Kids with LD and long division

leaf

Mon, Nov 12 2018, 3:00 pm

seeker wrote:
So I had to google digi blocks, and they look like a lovely tool for building conceptual understanding, but I'm not sure how that helps translate into 42 into 13,296...

Let me try to explain:
you wouldn't actually be able to divide 13,926 using digi blocks because the are no "10,000" blocks and I would divide by a 1-digit # in order to use the blocks to show the logic behind long division. (at a seminar for digi blocks, the speaker asked a 3rd grade daughter of one of the participants to show us how she does long division and of course she got confused, then the speaker taught her using the blocks, and finally had her solve a problem on her own and she got it straight b/c she understood the logic)...
anyway here goes. let's say you want to divide 467 by 3. You set aside 467 digi blocks I.e. 4 "100" blocks, 6 "10" blocks, and 7 "1" blocks. Then you start out by dividing the 4 "100" blocks into 3 piles by placing 1 "100" block in each pile (which is what we do when we write the #1 above the 4 in long division...). You are then left with 1 "100" block (which is what you do in long division when you subtract 3 from 4). You then remove the 10 "10" blocks from the remaining "100" block and add them to the 6 "10" blocks (the same 6 that you "bring down" in long division) for a total of 16 "10 blocks". you divide the 16 "10" blocks so that each pile receives 5 "10" blocks. One "10" block remains. you remove the 10 "1" blocks and add to the original 7 "1" blocks for a total of 17 "1" blocks. Divide by 3. Each pile receives 5 "1" blocks. So at the end each pile has 155 blocks with a remainder of 2 leftover "1" blocks....
If you are able to show how we write this out in lond division while using the blocks to solve the problem, the steps to long division will make a lot more sense.....

amother

Babyblue

Mon, Nov 12 2018, 3:15 pm

seeker wrote:

The "sense" of how many times a number will go into another is called estimation. And 40% off does not require long division, either (that lovely zero! And if it's 45% then it's half of a ten!) This is why I would rather spend instructional time on developing that "feel" than getting through 43 into 56,897 by hand.

And I'm not sure where you do business but I've been in some pretty heavy meetings with accountants and attorneys, respectively, and of course they all had their calculators out the whole time. They mentally estimate and use the calculator for detailed backup. Power performers don't waste valuable meeting time doing calculations that a machine can do in a second, and they also don't take the chance of getting the data wrong if they slip up somewhere.

Every accountant and lawyer should be able to divide 43 into 56,897 without a calculator and without long division. I would think less of a professional who needed to take out a calculator in a meeting for your example.

Power performers at meetings don't need calculators to know if a deal is a good deal. The first one who can't figure it out is the loser.

If an LD kid can't learn long division, so be it. But normal kids to appear as normal adults need basic skills.

seeker

Mon, Nov 12 2018, 4:14 pm

Thank you for the digi blocks example, that was really interesting! I like it!

Nicole, I didn't know you became a principal, congratulations! In the more distant past you posted a lot as a teacher Smile

Babyblue amother, maybe we need to agree to disagree on this one.
If you don't need calculators to know what's a good deal, it's because you're estimating. We all agree that estimation is an important skill. You don't need a calculator because you don't need long division.
And pray tell how you would do 43 into 56,897 without long division. I know people who can do it in their head, but that is because they are doing long division in their head - they just have a stronger visual working memory than most people so they don't need to write it down. I just did it in my head, with quite a bit of difficulty, and came out with the right answer, but still had to do long division to get there. I guess according to your last statement that makes me an abnormal adult?

seeker

Thu, Nov 15 2018, 12:14 am

Not necessarily. You might understand the concepts but still can't keep track of what you're doing. Or maybe you could but it takes an insane amount of your energy.

Definitely an inability to do long division probably does often come with at least a little place value confusion, but first of all not always, and secondly there's more to it because of the processes involved. I had kids who could do it shorthand with smaller divisors and they would do the subtraction mentally because these are kids who really do have an OK math sense, but when you have bigger numbers and you have to test the answers with multiplying and then subtract, they just lose track of all those different things going on and where they were up to. And with help and practice and conceptual strengthening and all that, they can force themselves through some but when there are 6 digits in the dividend and you have to do it all over several times without losing any numbers, something is going to go wrong. Even with graph paper and visual aids and "DMSB, DMSB, DMSB" it's just... too much.

DrMom

Thu, Nov 15 2018, 1:29 am

seeker wrote:

I went to school before "Common Core" and I must say this entire discussion sounds like word soup.

What are "12 facts?" Is that just the multiplication tables through 12x12?
What is DMSB?

Paging Tom Lehrer...

boots

Thu, Nov 15 2018, 10:57 am

seeker wrote:

That's really interesting, so it is more of a working memory problem? Or a vision tracking problem going up and down the long vertical number list?

amother

Mistyrose

Thu, Nov 15 2018, 11:24 am

Thank you for this thread. I never considered the possibility of letting my math challenged kid skip the hard work of calculating and focus on the logic of math instead. We’ve been stuck on multiplying and dividing for years.
Last night I gave him a calculator to do word problems and for the first time he was able to focus on understanding what the math question in the word problem was and wasted zero time on calculating endless numbers.

Thank you. We can finally move on.