# Should I make my son do subtraction my way?

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So I introduced the concept of regrouping to my 7yo son today, via Singapore 2A. I showed him on a place value chart with the orange and white c-rods. However, he's resistant to learning it that way, because he has his own way. He's only focusing on his way (because it does work), and he's not, as of yet, seeing it the way I'm showing him (the way Singapore does it). Yes, he understands that 10 white c-rods are the same as one orange c-rod, etc.

Here's what he's doing:

74-46 = ?

He says, "7 tens minus 4 tens leaves 3 tens, or 30. If you do 4 ones minus 6 ones, you have 2 ones left over, so you take those 2 from the 30, and you get 28."

My thought is that this method works fine for two-digit numbers but may be too hard to keep straight in his head when he gets to larger numbers, multiple regrouping, etc. So I feel like I really should insist that he learn it my way (which is the standard "cross out the 7 tens, and make it 6 tens; cross out the 4 ones and make it 14 ones"). He protested because, as he said, "you can't have 14 ones in that column -- you can only have 9 ones; I'm going to do it my way"). I tried to tell him that the 14 ones was only temporary, and that it's the final answer that can only have 9 in that column, but while a generally pretty compliant child, he gets singly focused on one thing and doesn't want to switch.

So what says the Hive? Insist that he learn it the other way now, or let him use his way as long as it works (and realize that he may always do it that way, if he can do so, unless the traditional way suddenly clicks with him)?

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His method will be useful for mental math. Your method is useful for written math. Give him a really large number, and see if he can use his method. ;)

..23438239

-12345678

_________

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His method will be useful for mental math. Your method is useful for written math. Give him a really large number, and see if he can use his method. ;)

..23438239

-12345678

_________

LOL, yes, he is good at the mental math. I'm going to try giving him a large number to see if he can use his method. I'm half-afraid to -- part of me is afraid that he *will* be able to do it his way, and then, oh my. ;)

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There is always more than one way to do math. I have watched my kids work things out so differently to the way I do. Firstly, be excited he has figured out his own way. Do you realize that is HUGE!!! With math understanding the concept is the big deal. After that, whatever method works - let him use it. If he understands what he is doing, if his way ends up too slow, it won't be hard to learn another method.

And one thing I like about Singapore is that it often introduces alternate methods to solve a problem. That means students can try different ways and find out what works best for them.

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There is always more than one way to do math. I have watched my kids work things out so differently to the way I do. Firstly, be excited he has figured out his own way. Do you realize that is HUGE!!! With math understanding the concept is the big deal. After that, whatever method works - let him use it. If he understands what he is doing, if his way ends up too slow, it won't be hard to learn another method.

Thanks -- that is what I'm hoping, that if his way is too slow, it'll be easy to show him another one later, not that that he'll be super overwhelmed and confused.

I do realize that it's huge that he figured out his own way -- I'm proud of him! (Actually, I can't wait to call Grandpa and tell him -- my dad is a math teacher and is amazing at mental math. I grew up playing math games for fun and loving the little tricks and all -- it's really cool to see DS1 find them too!)

And one thing I like about Singapore is that it often introduces alternate methods to solve a problem. That means students can try different ways and find out what works best for them.

Oh, cool! We're new to Singapore; we started with 2A a few months ago, so I haven't seen everything from it yet. :)

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Some kids get set on one way and have a hard time using another method. My oldest is this way. I introduce the concept, have her work through it a few times, but ultimately let her solve the problem any way she can correctly. Sometimes, days or weeks down the line she'll come out with the concept I've taught. It's like she has to let her brain simmer that new info.

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"Oh, that's so cool! I never thought about doing it that way! Now hang on a sec and I'll show you another way that makes even bigger numbers easy to subtract."

If you can figure out a way to frame an alternative as a , "Yes, and..." instead of, "No, but", kids (and adults! lol) are often more receptive to new ideas. Once he understands your method, I'd let him do it however he'd like to.

