Do kids need to understand "borrow and pay back" subtraction (vs regrouping)?

[Anonymous]

Hi, I noticed a question in my kid's math program that was talking about the borrowing and paying back method for subtraction. It seems to be just teaching it as an alternative method to regrouping.

It started stressing out my anxious kid (who understands regrouping and can do subtraction very well the regrouping way) and it doesn't seem very intuitive to me either so I just wanted to check whether kids are actually needing this these days, and if so, why. Is it useful for anything else later?

Thanks!

[Anonymous]

Please do not teach this nonsense of “borrowing & paying back.” What’s best for your kid is to develop a solid conceptual understanding of regrouping in a base ten system. What’s best is for your kid to be a flexible thinker and to pick which strategy is the most efficient to solve the problem in front of them.

For example: If presented with 1002-997=___, the most efficient strategy is NOT to set it up vertically and regroup. The most efficient way to solve this subtraction problem is to simply “add up.” 998-999-1000-1001-1002. The answer is 5.

[Anonymous]

If they understand one way, have them do it that way. This idea that we have to teach a million ways to do the same thing is ridiculous. If your child is presented with a subtraction problems and can repeatedly successfully solve them, it is good. My child also gets confused with multiple strategies.

The only challenge is that without textbooks, I have a hard time assisting my child with the language and methods they are being taught. I was raised on borrowing and carrying, so when I try to explain it that way, we get nowhere.

[Anonymous]

I agree with the PPs. Do what works for your kid. Math teachers are required to teach 50 kazillion strategies. Administrators and math educators, neither of which groups contain anyone who is a K-12 teacher with practical experience in the classroom, apparently hope that this multiple strategy approach will mean that something will catch. Unfortunately it just ends up confusing kids.

However, your kid should try to have one solid strategy and then a back-up for each concept. This will be very important as the child moves into things like fractions in elementary, and even more important as the child moves into higher math with algebra and beyond. Some level of flexible thinking and ability to move between a few preferred strategies will be helpful.

In your example OP I would encourage the kids to either count up or use the base 10 system mentally. When I look at the problem, I see the last digits. I see 7 and I know 3 more takes me to 0 (for a 10). From 0 I know 2 more takes me to the 2. So 3 + 2 equals 5. I see the Tens place has a 0 so that means my answer is 5. If the Tens place had a value (like 1032 - 997) then I would add 30 to my 5.

Anyway, if the strategy the program is offering stresses out your kid then just move on.

[Anonymous]

This is the reason I've hired a math tutor for the fall. I loved math through college, but nothing my daughter is learning matches up with how I've learned. I worked with her in the spring, but her teacher wants them to use the method they're being taught (which makes sense), which would require me listening to her zoom classes to learn the method in order to teacher her

[Anonymous]

As a teacher, no. As a former student, though? Maybe. I did have to take some tests and "show my work" using different strategies to prove that I was able to switch between them.
If they do have a test or quiz on the topic, it may not be teacher made. Some schools/programs provide them and the teachers can't deviate from it.

[Anonymous]

Anonymous wrote:Please do not teach this nonsense of “borrowing & paying back.” What’s best for your kid is to develop a solid conceptual understanding of regrouping in a base ten system. What’s best is for your kid to be a flexible thinker and to pick which strategy is the most efficient to solve the problem in front of them.

For example: If presented with 1002-997=___, the most efficient strategy is NOT to set it up vertically and regroup. The most efficient way to solve this subtraction problem is to simply “add up.” 998-999-1000-1001-1002. The answer is 5.

NP. So what I end up doing for a problem like that is to say, in my head “ok 997 to 1,000 is 3 and then 1,000 to 1,002 is 2, so 3+2=5.” I don’t have a school-aged kid, so I don’t know if that’s how they’re teaching it to kids these days, but it’s definitely how I think about it.

[Anonymous]

Anonymous wrote:

Anonymous wrote:Please do not teach this nonsense of “borrowing & paying back.” What’s best for your kid is to develop a solid conceptual understanding of regrouping in a base ten system. What’s best is for your kid to be a flexible thinker and to pick which strategy is the most efficient to solve the problem in front of them.

For example: If presented with 1002-997=___, the most efficient strategy is NOT to set it up vertically and regroup. The most efficient way to solve this subtraction problem is to simply “add up.” 998-999-1000-1001-1002. The answer is 5.

NP. So what I end up doing for a problem like that is to say, in my head “ok 997 to 1,000 is 3 and then 1,000 to 1,002 is 2, so 3+2=5.” I don’t have a school-aged kid, so I don’t know if that’s how they’re teaching it to kids these days, but it’s definitely how I think about it.

I add three to both numbers, and then do 1005-1000=5. Which is one of the strategies that my kid learned. She also learned a few other strategies, including regrouping. I don't know what the "borrowing and paying back" method is, if it's not regrouping (which was called "borrowing" when I was a kid but was exactly the same). I think the kid needs to learn as many of the strategies as she can, because they help develop number sense, and then master regrouping. If one of the strategies doesn't make sense, don't sweat it.

[Anonymous]

Kids with learning disabilities get very confused by being taught multiple ways to solve problems like this. Just teach them one way that works for them. I understand the need for number sense, but if your child gets confused, just stick with one way.

