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# Help teaching subtracting with regrouping!

Please, I need some good resources for teaching double digit subtracting with regrouping. I was taught to borrow, back in the 1970s, when I learned double digit subtraction. All the math books I've found use regrouping. I've tried to teach my son three different ways and he's frustrated and so I am. Is there any reason not to teach borrowing?

I spoke to several teachers for 1st and 2nd grade and they all shuddered and said, "It's really hard!" I used the tips they gave me to no avail. I've tried manipulative, diagrams, and legos. My son wants to know why he can't just count backwards.
Teaching subtraction via the "borrowing" method is valid. If that makes more sense to you, use that method. It sounds like your child doesn't care for "regrouping" either. Assuming he is homeschooled (since you posted here), I would do it the way that works best for you and him. Eventually, he will be "borrowing" anyways.

Amy
We're doing that now.. using Math U see. He calls it both regrouping AND borrowing at times in the videos?
Do you have base 10 cubes/rods? I find them really helpful for teaching any sort of regrouping.
Personally, I don't really see a difference between borrowing and regrouping other than the terminology. You don't actually do it a different way, right?

Also, I don't see a really good reason not to let him count backwards for now, if he can do it accurately. If he makes a lot of mistakes, it might show him that counting backward isn't really efficient, and that he might need to revisit borrowing/regrouping.

Are you using an actual curriculum, or are you making up your own? how have you used manipulatives to show him? Maybe we can suggest new ways to use them?

ETA: cross posted with annette marie - dd used 10s rods and cenitmeter cubes to learn regrouping, too.
We call it borrowing. Nothing wrong with that.

This is what helped my son grasp it. 21-8, for instance. "So, can you take 8 away from one? No? That's right, because 1 is smaller than 8. So what do we do? We borrow from neighbor 2 over there, just borrow one. That goes right in front of your first 1, and 1 next to 1 is 11. And can you take 8 from 11? Yes!"

It's probably the "wrong" way to teach, but that's how he first learned to understand it, and then as he learned about regrouping things, the two ways connected.
Quote:
 Originally Posted by eclipse Personally, I don't really see a difference between borrowing and regrouping other than the terminology. You don't actually do it a different way, right?
Thank goodness.. I thought I was stupid for a minute there I couldn't work out what the difference is supposed to be!

Quote:
 Originally Posted by NightOwlwithowlet I spoke to several teachers for 1st and 2nd grade and they all shuddered and said, "It's really hard!" I used the tips they gave me to no avail. I've tried manipulative, diagrams, and legos. My son wants to know why he can't just count backwards.
Of COURSE they say it's super hard... because if it's NOT then they have no reason to be adamant that parents can't teach their children

Quote:
 Originally Posted by cappuccinosmom This is what helped my son grasp it. 21-8, for instance. "So, can you take 8 away from one? No? That's right, because 1 is smaller than 8. So what do we do? We borrow from neighbor 2 over there, just borrow one. That goes right in front of your first 1, and 1 next to 1 is 11. And can you take 8 from 11? Yes!" It's probably the "wrong" way to teach, but that's how he first learned to understand it, and then as he learned about regrouping things, the two ways connected.
That's exactly how MUS teaches it. And using the blocks you would simply move the 10 block over to the units place and then you flip the 8 block upside down onto the 10 showing that there are 3 units left.

My big issue is getting my 8yo to IMMEDIATELY mark out the number in the 10's column and put one less.
DS1 was a math whiz. He still catches on quickly, but lacks motivation to go on to higher math. Plus, he does math differently in his brain than I was ever taught, so he's on his own (he's 18, anyway).

DS2 has always struggled. We tried MUS when he was younger, and regrouping confused him for both adding and subtracting. I finally just backed off and approached it again every few months until it looked like he was understanding. I don't think he really "got it" until he was about 10yo, and that was fine. What's the hurry, ya know? He's a smart kid; his strengths just lie elsewhere.
Quote:
 Originally Posted by CariOfOz Thank goodness.. I thought I was stupid for a minute there I couldn't work out what the difference is supposed to be!
I think math teachers changed it to "regrouping" in order to make it more clear to the student exactly what is happening and why - that you aren't crossing out numbers and adding ones and all that just because it works, but to teach them how it works. But if it's easier for the teacher (in the case of homeschooling, the parent) to explain it as "borrowing," I don't think it makes a bit of difference. I understood what was happening when I learned how to do it, even though it was called borrowing and not re-grouping . When I taught my kids, I used the two terms interchangably, because I figured that if I only taught them one, they might be confused if they ever encountered it called the other.

The term "borrowing" is being phased out because it implies that something will be 'given back' or 'replaced' and that is inaccurate. Borrowing and regrouping are the same though and the terms are still used interchangeably. There are different ways to regroup and it may just be that you have to find the way that makes most sense to him.

