Anyone else's dc totally flummoxed by double digit addition/subtraction?

[FairProspects]

What did you do?

 

I'm :banghead: here. I'm not mathy and there are only so many ways I can explain this. Ds does not get why you move the tens over in 29-6 = ___, for example. He will stare at it and start crying. Ideas?

 

It probably doesn't help that I think he is flipping the digits around in his head and may not be able to tell which is the tens (he sometimes reads it 92). Ugh!

[kalanamak]

I used the SM terminology, not "moving over a ten", and I used pennies, dimes and dollar coins on a place value sheet. I found that moolah was what it took to make kiddo watch closely. :lol:

[Soror]

We are doing subtraction with borrowing now in Math here and it started him out with the abacus and also using the place value cards- have you done any of that? We had a few days of the easier ones with no borrowing and then back to the abacus and we started borrowing with one number and the last problems we did had borrowing with multiple places. The right start abacus was really helpful for this. On the backside is the beads for 1000s, 100s, 10s and 1s so it is very easy to see if you don't have enough ones you just trade in a ten. Does he not have the best grasp of place value? When doing RSB last year we had to do a break while we worked on place value. When going over the problems you can also stress that it is 2 tens 9 ones- 6 ones. Also, as I mentioned we used our cards a bit as well- we have cube cards that represent 1000s, 100 squares for 100, line of 10, then 1 cube(if that makes any sense). We used that a fair bit last year when first introducing the concept.

[GingerPoppy]

I love the base 10 blocks for this (or if you can't get your hands on any, you can draw them out or print them out on cardstock, cut them out, and you have the same thing).

 

You be the banker and have a good supply of ones.

 

Give him a problem--let's say 31 - 5. Get him to model the first number (three tens and a single unit).

 

Ask him to take away five single units. He will soon realize that he can only do that if he "goes to the bank" and changes one of his tens for 10 individual units. Then he removes 5 of them and can tell you how many are left.

 

After playing this for a few days, you can start to write each step on a whiteboard as you go along. So, when he goes to the bank, you show on the whiteboard that he's taking a "ten" from his tens column and replacing it with 10 units to put with his ones column.

 

Be sure he has a firm understanding of place value as you cover this topic.

[Trilliums]

http://nlvm.usu.edu/en/nav/frames_asid_155_g_2_t_1.html?from=category_g_2_t_1.html

 

This is an online virtual manipulative site which shows borrowing in double digit subtraction. The site has many fun and useful manipulatives to help with math concepts.

 

Also, for what it is worth, my son had a hard time with reversals until his teens. Once he reached a certain developmental stage, his math abilities grew tremendously snd he now excells in math. You might want to reinforce the idea of reading the problem from the left to right. To us this seems obvious, but I know my son needed the reinforcement. You could even use an arrow pointing to the first number of the math problem or have a horizontal arrow at the top of the page. My son has interesting ways of visualizing math which translates into creative problem solving but was frustrating for early reading and math skills.

[Farrar]

We're in the middle of subtraction with borrowing here but it's not been too bad.

 

I'm not even sure what is meant by move over the tens? Oh, as in just subtract the ones in that case? Okay, I guess I get it.

 

One of the things I've done with my kids before is make them do a "duh" check on their problems. If it's subtraction and the answer (the difference) is larger than the minuend, then that's a DUH. If it's addition and the answer is smaller than either of the addends, then that's a DUH. One of my ds was making some bizarre errors so we did this for a few days and he got better about not making what I termed silly errors - places where the answer couldn't possibly make sense.

 

Do you use manipulatives for this at all? An abacus or some C-rods? We always find it useful to go back to those when we get stuck. If your ds could see with the C-rods that the tens are clearly unaffected in that problem, then maybe that would help?

[blondeviolin]

I did this with candy.

 

You: Here are two tens and one group of nine. You eat six. How many candies do you have left?

Him: 26.

You: Did you have to break up the tens?

Him: No.

You: So you could just take them away from the units pile...

Him: Yes.

You: So that's why the two moves over...because that two really means "2 tens" or "twenty".

 

You might want to mention that twenty-nine is really twenty-and-nine.

[GingerPoppy]

I did this with candy.

 

You: Here are two tens and one group of nine. You eat six. How many candies do you have left?

Him: 26.

You: Did you have to break up the tens?

Him: No.

You: So you could just take them away from the units pile...

Him: Yes.

You: So that's why the two moves over...because that two really means "2 tens" or "twenty".

 

You might want to mention that twenty-nine is really twenty-and-nine.

Just trying to understand your method here--can you explain a little more what you mean by "the two moves over"? I'm probably tired and missing something here... :)

[FairProspects]

Do you use manipulatives for this at all? An abacus or some C-rods? We always find it useful to go back to those when we get stuck. If your ds could see with the C-rods that the tens are clearly unaffected in that problem, then maybe that would help?

