your kids go into calculus later.

[Melinda TX]

This may be considered "dumbing down" - but after we explain....

divide

multiply

subtract

bring down

 

We learn:

Does

McDonalds

Serve

Burgers

[Melinda TX]

I have to add, my McDonalds saying looks really stupid after Darcy made a big mathematical statement.

Can you tell I prefer Language Arts?

[lmrich]

Here is a trick I have used:

This assumes they can do simple division.

First I model it like crazy - everyday for a week before they even get a chance and then we do several together saying outloud each and every step, by the way dividing by 5 makes it so easy to start with.

 

I start by having the kids just practice with one divisor say 4. Then they write all the multiplication facts for 4 (1x4=4, 2x4=8 etc..). Next they have to divide, but they can look at the facts that they have already written down to help them with their estimate. :001_smile: good luck and have patience