[Anonymous]

Anonymous wrote:If they understand one way, have them do it that way. This idea that we have to teach a million ways to do the same thing is ridiculous. If your child is presented with a subtraction problems and can repeatedly successfully solve them, it is good. My child also gets confused with multiple strategies.

The only challenge is that without textbooks, I have a hard time assisting my child with the language and methods they are being taught. I was raised on borrowing and carrying, so when I try to explain it that way, we get nowhere.

A million ways is the way to true number literacy. Which is the important part and not being able to do just one kind of problem one way. The way many of us were taught were very limiting. It was procedural and not drilling down to true math understanding. The current way is actually better but harder in the beginning. It leads to better number understanding. It's also the way people were taught a couple generations back and in other countries.

[Anonymous]

Anonymous wrote:

Anonymous wrote:If they understand one way, have them do it that way. This idea that we have to teach a million ways to do the same thing is ridiculous. If your child is presented with a subtraction problems and can repeatedly successfully solve them, it is good. My child also gets confused with multiple strategies.

The only challenge is that without textbooks, I have a hard time assisting my child with the language and methods they are being taught. I was raised on borrowing and carrying, so when I try to explain it that way, we get nowhere.

A million ways is the way to true number literacy. Which is the important part and not being able to do just one kind of problem one way. The way many of us were taught were very limiting. It was procedural and not drilling down to true math understanding. The current way is actually better but harder in the beginning. It leads to better number understanding. It's also the way people were taught a couple generations back and in other countries.

I guarantee you in Asia no one is learning the borrow and pay back method (ex. 72-29 = 7 tens 12 ones minus 3 tens 9 ones/ this is not the standard subtraction algorithm of 6 tens 12 ones minus 2 tens 9 ones.)

This is why math instruction is so awful in this country. There is no added conceptual benefit of learning this method. OP your child doesn't have to learn it and I would discourage my child from using it. I would be really annoyed if they were taught this method.

[Anonymous]

Anonymous wrote:

Anonymous wrote:Please do not teach this nonsense of “borrowing & paying back.” What’s best for your kid is to develop a solid conceptual understanding of regrouping in a base ten system. What’s best is for your kid to be a flexible thinker and to pick which strategy is the most efficient to solve the problem in front of them.

For example: If presented with 1002-997=___, the most efficient strategy is NOT to set it up vertically and regroup. The most efficient way to solve this subtraction problem is to simply “add up.” 998-999-1000-1001-1002. The answer is 5.

NP. So what I end up doing for a problem like that is to say, in my head “ok 997 to 1,000 is 3 and then 1,000 to 1,002 is 2, so 3+2=5.” I don’t have a school-aged kid, so I don’t know if that’s how they’re teaching it to kids these days, but it’s definitely how I think about it.

I just quickly recognize that they’re only a few digits apart, and subtract 7 from 12. The answer is 5. It takes two seconds. Maybe less.

[Anonymous]

Anonymous wrote:If they understand one way, have them do it that way. This idea that we have to teach a million ways to do the same thing is ridiculous. If your child is presented with a subtraction problems and can repeatedly successfully solve them, it is good. My child also gets confused with multiple strategies.

The only challenge is that without textbooks, I have a hard time assisting my child with the language and methods they are being taught. I was raised on borrowing and carrying, so when I try to explain it that way, we get nowhere.

We are in DCPS, which uses Eureka, and the whole curriculum is available online. https://www.engageny.org/ I found it really useful.

[Anonymous]

Anonymous wrote:Kids with learning disabilities get very confused by being taught multiple ways to solve problems like this. Just teach them one way that works for them. I understand the need for number sense, but if your child gets confused, just stick with one way.

+1 It's good to know how to solve something 10 different ways as long as they also know a single consistent, fast method.

I have a rising 5th grader who struggles in math and she once was told to pick her favorite way to solve 14*12. Unfortunately, her "favorite" was to add 12 fourteen times because she didn't really understand what we would view as the standard multi-digit multiplication algorithm since it was presented as just 1 method out of a bunch of different ones, not the default. Her other favorite was lattice multiplication, which I tend to think of as a cool trick but realistically wouldn't be super efficient for solving 14568*459, for example. But the teacher never told them to pick just one and practice it for speed and fluency, so nothing ever really stuck.

[Anonymous]

Anonymous wrote:

Anonymous wrote:Kids with learning disabilities get very confused by being taught multiple ways to solve problems like this. Just teach them one way that works for them. I understand the need for number sense, but if your child gets confused, just stick with one way.

+1 It's good to know how to solve something 10 different ways as long as they also know a single consistent, fast method.

I have a rising 5th grader who struggles in math and she once was told to pick her favorite way to solve 14*12. Unfortunately, her "favorite" was to add 12 fourteen times because she didn't really understand what we would view as the standard multi-digit multiplication algorithm since it was presented as just 1 method out of a bunch of different ones, not the default. Her other favorite was lattice multiplication, which I tend to think of as a cool trick but realistically wouldn't be super efficient for solving 14568*459, for example. But the teacher never told them to pick just one and practice it for speed and fluency, so nothing ever really stuck.

I have an upcoming 5th grader whose multiplication skills are shockingly weak bc of this too —-teaching widely but not deeply. Lots of methods, but none well. This summer I’m drilling down on the standard method that we learned and having her master that. Screw everything else. I’m also having to go over math facts! Because while she learned these in first grade and second and third....she still has to think about the answers.