 

This is what we have been doing working with both c-rods and the place value cards. It just doesn't seem to click. Its like we've run smack into a developmental wall. He can sort of muddle through if I do the c-rods for him, but he couldn't do it on his own so I'm not sure he "gets" it. I thought he had a good concept of place value, he did all of RS A and half of B, and whizzed through the MM chapter on place value, but double digits really have him confused (unless they are in columns and then spacially they are super easy).

[FairProspects]

Also, for what it is worth, my son had a hard time with reversals until his teens. Once he reached a certain developmental stage, his math abilities grew tremendously snd he now excells in math. You might want to reinforce the idea of reading the problem from the left to right. To us this seems obvious, but I know my son needed the reinforcement. You could even use an arrow pointing to the first number of the math problem or have a horizontal arrow at the top of the page. My son has interesting ways of visualizing math which translates into creative problem solving but was frustrating for early reading and math skills.

 

I think this is ds as well. He is definitely a late bloomer, and most likely VSL. It does make things like arithmetic tough!

[Alte Veste Academy]

I used the SM terminology, not "moving over a ten"

 

:iagree:

 

I love the base 10 blocks for this (or if you can't get your hands on any, you can draw them out or print them out on cardstock, cut them out, and you have the same thing).

 

You be the banker and have a good supply of ones.

 

Give him a problem--let's say 31 - 5. Get him to model the first number (three tens and a single unit).

 

Ask him to take away five single units. He will soon realize that he can only do that if he "goes to the bank" and changes one of his tens for 10 individual units. Then he removes 5 of them and can tell you how many are left.

 

After playing this for a few days, you can start to write each step on a whiteboard as you go along. So, when he goes to the bank, you show on the whiteboard that he's taking a "ten" from his tens column and replacing it with 10 units to put with his ones column.

 

Be sure he has a firm understanding of place value as you cover this topic.

 

:iagree: This is exactly the way I've taught my kids. So easy to understand this way!

[ElizabethB]

The right start abacus, exchanging beads, really helped my daughter get it, I had to try several things as well. Physically exchanging the beads and seeing the beads in their place value row has very helpful.

 

Money also got her attention, although that did not seem to actually make anything click. She did watch attentitively, though.

 

Have you had a vision check? It almost sounds like there might be a possibility of an underlying vision problem.

[prairiegirl]

We use the RS abacus as well to show double digit addition and subtraction. It works very well. I also use the terminlogy 'trading' as in trading 10 one beads for 1 ten bead. My kids, especially my math-challenged dd had no problem with double digits in doing it this way.

[blondeviolin]

Just trying to understand your method here--can you explain a little more what you mean by "the two moves over"? I'm probably tired and missing something here... :)

 

It was the OP's term. I believe her son was confused about why the "two moves over" to the other side of the equals sign...and that would be because the two groups of ten are untouched and not subtracted from. ;)

 

I also agree with farrar that this is a great problem to use c rods for it. It is so easy to see that you aren't moving any orange rods, just the units.

 

FWIW, when my oldest would get tripped up on a problem like this, I would emphasize "What is two-ten-nine minus six?" It really did help.

[LittleIzumi]

My VSL hit a wall with that, too. I actually ended up skipping to multiplication, which went over MUCH better, and working on her facts with daily math bingo, and we're slowly picking it back up now. I do like the money idea. I think that would go over well with dd. Hmmm....

[bnrmom]

I don't know what materials you are using, but I thought Math Mammoth 2A did a fantastic job explaining double digit addition and subtraction. My son got it right away. She doesn't start out with "moving" or "borrowing," but rather creating or breaking apart groups of tens.

[Lizzie in Ma]

What did you do?

 

I'm :banghead: here. I'm not mathy and there are only so many ways I can explain this. Ds does not get why you move the tens over in 29-6 = ___, for example. He will stare at it and start crying. Ideas?

 

It probably doesn't help that I think he is flipping the digits around in his head and may not be able to tell which is the tens (he sometimes reads it 92). Ugh!

 

I have found, on occasion, that it is a developmental difficulty more than one in understanding. I forget how old dd was when she hit a total block in subtraction but it was agonizing til I put it away for a couple of months. Picked it up again and all of a sudden she was fine. Worth a try?

[Edwena]

We do the arrow thing. Explain things with MUS blocks. The other thing is if the problem were 32-9, I have them circle the Bigger number. IF the bottom number is circled, then they have to borrow back. If the top number is circled just work as usual.

[Jess4879]

We had trouble with that concept here as well. We had to slow down and add in a bunch of games and hands on things to really get her to grasp what was going on. Does he understand place value? That might need a refresher before he will full grasp regrouping, also.

