How to teach long division these days

[Omma]

I am using BJU Math and see that they teach long division a different way than I learned it. Let's see if I can explain it. When using 3-digit numbers, such as: 369 divided by 3, they have you multiply 3 x 1 = 300 since the 1 is in the hundred's place. This gets confusing when you have a 0 in the 10's place, such as: 738 divided by 7 = 105 r3 because my son wants to say the answer is 150 r3. I think he is extra confused because my dh taught him this last summer 'the old way' where you'd say 7 x 1 = 7 and carry down the next number, instead of saying 7 x 1 = 700.

 

Can anyone follow this? Does 'your' math curriculum do it this new way, too? Is this an example of 'conceptual' math?

 

Thanks for your help!

 

Brenda

[TracyR]

Yes, its conceptual math. I tried to understand it that way ,and if I can't, I don't see my daughters learning it that way either at the moment.

I like the way Touch Math teaches division. It makes sense to kids and get them learning how to divide , once you get them doing that then doing stuff as you mentioned will actually make sense. LOL.

You have to order their free teacher training video to see how it makes sense. But it does.

[Capt_Uhura]

369/3

 

We're using RS. That would be short division and is taught as 300/3 is 100 so you write the 1 above the 3. THen 60/3 is 20 so you write a 2 above of the 6 and 9/3 is 3 ones so you write a 3 above the 9.

 

RS starts off by dividing by 2 on the abacus. 8796/2. 8000/2 then 700/2, then 19/2 (from the remainder) and then 16/2 (from the remainder).

 

I found the lesson. 6747/2

 

1. 6000/2=3 thousands. Write the 3 in the thousands place. THere is no remainder.

2. 700/2=3 hundreds with a remainder of 1 hundred. WRite 3 in the hundreds place.

3. The extra 1 hundred=10tens. 10tens+4tens=14tens. Show the 14 tens with a little 1 before the 4. 14tens divided by 2=7 tens. WRite 7 in the tens place.

4. 7 ones/2=3 with a remainder of 1. Write the 3 in the ones place. Write r 1.

 

 

Rightstarts main approach I think is through division. I think of it as multiplication. two times what is 6000? 3000 so a 3 goes in the thousands place. For your problem, 738/7 ..... what times 7 is 700? 100 so put a 1 in the hundreds place. What times 7 is 3? nothing so put a 0 in the tens place. Then put those 3 tens w/ the ones to get 38. What times 7 is 38? 5 with a remainder of 3.

Edited April 10, 2010 by Capt_Uhura

[Omma]

Thanks, guys! That is helpful info. I like the way you explained that 7 cannot go into 3. I get so bogged down in my old way of doing math that I have trouble switching gears. Now, this is a stupid question, but why don't you think of that 3 as 30 since it is in the 10's place? That is where I still have problems conceptualizing this myself so that I can teach my son.

 

Brenda

[Ray]

but why don't you think of that 3 as 30 since it is in the 10's place?

Brenda

 

 

Maybe think of 30 as 3 ten bundles, that cannot be shared until they are unbundled into ones- good opening to refresh the placeholder function of zero.

[Karen in CO]

Wow - I think between Ray and Capt_Uhura, I am exceeding happy about math right now. I'm just going to sit here and imagine that my dd will think this is as brilliant as I think it is.

[Omma]

Wow - I think between Ray and Capt_Uhura, I am exceeding happy about math right now. I'm just going to sit here and imagine that my dd will think this is as brilliant as I think it is.

 

Why? How does Saxon handle long division (looking at your notes, it appears that you have a dc who's 9 using Saxon)? Just curious!

 

Brenda

[Omma]

Maybe think of 30 as 3 ten bundles, that cannot be shared until they are unbundled into ones- good opening to refresh the placeholder function of zero.

 

That's good. Thanks!

 

My ds happens to hate manipulatives (so Right Start would've driven him nuts... but my dd LOVES them... go figure), but I had shown him on paper how the 3 bundles needed to be undone to hand them out to his 7 friends equally!

 

I like the way you concisely stated it!

 

I wrote this thread because my dh and I had an argument about which way we should teach long division. He thought I should abandon the conceptual way and just teach it the good ol-fashioned way that we learned. :lol: Isn't learning and teaching fun?!!! It brings out the best in us (not to mention all the stuff I learn and re-learn during the whole home schooling process!)

:),

Brenda

[LinRTX]

Saxon teaches long division the old-fashioned way. The algorithm is divide-multiply-subtract-bring down, then repeat as necessary.

 

Linda

[Capt_Uhura]

RS starts off conceptually and then 2 lessons later moves into the standard algorithm when you really need it for longer, long division. RS uses the analogy of sharing pencils.

 

If you're doing that problem on the abacus, you'd only have 3 beads (bundles of pencils) in the 10s column. You can't divide those 3 beads (bundles) by 7 (hence the zero) until you break them into 30 ones in which case, you add them to the 8 ones you already have. Make sense? So then it's 38 ones divided by 7.

 

I at first wasn't sure about the short multiplication and then this method of multiply called octopus multiplying in the lesson before longer, long division but my DS9 didn't bat an eye. I've heard from friends that the long division algorithm is so hard to remember, kids forget and need an an acronym to recall but if you understand it conceptually, things like pesky zeros don't phase you.

 

I know I love re-learning math and understanding the whys and not just the hows! When you understand the why, you'll never forget it. I always had trouble memorizing things in school that I didn't understand but once I understood the process, memorizing was easy.

[wapiti]

I'm using Khan Academy http://www.khanacademy.org/

 

There are 4 videos on divison there. I think the second one introduces long division the usual way. http://khanexercises.appspot.com/video?v=8Ft5iHhauJ0

 

FWIW, I learned to carry down the 7x1 way rather than the 7x100 way, and I think the 7x100 way makes more sense. But I don't think it matters, ultimately.

 

Re: the zero, maybe show him using lined paper turned sideways so that the numbers all stay in the proper columns.