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"Oh, that's so cool! I never thought about doing it that way! Now hang on a sec and I'll show you another way that makes even bigger numbers easy to subtract."

If you can figure out a way to frame an alternative as a , "Yes, and..." instead of, "No, but", kids (and adults! lol) are often more receptive to new ideas. Once he understands your method, I'd let him do it however he'd like to.

Yes, this is what I do also. On occasion, my son's method has been better than the one in the book. ;)

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With Singapore math the mental math skills (such as the strategy your son is using) are generally introduced first, as these methods take mathematical understanding of place value (which he is demonstrating) as opposed to the potential of being able to do the re-grouping you are trying to teach as a purely procedural operation w/o understanding.

Singapore does teach the standard algorithms. You don't need to worry about that. But your son is demonstrating a sophisticated understanding of this level of math. I would not discourage this. You are fortunate. He has plenty of time in the future to re-group numbers on paper.

Bill

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Both my kids do this kind of thing in their head far before it make sense to them on paper.

I was taught how to memorize. I swear I did not know arithmetic until I started teaching it with SM. I used to get pissed off at DH because he would try to explain it to me :lol:

I mean, obviously I understood but never thought it was easier than adding in columns. Now I totally get it. My kids are far better at understanding mental math than I ever was as a kid

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Actually, RightStart Math teaches 2-digit addition that way (starting in the 10s column) because it's faster for mental math and only does it the "traditional" way for 3-digit problems and above.

So long as the way he is doing it shows that he correctly grasps the concept, I wouldn't worry about it.

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His method will be useful for mental math. Your method is useful for written math.

As was done in MEP, my son was adding and subtracting two and three digit numbers with "borrowing" / "carrying" in his head easily way before performing the calculations on paper. I thought it was a bit scary that written methods hadn't been introduced at one point, but it seems to be working, and he has a good "feel." There are members on here who have posted before that their kids do arithmetic successfully from left to right, and I have seen it in books, too.

I have never used c-rods, mind you.

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My DS does all his mental subtraction left to right, three and four digit numbers. His SM tutor encourages him and told us not to correct him. He has amazing mental math abilities, it's just the way his brain works.

Just lurking...

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Just my experience...ds has been adding/subtracting numbers tens and then ones and when we got real heavy into borrowing and carrying numbers he started to get messed up, especially when he was adding 3 or more numbers in a problem. Anyway, I have had to back up with him and we are working through that right now. Some kids might not have problems with that, but I will most likely make sure I teach dd to start in the ones and then work her way up :)

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Thanks, everyone. I had him show DH his "cool new way of doing it" at dinner, and he was thrilled to show Daddy. So I'm not going to worry about it right now. I was pretty enthusiastic when he first showed me (actually, I was kind of floored; I do that kind of thing, but I wasn't expecting him to), just a little wary that it would backfire on him on the long run. Well, if he gets confused later, we'll cross that bridge when we come to it; I'm glad to hear so many people say that it's not a big deal.

Last week, this is how he wanted to do addition with carrying:

47

+16

_____

He wanted to add the 7 and 6 and write 13, with the 1 in the tens column and the 3 in the ones column, all down in the answer column, rather than with the 1 up above the 4. Then he wanted to add 4 + 1 + 1, erase the 1 in the answer, and write a 6 in its place. He clearly understood the place values and everything (and could add the numbers in his head just fine), but I did insist (after first congratulating him on understanding the concept, and after acknowledging that his way would indeed work) that he do it the way Singapore was telling him, mainly because I thought a lot of erasing would be a pain in the neck. Maybe I should just get out of his way and let him do it however he wants. ;) Tough question -- when to nip potentially bad habits in the bud vs. how to encourage their own exploration and understanding.

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Just my experience...ds has been adding/subtracting numbers tens and then ones and when we got real heavy into borrowing and carrying numbers he started to get messed up, especially when he was adding 3 or more numbers in a problem. Anyway, I have had to back up with him and we are working through that right now. Some kids might not have problems with that, but I will most likely make sure I teach dd to start in the ones and then work her way up :)

That's what I thought as well. This concept required quite a ridiculous visual explanation for my daughter to understand it, so I wanted to emphasize starting in the ones for my son -- but he's got his own idea that works. I'm just going to wait and see how it plays out.