[In the Rain]

I love the base 10 blocks for this (or if you can't get your hands on any, you can draw them out or print them out on cardstock, cut them out, and you have the same thing).

 

You be the banker and have a good supply of ones.

 

Give him a problem--let's say 31 - 5. Get him to model the first number (three tens and a single unit).

 

Ask him to take away five single units. He will soon realize that he can only do that if he "goes to the bank" and changes one of his tens for 10 individual units. Then he removes 5 of them and can tell you how many are left.

 

After playing this for a few days, you can start to write each step on a whiteboard as you go along. So, when he goes to the bank, you show on the whiteboard that he's taking a "ten" from his tens column and replacing it with 10 units to put with his ones column.

 

Be sure he has a firm understanding of place value as you cover this topic.

 

:iagree: Base 10 blocks are awesome for helping kids with the concept of "trading in", "borrowing", or whatever you choose to call it. :D

 

Before working problems with the blocks we played a game called Race to 100. On each player's turn they roll a die and take that many blocks. At some point, the kids realize they can trade in units for "10 sticks". After every turn, they state what their new total is. After someone earns the "100 waffle" (as we call it), we race to 0. Sometimes we would write the scores on a white board for practice writing double digit numbers, and reinforcing place value. My kids love this game, and see it as a game, not math.

 

When we switched to solving problems on papers, I would refer back to the game, and they immediately understood what I was talking about.

[chepyl]

My son played on this software. It has a bean counting game that taught regrouping, I like thos term much better than borrowing or moving over, he had to add beans and regrouping them when there were more than 10 in the last jar, withheld subtraction he had to move the beans the other way. He loved it! When it came time to teach the topic on paper, he already knew what he was doing, O just taught him to write it out.

 

You can use manipulatives the same way. Just make bas of tens and a bowl for ones and start adding. I just Luke the computer because there was no mess to clean up ;)

[GingerPoppy]

:iagree: Base 10 blocks are awesome for helping kids with the concept of "trading in", "borrowing", or whatever you choose to call it. :D

 

Before working problems with the blocks we played a game called Race to 100. On each player's turn they roll a die and take that many blocks. At some point, the kids realize they can trade in units for "10 sticks". After every turn, they state what their new total is. After someone earns the "100 waffle" (as we call it), we race to 0. Sometimes we would write the scores on a white board for practice writing double digit numbers, and reinforcing place value. My kids love this game, and see it as a game, not math.

 

When we switched to solving problems on papers, I would refer back to the game, and they immediately understood what I was talking about.

That game sounds great! I'm going to borrow the idea and use it with students. Thanks!

[GingerPoppy]

It was the OP's term. I believe her son was confused about why the "two moves over" to the other side of the equals sign...and that would be because the two groups of ten are untouched and not subtracted from. ;)

 

I also agree with farrar that this is a great problem to use c rods for it. It is so easy to see that you aren't moving any orange rods, just the units.

 

FWIW, when my oldest would get tripped up on a problem like this, I would emphasize "What is two-ten-nine minus six?" It really did help.

 

Thanks for explaining. I see what you mean now. :)

[Haiku]

Ds does not get why you move the tens over in 29-6 = ___

 

I believe her son was confused about why the "two moves over" to the other side of the equals sign

 

If this is an accurate explanation of what you meant, then I would simply write the problem vertically, not horizontally, so that the ones line up in a column. Then he can see that you subtract from the ones but do nothing to the tens so they remain unchanged and are written as such in the answer.

 

Tara

[boscopup]

If this is an accurate explanation of what you meant, then I would simply write the problem vertically, not horizontally, so that the ones line up in a column. Then he can see that you subtract from the ones but do nothing to the tens so they remain unchanged and are written as such in the answer.

 

Tara

 

 

:iagree: You're working through MM1A chapter 7, right? I just looked at that, and I think I'd just do the columns step longer than what MM includes. Get some graph paper and transfer the horizontal problems to the graph paper and make them vertical. Continue to use your C-rods so you have your 2 orange rods and 9 white rods, then take away 6 of the white rods. Your 2 orange rods are still there, so it's 2 tens and 3 ones, or 23.

 

I also agree that if you're truly at a wall, you might head over to a completely different topic for a bit, then come back to it. If what he's learned in this chapter has been a struggle, his brain may need some time to absorb it.

 

This is a topic I'd want to get covered before doing addition/subtraction with regrouping in 2A, but there are some other topics you could hit in 2A before you hit that one. :)

[Sebastian (a lady)]

What did you do?

 

I'm :banghead: here. I'm not mathy and there are only so many ways I can explain this. Ds does not get why you move the tens over in 29-6 = ___, for example. He will stare at it and start crying. Ideas?

