Long Division – Eli’s Way

Someone shared an on-line resource about long division on my Homeschooling Creatively list about right-brained learners. When I went to the site, their “method” immediately reminded me of how Eli figured out how to do long division all by himself, using his own way to understand. (Actually, I think Eli’s way was easier compared to the “steps” the on-line resource is instructing one must do before actually solving the problem . . . I wonder if they stuck in some left-brained thinking anyway: those sequential steps and showing one’s work . . . for the conditioned parents out there checking out the resource. . . LOL!) Here’s a sample page of him working through problems:

For those of you who need a sample pulled from the chaos:







Answer: 12,681, R2

Alright, I can’t get the formatting on the blog to have that problem come out nice and neat, but hopefully, you get the idea.

What’s really sad is at the time, I had no clue as to what he was doing or how he was doing it. It’s fairly clear to me now, but what I’m trying to say is that the “way” school taught me was so ingrained as the “only way” to do it, that I couldn’t open my eyes enough to see another way, or at least for it to make sense to me. At first, I tried to teach him the “easier way”, or at least I thought it was easier from my perspective, but luckily, after a brief but ineffective attempt on my part at teaching him, I let him be and said, “If it makes sense to you, go for it!”

The book Eli was working out of at the time showed the “school way” when he was first introduced to long division, but it didn’t make sense to him, so he invented his own way based on the fact that he UNDERSTOOD the concept of long division. That’s kinda huge, because as a left-brained learner and one who “did well in school”, I easily learned long division simply because I was good at short-term memory of plugging in formulas as blindly taught and learned. Thus, that’s probably the reason I didn’t “get” how Eli was doing it his way when I noticed. About a year or two later, Eli adopted the “short cut” way on his own timeframe as I had learned in school because it finally made sense to him and it was faster, according to him. Plus, I think being able to work at it in this visual manner as long as he needed to helped him eventually come to a place that leaving out some of the whole could finally make sense to him.

3 responses to “Long Division – Eli’s Way

  1. I’m confused, because I don’t see the original problem (what was being divided by what to get 12,681 R2?) It’s probably there and I’m missing it. Anyway, I am intrigued by his method. 🙂

    I hope you’re working on your book. 😉 I can see a lot of this material (including photos) being used in it!

  2. Hey Steph,

    I know . . . the formatting didn’t work on the blog, and everytime I hit a return, it always puts in a double space, soooo

    the original problem is 5/63,407 or 63,407 divided by 5. He had to meticulously times a guessed whole number by the 5 and keep subtracting until he got the end product. He would stack the whole numbers on top of each other and then add them all together at the end. This particular sample turned out precise with a 1,000s, 100s, 10s, and 1s, but some would have double 100s numbers or double 10s numbers, depending if his guess was most accurate, if that makes sense. I saw it as a lot of extra writing, but it made sense to him to see the whole, so I figured let him be. Eventually, he shortened.

    If you click on the photo, it enlarges and you can see other samples if you are able to pick out each problem . . . this was a “scratch paper”.


  3. Wow, is all I can say… I’m not sure I understand how he got his answer, but if he understands it that’s all that’s important. 🙂 M’s papers can look like that sometimes.. only with much bigger writing. The trouble is he can’t keep himself organized long enough, and doesn’t have the memory, to follow what he’s doing to completion.