What types of things have you tried? Unifex cubes can be really helpful but if he has a firm understanding of coin value using dimes and pennies are really great. It can offer a great representation of place value as well as the need to regroup.
In addition to teaching any other way, I LOVE this way for the mental math aspect (and hopefully this formats correctly! I like this as an alternative and to go along with other methods. This is the way I subtract IRL.
Left to Right Subtraction

The second standard method of EM is left to right subtraction, the way one might well do the problem mentally, but carried out with paper and pencil. Here "left to right" refers to the decomposition of the second number. In the example at right, 325-58, the 58 is decomposed as 50+8. The individual subtractions are done mentally.

325
- 50
---
275
- 8
---
267
My son also figured out that he prefers to just use negative numbers rather than regrouping. So the problem in the pp would be

3 2 5
- 5 8
-------

5-8= -3
2-5= -3
3-0=3

300-30 =270
270-3= 267

He's very fast doing it this way. He "got" negative numbers from a very young age, though. It's just another way of showing that you don't have to stick with the "official math teacher" methods. If you think he might be interested in learning about negative numbers, you might whip out a -/+ number line and show him how this works.
How quickly are you moving on to different methods? Learning the subtraction algorithm is a longer process than the addition one and moving methods too quickly may add to confusion no matter what type of math you are doing. My dd was having some trouble with addition in PS because her teacher was quick to assume a problem that wasn't there and was flooding her with strategies without giving her time to learn one well. When I pulled her home I found that she just needed a little more time to learn the strategies well and she has now doing wonderfully. If you have been giving very little time for him to learn a strategy then I think that you should pull back and choose the one that you are most comfortable teaching and start again with that one.

It may help to use numbers that are too high to use fingers for and to have a paper with a tens and ones column. When dd learned subtraction I used legos linked as ten sticks and I had her keep the ten sticks in the tens column and the ones in the ones column. When she regrouped I had her physically break the ten stick into ones and put them in the ones column then I modeled for her what that looked like with the algorithm. We only did two or three problems a day because they were time consuming. After a few days of practice with hands on problems only I had her do both the hands on and the algorithm together. I found that she needed to have the numbers in each column separated and labeled until several days after she started doing the work on paper only. It took about ten days for her to move to paper only, but once she did she really had it down and does the work quickly and easily.
Quote:
 Originally Posted by CariOfOz My big issue is getting my 8yo to IMMEDIATELY mark out the number in the 10's column and put one less.

My 8yo doesn't seem to understand what she's doing when she regroups. I made up a flow chart for subtracting double-digit numbers and that resulted in a huge change from 'I can't do this' to 'I can follow a chart.' But I think there's an a-ha moment coming any day now...
Quote:
 Originally Posted by eclipse I think math teachers changed it to "regrouping" in order to make it more clear to the student exactly what is happening and why - that you aren't crossing out numbers and adding ones and all that just because it works, but to teach them how it works. But if it's easier for the teacher (in the case of homeschooling, the parent) to explain it as "borrowing," I don't think it makes a bit of difference. I understood what was happening when I learned how to do it, even though it was called borrowing and not re-grouping . When I taught my kids, I used the two terms interchangably, because I figured that if I only taught them one, they might be confused if they ever encountered it called the other.
Ahhh I suppose that makes sense... We use both terms, and he 'gets' that they mean the same. I'm glad there wasn't some new fangled math that I knew nothing about
I always liked "borrowing". It seems friendlier.
I thought that the regrouping implied a better grasp of place value than borrowing. Borrowing was mechanical, but it seemed that "regrouping" as a method expected the kids to understand more. Since I have found that some kids understand only after they are doing something, I would have no problem teaching them to follow the steps of borrowing. Then, I would at a later time go back and make sure they understand why it is possible. That is why I thought there was a bit of difference.

Amy
"Regrouping" is something that is done in all four operations. When multiplying 18x3, I multiply 3 times the 8 first, get 24 as my result, and write the 4 in the ones column. Then I "regroup" the 2 by noting it in the tens column above the 1, and adding it to the result of that multiplication.

In other words, regrouping refers to either constructing or deconstructing a unit of greater value (eg. making a ten from ten ones, or making ten ones from a ten). So it's a more useful word, and demonstrates the common concept of constructing or deconstructing units of place value.

My favourite way to teach regrouping in subtraction is to use money. Take a sheet of paper turned sideways and divide it into columns for dollars, dimes and pennies. Ask your child to place \$4.35 in dollars dimes and pennies in the corresponding columns. Then ask her to take away 8 cents. She'll look at the 5 pennies and hopefully she'll see that there aren't enough pennies, and that one of the dimes needs to be traded in for ten pennies, allowing that value to be "regrouped" into the pennies column. Show her how you would write that process if you were doing the problem on paper. You've made \$4.35 into "four dollars and twenty-fifteen cents." Now there are enough pennies that you can remove 8.

HTH.

Miranda
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