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My son has been practicing the adding and subtracting of double digit numbers with and without regrouping. He's doing very well with addition but subtraction is causing a couple of problems.

He can, and does, do both the addition and subtraction in his head and I have encouraged this while also teaching him how to do it on paper.

Problem 1. With or without regrouping, he doesn't completely grasp that "finding the difference" in a word problem is "supposed to be" subtraction. He will quite honestly say he is adding to solve the problem. For example, he would find the difference between 54 lbs and 18 lbs and by adding up from 18 (2 + 30 + 4 = a difference of 36). I have to use algebra to explain how what he's doing relates to what he's "supposed" to be doing (ie. 18 + x = 54 ---> x = 54 -18; using his experience with the Dragonbox iPad app has facilitated this). He's still looking at me like ...... why must I?

Problem 2. He is in full rebellion against regrouping on paper to facilitate subtraction. The whole conversion of the 54 into 4 tens and 14 on the paper (to use the same numbers purely for example) is just a no go so far. Yes, he gets it. We've done it over and over with base-10 blocks. He's just having none of it. He can take 8 from 54 and then take the 10 OR he could take the 10 first and then the 8 and the regrouping of the 54 is deemed unworthy of his regard.

Questions: Is there a "must" for problem one and if so, how do I explain this need? The problem he does run into with problem two is that if he's having trouble focusing he gets numbers confused up in his head and will make mistakes. It doesn't happen a lot but it can and does happen and doubtlessly will all the more as the numbers get larger. Should I persist in teaching the doing of these problems on paper or leave it off, allow him to continue working in his head, and come back to it at a later time?

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Maybe try the Singapore bar diagrams to help him see what the "missing piece" is in the equation?

I would say, in my complete inexperience with teaching (but relatively good experience with math) that as long as he understand conceptually what he is doing and he is getting the right answer, the algorithm should not be particularly important.

But I'm reading a book by John Holt right now, so that may be coloring my view... :D

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I've been using the bar diagram, too. He really does get it. What he doesn't seem to get is why to work out 54-18=x if 18+x=54 is easier.

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Problem 1. With or without regrouping, he doesn't completely grasp that "finding the difference" in a word problem is "supposed to be" subtraction. He will quite honestly say he is adding to solve the problem. For example, he would find the difference between 54 lbs and 18 lbs and by adding up from 18 (2 + 30 + 4 = a difference of 36). I have to use algebra to explain how what he's doing relates to what he's "supposed" to be doing (ie. 18 + x = 54 ---> x = 54 -18; using his experience with the Dragonbox iPad app has facilitated this). He's still looking at me like ...... why must I?

He has understood the problem and is solving it correctly. He is finding the difference - so no, solving it "by subtraction" is not a "must".

Problem 2. He is in full rebellion against regrouping on paper to facilitate subtraction. The whole conversion of the 54 into 4 tens and 14 on the paper (to use the same numbers purely for example) is just a no go so far. Yes, he gets it. We've done it over and over with base-10 blocks. He's just having none of it. He can take 8 from 54 and then take the 10 OR he could take the 10 first and then the 8 and the regrouping of the 54 is deemed unworthy of his regard.

If he can solve the problem without "regrouping" , I do not see why he should have to.

Once he gets into actual trouble when the problems are so hard as to require this, he might be more open to accepting this. But honestly: I don't regroup either when I subtract - certainly not into 4 tens and 14. I "see" the 54 as a 46 and two 4's for the purpose of subtracting 8.

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He has understood the problem and is solving it correctly. He is finding the difference - so no, solving it "by subtraction" is not a "must".

If he can solve the problem without "regrouping" , I do not see why he should have to.

Once he gets into actual trouble when the problems are so hard as to require this, he might be more open to accepting this. But honestly: I don't regroup either when I subtract - certainly not into 4 tens and 14. I "see" the 54 as a 46 and two 4's for the purpose of subtracting 8.

I agree.

I wouldn't regroup either -- I would subtract twenty and then add two.

If he understands how regrouping works and just doesn't like to do it that way, I'd let him alone. I'd turn any incorrect problems back to him with an x and have him fix them.

