Long division woes (MM and BA help)

[DesertBlossom]

Dd9 has been working in MM4B doing long division and after several weeks it is still long and painful. She seems to be having trouble memorizing the steps, and it concerns me that she's not really understanding what's going on, which is why she can't memorize the steps.

 

I pulled out the BA books I happened to have to see if their long division lessons would be helpful. I am really not impressed with how it starts out having them guess the quotient and adding the quotient in parts vertically. (If that makes sense. Pages 60-66 in the 4B guide) I feel like that's going to be more confusing for her as she's already been doing some long division.

 

I am at a loss as to what to do. Help.

[Guest]

Long division is one of those things where I just introduce the concept hey already get (manually splitting fractions and simple numbers like 25/5, which they can do in their head) and then show them the algorithm on simple numbers, then the more complex ones. Sometimes showing the remainder as a fraction and then working back, multiplying back out to reverse the process, helps solidify what is being done.

 

It IS still a lot of paperwork steps, but as long as she gets the concept going both directions I wouldn't be concerned if the memory of each bit of the procedure is slower to solidify. Practicing it a little each day should help, provided she actually gets what is happening in division and multiplication, and how they work together as parts and wholes.

 

Long division is kind of tricky to remember, just like writing out the steps of multiplying big numbers. Lots of paperwork even if you 'get' what's happening and could do it faster in your head.

[wendyroo]

In cases like these I always take the algorithm completely out of the picture and come up with problems that force the child to really think about how the numbers need to be manipulated.

 

A couple days ago DS and I were gazing longingly at a carton of Junior Mints at Sams.  If we bought it, how many would we each get?  There were 24 boxes in the carton and prior experience tells us the boxes average 20 Junior Mints each = 480 Junior Mints.  There are 6 people in our family.

 

"How could we divide 480 by 6?"  And then I waited and waited and waited while he thought about it. 

 

He offered that we would each get less than 100, and I ran with that line of thought.

"Okay, we can't each have 100.  What about 50?  Can we each have 50?"

 

He confirmed that yes, we could each have 50 because 50 * 6 = 300.

"So if we each took 50 out of the box, how many would still be left?"

 

180 he said and I immediately asked how he came up with that to highlight that he was subtracting.

"Now how many should each person take?"

 

He said 10, which is clearly not the most efficient answer, but that doesn't really matter.  The goal is to understand that you can subtract any multiple of the divisor that is less than or equal to the remaining portion of the dividend.  If we had time on our hands we could hand out the Junior Mints one by one like dealing cards.

 

We repeated the steps until we discovered that we could each have 80 Junior Mints.  If there had been any left over I would have "left those in the box" and called them the remainder.  When we got home we wrote out the long division several different ways.  First we did it his way of subtracting 300 right off the bat and starting with a 50 in the quotient and then subtracting 60 and adding 10 more to the quotient and so on.  Then I showed him how the standard algorithm would look slightly different.

 

If you want to explore a visual representation, you could break out the graph paper.  Draw a shape (following graph lines) containing an unknown number of squares and try to divide it into groups of a certain size.  Say you are dividing by 8.  First find the biggest 8 by x rectangle you can and put a box around it.  How many groups of 8 is that.  Now "subtract" that from the original shape and find another 8 by x rectangle...lather, rinse repeat.  At the end combine straggler squares into groups of 8 and see if you have a remainder.  THEN, try to figure out how big your original square was by multiplying your quotient by 8 and adding back in the remainder.

 

There are lots of ways to demonstrate long division that can help cement conceptual understanding.

 

Wendy 

[Guest]

What Wendy said :). Much more concise and I was getting at the same thing.

[Ravin]

The current strategy I am teaching DD is to skip the algorithm altogether. Instead, I have her put the number in expanded form (e.g. 245 = 200 + 40 + 5), divide each of those numbers, then add the dividends together.

[MotherGoose]

I focused too on getting them to think about 200+ 40+ 5 instead of 245 as a whole. Also used place value discs or manipulatives with small numbers (going up more than 1,000 or so can get cumbersome) so they could really see. Repeat repeat untik they have it down before going up. Also if we get stuck on something I stop it for a few weeks then come back. Something usually clicks in their brains by then, or at least we have both had a break and can give it a fresh go.

