help with teaching borrowing

[lisamarie]

My DS has started on borrowing and I'm having trouble getting him to understand it. He can do carrying great, but borrowing is just not going well. I have been using money to illustrate, we've gone over it many times, and he seems to get the concepts. But when it comes time to do the work on his own, the concept leaves his brain. The hardest is when he has to borrow from 0. Then he's really struggling.

 

Are there other ways to show this besides using pennies, dimes and dollars? And repeated problems on a white board going over them together?

[Closeacademy]

I really like the place value rainbow or using base 10 blocks for this. You can find the rainbow idea here. You will have to page down to find it.

 

But basically with the rainbow rods or the rods in a base 10 set it is easy to see all the little parts in the 10s and 100s pieces and how we break them down to borrow.

 

The AL Abacus is great for this too. I use it a lot when working on subtraction with regrouping.:001_smile:

[ChrissySC]

It sounds like he doesn't understand the "homes." You need to look up number houses. This was a concept taught some time ago. The home of the ones has nine rooms. When an extra "one" moves into the home, the ones move into the home of the tens. Each room in the tens home can hold 10 ones. From there you move out and on to carry and borrow. :) I summarized a great deal. MUS was one of the better programs long ago that used this concept to teach number placement for young students. I have used this program twice in grades 1 - 3.

[Shelly in the Country]

I'd try Base 10 blocks. I love those things :001_smile:.

[Dana]

I really like the place value rainbow or using base 10 blocks for this. You can find the rainbow idea here. You will have to page down to find it.

 

But basically with the rainbow rods or the rods in a base 10 set it is easy to see all the little parts in the 10s and 100s pieces and how we break them down to borrow.

 

The AL Abacus is great for this too. I use it a lot when working on subtraction with regrouping.:001_smile:

 

:iagree: Yup... Base 10 blocks.

Work problems with the manipulatives first (for at least a day doing every problem with the blocks). Write down answers.

Next day, do one or two with the blocks (same problems as before) but also show the traditional algorithm (borrowing). Hope the connection is made. If not, keep using the blocks until the concept gets set.

 

Miquon was helpful for us and it did take over a week to get the concept with me pushing ds back to the blocks for any problem he got wrong.

[Karen in CO]

My dd was stuck on borrowing too. What helped her was money, BUT... We only used dollars, dimes, and pennies. We did every single problem using the manipulatives until she could do them on her own.

 

I'd set up each problem for her at first - I'd put out the number of dimes and pennies she needed into columns for each number in the problem, show her that each was the same as th enumber in the problem, then talk her through the trading (the borrowing term confused more than helped).

 

That was before I read Laping Ma's book. I'm hoping the next student doesn't get stuck, but I think that using manipulatives to work the problems for as long as is needed is important. I also had my dd explain the problems to me when she was doing them on her own. Eventually, she thought the money was a waste of time and it was faster to do without.

[Crimson Wife]

Using the AL Abacus and the Base 10 tiles (or blocks if you have those). My MIL, who is a retired teacher, gave me a set of Digi-Blocks so I pull those out from time to time as well.

 

Since I read Liping Ma's book, I've used the term "decomposing" instead of "borrowing".

[WishboneDawn]

 

Here's a link to a virtual manipulative that demonstrates the concept very well.

[Maverick_Mom]

Another vote for Base 10 blocks.

[wy_kid_wrangler04]

Use money- pennies, dimes, dollar bills and 10 dollar bills.

 

 

Example (ETA: I had to use a 0 to get it to line up right after i sent reply LOL)

023 <---- use 2 dimes and 3 pennies

-17 <---- use 1 dime and 7 pennies-

_______

 

Tell ds to take 7 pennies away from his 3 pennies. He will say he cant. So then show him how you have to take a dime, turn in into pennies and "share" then with the ones (because pennies are worth 1) Then when you get to hundreds use dollars and dimes and thousands $10 bills. Explain that in a dollar there are 100 pennies (hundreds) and in $10 there are 1000 pennies (thousands) and so on! It worked GREAT for my dds! We started with base 10 blocks but money really helped them to understand better! I plan on just doing that instead of base 10 blocks with my ds's!

Edited August 24, 2010 by wy_kid_wrangler04

[lisamarie]

I tried teaching him with base ten blocks today and here's to hoping it sunk in. I also told him that any problem he didn't show his work (crossing out numbers and putting new numbers above it) I would mark as wrong and make him do over. He got all of them right. I will have him do tomorrow's work without further teaching and see if he can do it on his own. We're on a review section of SM, so I'm having him do all the problems 1 page at a time to make sure he gets it before moving on to a new concept.

[Tracy]

You have to read Knowing and Teaching Elementary Mathematics by Liping Ma. There is a fabulous chapter on teaching borrowing. DH and I read it just a couple of weeks ago, and we could not believe how much we learned about doing and teaching subtraction. (And he is a high school physics teacher!)

[mom31257]

It could be he's just not ready developmentally. I tried to teach it to my ds last December, and he didn't get it well. I left it behind, actually switched curriculum as well, so it didn't come up again until 3 weeks ago. I taught it to him the exact same way and he understood fully. I think his brain was just no ready to "get" it. If the teacher and method didn't change, doesn't it have to be that?

[crazyforlatin]

 

Since I read Liping Ma's book, I've used the term "decomposing" instead of "borrowing".

 

I switched terms as well since reading the book and have been using base ten blocks, which demonstrates the concept of decomposing a ten into ones perfectly.

 

By the way, why is Ma's book $130 now?:confused:

[ElizabethB]

The AL abacus was the thing that finally did it for my daughter, physically exchanging a 10 bead for ten ones was helpful.

 

I did all the other things listed first, too, and more!! If I remember what else I did, I'll reply again.