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Sounds like he's doing great to me!

Problem 1. Subtraction is the inverse of addition---which means that essentially, they are the SAME operation. What he's doing is perfectly logical.

Problem 2. If I were him, I'd be in rebellion, too. There is no point in the pencil-and-paper algorithm until one wants to do math bigger than what one can work mentally. And using the pencil-and-paper algorithm means turning off one's brain and following rote steps. That's the whole point of it, that it can be done without thinking.

Questions. I would leave it for now. I'm afraid that pushing it when he's resistant may turn him off on math, because you are asking him to replace a method that makes sense to him (and works) with one that does not make sense (to him).

Articles that you might find useful:

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I wouldn't regroup either -- I would subtract twenty and then add two.

:iagree:That's what I did, too.

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Thank-you, ladies. I'm sure he thanks you, also. :)

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And using the pencil-and-paper algorithm means turning off one's brain and following rote steps. That's the whole point of it, that it can be done without thinking.

I forgot that I wanted to comment that I have seen this dramatically with this child. After I first taught him to add on paper he stopped working the amounts in his head (seeing the 54 as 46 and two 4s, for example) and started visualizing the sum on the paper and using the algorithm. I put away the workbook and worked with him using C-rods and word problems again until it came back.

After the issues today with the regrouping I think I should have gone with my initial instinct to keep it mental for now.

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I have one like this, too. Just hates subtraction and loves addition. He refused to subtract for quite awhile in favor of adding negatives. :lol: After a few brief squirmishes, I let him go out in and figure he'll cotton to the algorithm if he needs it with bigger numbers.

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I found the book Knowing and Teaching Elementary Mathematics by Liping Ma to be indespensible in my understanding of teaching math.

She references the Singapore series in her explainations of teaching math, but you can apply the concepts across the board.

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Sounds like he's doing great to me!

Problem 1. Subtraction is the inverse of addition---which means that essentially, they are the SAME operation. What he's doing is perfectly logical.

Problem 2. If I were him, I'd be in rebellion, too. There is no point in the pencil-and-paper algorithm until one wants to do math bigger than what one can work mentally. And using the pencil-and-paper algorithm means turning off one's brain and following rote steps. That's the whole point of it, that it can be done without thinking.

:iagree: with this.

If it makes you feel any better, in Rightstart, what your son is doing is *exactly* what the program is trying to teach them for mental math! First it focuses on doing mental math of two digit numbers in addition (and later subtraction), and then later on when they start working with 4 digit numbers, *then* it teaches regrouping (or "trading" as it's called in Rightstart terms).

You should let him continue to do what he's doing when working with two digit numbers, maybe even have him do all the 2 digit problems mentally. (It's good brain exercise!) There will be plenty of time for regrouping when he starts working with 3 or 4 digit numbers. (Especially since it sounds like he does "get it" but just doesn't want to do it that way.)

For what it's worth, my DS also doesn't like to learn new ways of doing math problems. Rightstart does try to show them different ways of attacking problems mentally, and then usually has a couple problems to illustrate the different way. Sometimes he'll come up with the answer using the way he's most comfortable with, and I'll say that's great, but we're going to practice it a different way for this problem. At this point he usually grumbles... which leads to the speech where I tell him that it's good to learn to do the problems in different ways, because sometimes one way is easier than another, but that after he understands both ways, he can of course do them whichever way he wants.

Later on down the road, sometimes he picks the more clunky way of doing the problem mentally and gets a problem wrong because of doing too many steps and basically just forgetting where he is in the problem. This is when I reintroduce a smoother way of doing the problem.

What I'm trying to say is, if you let him go ahead and do (especially these) 2 digit problems his way, when the numbers become larger and he has more difficulty holding them in his head and starts making mistakes, then you'll have a prime opportunity to show him regrouping again, and then hopefully he'll see it as a useful tool in some circumstances.

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With the problem you gave I would do it the way you say he does. When I got to 4 digit numbers I would switch to an algorithm. I wouldn't regroup but it is good to know how for the concept. But then he seems to understand the concept doesn't he?

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