Menu
Jump to content

What's with the ads?

Sarah0000

Long division

Recommended Posts

So I've read on many old threads on the K-8 board that long division is typically a hang up topic for many kids, requiring working with manipulatives again and focusing on dividing by place value. Has this been true for your accelerated kiddos as well? Did you notice that long division was perhaps the first time your kid said they didn't conceptually understand what was going on? What happened?

Share this post


Link to post
Share on other sites

Not here, either, but I don't know if it is how it was presented or how he just intuitively got it.  I made a point to say "first we're going to divide the biggest units, the hundreds.  How many hundreds would go in each group?  How many are left over?" 

It didn't take more than one or two lessons before he was on his own.

Share this post


Link to post
Share on other sites

Yes. DS has trouble accepting standard algorithms until/unless you prove it must be done this/that way. The concept of division (dividing into equal groups) was easy but he refused to accept that he needed to start with the largest units first. Why can’t I start with the smallest pieces first?! Why do I have to start with the biggest?! It was more of a stubbornness/contrarian/skeptic issue than anything else. We have to physically model why his approach won’t work or is less efficient before he abandons the idea. That isn’t an issue limited to math tho. It’s EVERYTHING. DS won’t take anyone’s word for anything. He comes by this honestly.

Share this post


Link to post
Share on other sites

No trouble with the math, but she hit it young enough that writing and organizing was more of an issue. We did a lot on a graph paper wipe-off chart with one inch squares for awhile, until she was able to shrink it, and she dictated a lot, where she would do a few problems independently and then I’d scribe for her. 

  • Like 2

Share this post


Link to post
Share on other sites

DD does it the way that Beast Academy teaches it, and has not had a bit of trouble with it. She refuses to use the standard algorithm, as she finds it non-intuitive.

  • Like 2

Share this post


Link to post
Share on other sites

Ok Thanks. I was just starting to learn how to introduce it when I noticed so many seemed to have problems and started wondering if I'd need to do something special for it. 

I think writing will be a problem for him so I'll probably stick with just c rods for awhile then do the box chart method. How is it done in BA and in what level?

Share this post


Link to post
Share on other sites

One for my kids didn’t blink. My other child was very skeptical of long division algorithm (he could do it but didn’t understand why it worked) until we opened BA. Then he smiled and said that’s how he always divides in his head. BA uses a method I think (but I am not sure) called partial quotients. It’s very clear and easy.

  • Like 3

Share this post


Link to post
Share on other sites

My DS picked it up easily, and in fact it was the first thing he asked to learn when we started homeschooling in second grade. DD had trouble with the way MUS taught division, but learned the traditional algorithm without any real difficulty. 

Share this post


Link to post
Share on other sites

DS#1 and DS#3, no, no issues, and DS#1 has done some pretty impressive long divisions entirely mentally because of his resistance to writing anything.  He started using the standard algorithm only when the divisions got long enough, 5 or 6+ digit quotients.  DS#3 intuitively did long division in an interesting way kind of like a mix between the way BA teaches it and standard short division.  With bigger divisions his work is starting to look a little more like a mix between the BA way and the traditional algorithm.  It's a new and still developing skill, though.

DS#2 learned long division in PS and was fine until he could no longer do the problems mentally.  When he needed to start writing his work, it got very jumbled and almost always came out wrong.  I went ahead and taught him the BA way at home, and from there he was able to transition to the traditional algorithm as expected by his teacher.  He continues to have some trouble keeping things organized (even when using grid paper), and he occasionally still confuses the steps.  He's my extremely visual-spatial, non-linear thinking kid with stealth dyslexia, moderate combined-type ADHD, and probably dysgraphia.  This is the kid who used to do large multi-digit subtraction problems by alternating between the largest and smallest place value or by starting in at the middle place value and working out.  A linear process like the long division algorithm is fundamentally opposed to the way his mind works.

Share this post


Link to post
Share on other sites

My DS sounds a little like your DS2. Sometimes he'll draw little robot helpers for each place value digit and all these arrows and lines for where they walk and when I ask him to write his final answer he basically has to do half the problem again to make sense of his work. 