I should no longer be flabbergasted at how different two children can be, but it still always amazes me that my older two learn and process so completely differently.

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Last week, this is how he wanted to do addition with carrying:

47

+16

_____

He wanted to add the 7 and 6 and write 13, with the 1 in the tens column and the 3 in the ones column, all down in the answer column, rather than with the 1 up above the 4. Then he wanted to add 4 + 1 + 1, erase the 1 in the answer, and write a 6 in its place. He clearly understood the place values and everything (and could add the numbers in his head just fine), but I did insist (after first congratulating him on understanding the concept, and after acknowledging that his way would indeed work) that he do it the way Singapore was telling him, mainly because I thought a lot of erasing would be a pain in the neck. Maybe I should just get out of his way and let him do it however he wants. ;) Tough question -- when to nip potentially bad habits in the bud vs. how to encourage their own exploration and understanding.

When I run into a "my way only" situation with DS, I'll say, "Great job! Here's another way to do it. Pick one."

In the case of the adding two digit numbers, I would correct it immediately if it were my son. Unless it's an obvious mental math problem, I think showing the work is a good skill to encourage from the beginning. I've used this explanation:

Sometimes in math we do things so people can see our brain working. When you get into more difficult math, a small mistake can make the entire answer wrong. If you add together numbers, but then erase part of the work, how do I know what's going on in your brain? I can't peek in your ears and see your brain computing. If you've given a wrong answer and you haven't shown your work, I have to make you do the WHOLE thing over again as opposed to seeing your thoughts on paper and finding that one small thing that needs to be fixed.

Once ds hit third grade and multi-step problems, I made it clear that the problem wasn't complete if he hadn't shown his work.

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With Singapore math the mental math skills (such as the strategy your son is using) are generally introduced first, as these methods take mathematical understanding of place value (which he is demonstrating) as opposed to the potential of being able to do the re-grouping you are trying to teach as a purely procedural operation w/o understanding.

Singapore does teach the standard algorithms. You don't need to worry about that. But your son is demonstrating a sophisticated understanding of this level of math. I would not discourage this. You are fortunate. He has plenty of time in the future to re-group numbers on paper.

Bill

:iagree:

Think about it this way. It is really easy to teach a kid who can swim how to climb onto a life raft. But it's really hard to teach a non-swimmer how to get off of the life raft and get in the water.

Traditonal algorithms are like a raft. They are really important to get you over big waters. But we would never send our second graders off into a pool on them, and then say "Look! My kid is water safe!"

That's why I like the Singapore approach which emphasizes thinking first, before traditional algorithms are taught. (Ditto with Right Start.)

Btw I've been blogging about mental math this week as part of Math Boot Camp for Moms.

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Think about it this way. It is really easy to teach a kid who can swim how to climb onto a life raft. But it's really hard to teach a non-swimmer how to get off of the life raft and get in the water.

Traditonal algorithms are like a raft. They are really important to get you over big waters. But we would never send our second graders off into a pool on them, and then say "Look! My kid is water safe!"

:iagree: This is a great metaphor!

My DS has been thriving with the mental math in RightStart. He's been doing problems in his head lately that I'd never have thought he could, including 4-digit plus 3-digit numbers. He tends to "talk out" his process as he's solving a problem, and while he does it differently than I was taught, he's right almost all of the time. I'm not going to shoot him down for going his own way as long as it works.

Sometimes we reach a point where his self-discovered mental tricks don't work, and then I'll bring up the alternative methods he's learned and ask him to decide if it makes more sense to use one of them. If I just tell him to do it, he balks; if I give him the choice and ownership of it, he gladly tries the other way. It's made for some interesting "Wow, Mom, you were right!" moments.

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