Edited September 12, 2016 by MotherGoose

[Elizabeth 2]

I had to use manipulatives while writing the answers on paper.  Specifically we used dollars, dimes and pennies divided into groups to demonstrate what we were doing.  Then, we used the format written on the white board in Sharpie so he didn't have to worry about writing the skeleton while he solved the problem, just doing the work. After cleaning the board, he kept working it on the board so I could correct it immediately until he got the rhythm of the problem.  It took about a week working through the steps, but he got it in the end!

[deerforest]

I recommend the videos at Education Unboxed. Also, BA's method of partial quotients does build conceptual understanding.

 

http://www.educationunboxed.com/multiplication-and-division-with-large-numbers/

[LMD]

I pulled out the base 10 blocks to really illustrate that we were just regrouping down.

We did a bunch together like that.

Then I had them practice some with drawings to represent the base 10 blocks.

Then we moved to just drawings of the groups of the divisor, as a reminder of what he's doing!

Then lots of practice of the steps over and over with me there to ask lots of reminder questions.

 

It is exhausting, my commiserations!

[EMPgirl]

My ds had trouble keeping the columns lined up as the problem was going down the page, it stressed him out. I gave him graph paper, it all lined up perfect and he was able to focus on the actual algorithm much better.

[Alessandra]

You might enjoy the app, Long Division Touch. We have the iOS version, but I think there is an Android version too.

[Clemsondana]

My son had a hard time with just memorizing the algorithm without understanding it, but when I explained that, when you have 4869/25, you put 1 above the 8 because you're showing that it goes 100something times, so you subtract the 2500 that you've accounted for and see how many times 25 goes into whatever is left, and then repeat the process.  As the numbers got bigger, it was a pain to always write out the zeros but it really seemed to help his conceptual understanding.  And, I used excel to print gridlined paper with big blocks so that he could write and keep his numbers orderly. 

[Hunter]

I had this problem with my oldest and someone told me to make a bunch of practice sheets dividing by 2. Dividing by such an easy number means you can make really long dividends which gives them loads of practice with the steps. To paraphrase SWB, one hard thing at a time. Then to understand what is happening, have her take her answer and double it. It's super simple and not difficult to explain this way. HTH!

 

Plum Crazy beat me to it. This WORKS!

 

Also making up a board game with division problems. For kids that really struggle, watching someone else solve a problem is beneficial. And having the problems spread out and their occurrence being random is less overwhelming that a worksheet for some kids.

 

Once the student is able to get a few problems right in a row, I cut long division down to one problem a day. Just one. Spread out over a year.

 

Many 9 year-old girls are not ready for long division. Period. I will go to my grave chanting that. I believe that more certainly than I am certain we have sent men to the moon. :lol:

 

Some 11 year-old girls can do in a couple weeks what is impossible at 9 even with hours of work spread out over months. I find age 11 is when long division clicks for the AVERAGE girl and a bit earlier for boys.

 

Arithmetic is not easy for average humans. Because of international competition we think calculus is a high-school senior must, so algebra must be grade 8 and then we squish the arithmetic. That isn't working out so well. We keep doing it anyway.

 

There is a saying among mentally ill homeless people. I may be crazy, but I'm not a fool. Continuing to do something that has proven not to work in the past and expecting a different result is the sign of a fool, they say.

 

Long division for 4th graders. Hmmm. Well, I'm crazy. We all know that. But a fool? That is up for debate. Unless the kid is gifted and/or male, I just don't think it is a good idea. I don't. I think it makes too many kids feel stupid and lose their confidence.

Edited September 13, 2016 by Hunter

[SparklyUnicorn]

Another thing I did was have my kid draw an arrow from the number to be brought down so he remembered to bring down each digit.  That was helpful for staying organized.  I also allowed him to use the multiplication table if needed.  I think sometimes he got hung up on trying to remember the facts and that added to the frustration.

 

 

Edited September 13, 2016 by SparklyUnicorn

[Hunter]

Another thing I did was have my kid draw an arrow from the number to be brought down so he remembered to bring down each digit.  That was helpful for staying organized.  I also allowed him to use the multiplication table if needed.  I think sometimes he got hung up on trying to remember the facts and that added to the frustration.