Thinking about that...yep, I'm going to hold off on the traditional algorithm for a good long while.

Share this post


Link to post
Share on other sites

My daughter always resisted any algorithms. She didn't like or need all those steps, and she just kind of did it intuitively.  She had her own way of pulling numbers apart and putting them back together again.

At the time, I wasn't sure if I was doing her a longer-term disservice by allowing her to avoid using algorithms, but here we are many years later and her maths in still strong without any obvious gaps.

Share this post


Link to post
Share on other sites

I taught my kids using the Singapore Math method, with little squares of paper with labels "1" "10" "100" and they got it.  But I recently tutored some kids with the BA partial quotients method, and I like that better.  

Share this post


Link to post
Share on other sites

No, but both were proficient in mental math and the concept before moving to the algorithm. We used SM technique.  Colored markers on the whiteboard took care of the rest.  The extension is division in other bases.  The big idea here is that the long division algorithm is a notation method for what we are already doing with our brains -- using the part to whole/whole to part concept, but grouping in a way that is easy to see on paper with symbols.  They should have this concept already from clock and from adding/subtracting money. 

The students I have helped thru this typically cant mentally divide anything- they see division as part of a fact family to remember and don't have an understanding of division (beyond splitting a pizza in equal slice),  place value or expanded notation.  Then add the expectation that they remember a multi step procedure, and they give up.  DIviding an hour up, or a dollar is beyond them.

  • Like 1

Share this post


Link to post
Share on other sites

Strangely, DD9 who is super-mathy did not "get" long division when we first went over it a few years ago. She ended up learning the Beast Academy method, which is bulky and requires entire sheets of paper to solve one problem.  My DS7, who is not the "mathy" one, got long division with minimal difficulty. He learned it earlier this year. I reintroduced it to my DD9  this year, since her younger brother was learning it, and she learned it in 5 minutes. Go figure. 

Share this post


Link to post
Share on other sites

I think they got it pretty well conceptually, but becoming fluent in the algorithm was not a good time. 

  • Like 1

Share this post


Link to post
Share on other sites

Not accelerated learners here but I think the common issue with it on the board is Singapore math... I think they introduce it too early before multiplication facts are mastered and it just makes things harder than they need to be.

 

honestly I think the standard algorithm for long division is confusing and a waste of time - short division is so much easier and quicker anyway.

Share this post


Link to post
Share on other sites

My kids didn't have trouble with understanding the concept, but they did have trouble with the algorithm and holding it together when doing big, hairy problems.  It helped to teach them short division first and then have them apply the principles of short division to a problem with a multidigit divisor.  It is possible but you end up having to do a lot of scratch work on the side, which brings home the point that the algorithm is helpful.  Once I got them on board with the idea that the algorithm was necessary, it was just a matter of practice.  I had them do one big, hairy problem each day (on top of their other math work) until they were mostly error free.  A large whiteboard mounted on the wall was helpful for this.

Share this post


Link to post
Share on other sites

+1 on using graph paper though. It really helps to organize the problem and not lose track of where they are in the problem when doing the standard algorithm.

Share this post


Link to post
Share on other sites

I taught ds11 the traditional algorithm when he was about 8 and he didn't like it at all.  He still prefers the partial quotients method.  It is not too bulky if your multiplication is solid.

  • Like 1

Share this post


Link to post
Share on other sites

My son, no. My dd, she's had no problem with the standard algorithm which I taught her out of desperation when she didn't really get it the BA way.  I wonder if down the road we will have issues but we haven't yet. 

Share this post


Link to post
Share on other sites

I made the mistake of pre-reading about struggles kids have with long division and had all sorts of things ready, and DD didn't have any issues at all. We still joke about that around here.

Share this post


Link to post
Share on other sites
On 4/15/2018 at 3:09 PM, katilac said:

I think they got it pretty well conceptually, but becoming fluent in the algorithm was not a good time. 

My 2e kids were like this. They both did partial quotient division as they were learning, which helped.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

×
×
  • Create New...