 

 

Must have been you!!! Of course. Should have known. :) That was when my oldest was in 5th so....6 years ago! Time flies. 

 

My kid just didn't have his multiplication facts down cold. He was still in PS. We hit long division, and I don't know. I think it was good that we didn't have any books or any resources at all to distract us. I looked at my kid, really looked at him, and made stuff up. If I was going to make up problems, might as well make them up for the 2's which were the only ones he knew. :lol:

 

I was a teenaged mom living in poverty and domestic violence. I often say I parented more like a she-wolf than a human. Thank God I had boys. I just went by the seat of my pants and by instinct. I was always focused on what we had and what we could do with what we had. He knew the 2's tables. So, yuh, we went with that.

 

And I made a game, because, I don't know. It just seemed logical at the time. Yes, he was gifted in maths, but he learned the basics of long division in about 2 hours with no tears.

 

On the other hand, I cried many tears over long division. I remember being screamed at by my teacher. I remember folding my arms over my head and trying to make myself as small as possible, I was so afraid. I remember my mom being angry; I'm not sure who she was angry at, but she was angry and angry near me and I was afraid.

 

With my boys, I gave long division a lot of special attention and thought. I just wanted them to feel safe.

 

Modern arithmetic instruction reminds me of child labor. I think it is sad in too many cases. Was/is child labor necessary? Is modern arithmetic instruction necessary? I don't know. But I do know that seeing overwhelmed children working at things beyond the current development of their immature bodies and brains is sad. At least to me.

[Tiramisu]

"Does McDonald's see cheeseburgers?" was very helpful here with two kids who couldn't remember all the steps in the algorithm.

 

Some kids who understand division conceptually still could really benefit from the traditional algorithm, and having those steps spelled out for them. I think there's a common misconception that if the understand the math well, it will come easy. Nope. Not with all kids. Anyone with an executive function weakness could grasp the concept but struggle with remembering and carrying out the steps.

 

There were times when long-division was frustrating and we'd do two a day max. But I like Hunter's method even more. Start with two's, and then move up.

 

For a year or more, I wrote DMSC vertically along the margin of any page with long division, with the corresponding symbols next to each letter. Then the dc would write it in their own to remind themselves when they needed it.

 

Like Sparkly mentioned, we also used the arrows going down. My two kids who had the most problem with long-division also has developmental vision problems so those arrows were a concrete help, even before I realized there was an issue.

Edited September 14, 2016 by Tiramisu

[Mama Geek]

I was thinking watching someone else solve the problems while talking through it.  We are working hard on math facts and then covering concepts for exposure right now.  We started dividing pizzas and m&m's a long time ago and had 6 she has a good grasp of fractions and division.  We are now showing her long division and long multiplication and talking through it every time we do it.  That is also how we did long addition and subtraction.  So far that has worked great.

[Jess4879]

I used this method with both of my kids and it's amazing.  Everything just clicked for them.  It really helped them to see the why's of each step. 

https://denisegaskins.com/2010/04/12/the-cookie-factory-guide-to-long-division/

[daijobu]

Singapore math has a nice way to learn it.  I remember cutting out little pieces of paper with "100" or "10" or "1" written on them, putting them all on a white board, and manipulating those while doing long division with a marker alongside it.  I don't remember the specifics, but it seemed to click when we were dealing with concrete objects.  

[cintinative]

I used this method with both of my kids and it's amazing.  Everything just clicked for them.  It really helped them to see the why's of each step. 

https://denisegaskins.com/2010/04/12/the-cookie-factory-guide-to-long-division/

 

We use MIF and this is the method they use. After they get this "longer" ??  long division down, they graduate to the one with the carrying.  Also we label each number above it Ten thousands place (TT), Thousands (Th), Hundreds (H), Tens (T) and Ones (O).  So, you ask, " 3 times how many ten thousands gets us close to 77 thousand?"  " Two, good.  Three times two ten thousands gives you 60,000"  Then, it is "3 times how many thousands gets you close to 17,000?"  "Five. Okay, three times 5 thousands gives you 15,000."  etc. etc.

 

Here is an example from the site in Jess' post:

 

Edited September 20, 2016 by cintinative