 

It probably doesn't help that I think he is flipping the digits around in his head and may not be able to tell which is the tens (he sometimes reads it 92). Ugh!

 

Money, money, money.

 

Grab a bunch of empty boxes from the kitchen or some toys. Label them with two digit prices. Have a good mix of prices that end in a digit > 5 and a digit < 5.

 

Then grab some pennies and dimes. Play store. Let him pick two things to buy and "pay" using the fewest number of coins (pennies and dimes only, keep nickels and quarters out of it).

 

If he's buying something that where the pennies add up to more than 9, then make him trade 10 pennies for a dime.

 

I wouldn't even tell him this is "math". Just tell him that you want to play a fun game. Do it for a couple days. Then you could add in "receipts" where he fills in the price of each item and the total price. Let him keep using the coins to figure out the price. You can model on the receipt the trading that he is doing (by showing the one carried into the tens place).

 

Then you can introduce some you model taking where he doesn't do the physical act of trading first, but plans through the total price by adding the numbers. Let him check his work using the coins.

 

It's ok to let the book sit there for a couple days while you work through this in a concrete way.

 

ETA: For subtraction, one person pays with a dollar and the other person makes change.

Edited February 3, 2012 by Sebastian (a lady)

[PollyOR]

...I used pennies, dimes and dollar coins on a place value sheet. I found that moolah was what it took to make kiddo watch closely. :lol:

 

Using money with a place value chart is what worked here too. And, my kids were older when I taught borrowing.

 

One more idea from Rod & Staff math ... have the child circle the larger number. This helps them see that they have to "make" the minuend(number on top) larger before they can subtract. (edit: this is for vertical problems)

Edited February 3, 2012 by PollyOR

[happypamama]

I had to relate it to food so that DD got what borrowing was. (I also stopped calling it "borrowing," because "regrouping" sounded more accurate.) Once I talked about how the tens were like hams, and the ones were the hams sliced into ten slices each, she understood. Relating math to food often works for her.

[EKS]

If this is an accurate explanation of what you meant, then I would simply write the problem vertically, not horizontally, so that the ones line up in a column. Then he can see that you subtract from the ones but do nothing to the tens so they remain unchanged and are written as such in the answer.

 

Tara

 

This. And I would be sure not to use terms like "move the two over" because it doesn't accurately reflect what's going on.

 

You also need to be sure he understands that 29 is a number, we are taking 6 away from it, and we want to know how much that is. It is *not* a 3 with the two "moved over." It is 23. Have him count out 29 counters, have him remove 6 of them, and have him count the remaining counters to reinforce this idea.

 

Then you can work on making sure he is understanding place value (because that is likely at the core of the problem). If you don't have one already, I'd invest in a set of base 10 blocks and have him do these problems with them.

[FairProspects]

Ok, I think that because MM tries to create a "helper" problem within a problem, they purposely set up the problem horizontally and basically tell you to ignore the tens and just focus on the ones (or maybe that is just my math-challenged interpretation of the technique).

 

However, this is causing the additional problem of ds not realizing that we are talking about "29" as a whole number since the problems keep asking him just to look at the ones and subtract. I think this is supposed be less intimidating since it is boiling it down to single digit subtraction, but in reality is actually more confusing for ds. It is probably a technique I should just avoid for him, and pull out the base-10 blocks instead.

[FairProspects]

Ack! Looking ahead I'm not even sure I can teach this to ds! Does math have to be taught this way?

 

Giving a problem 8 + 6 = ___ and then asking the student to think that the first number wants to be a 10? Is the student supposed to split the 6 into 4 & 2 in their head? Honestly, thinking about math like that makes my head hurt and I don't think ds has the number bonds memorized well enough to do this in his head. He has serious math fact issues.

 

I can't even conceive of how best to present this spatially with c-rods. Ds won't know what he needs to make the 8 into a 10 because he doesn't have his 10 number bonds memorized. So, do I line up the 8 next to a 10 c-rod and ask him to find the difference? Then do I put the 2 next to the 6 and ask him to find the other part of the bond and add them? Do you see how many steps that is? Ds would never figure out (and remember) how to compare all that on his own. Is he supposed to? Because of working memory problems he can't remember that many steps to find an answer.

 

I do not feel confident teaching this way because I don't even feel like my brain gets it. I certainly can't anticipate how to explain and scaffold this for a kid with LDs! So frustrated!

[GingerPoppy]

Ack! Looking ahead I'm not even sure I can teach this to ds! Does math have to be taught this way?

 

Giving a problem 8 + 6 = ___ and then asking the student to think that the first number wants to be a 10? Is the student supposed to split the 6 into 4 & 2 in their head? Honestly, thinking about math like that makes my head hurt and I don't think ds has the number bonds memorized well enough to do this in his head. He has serious math fact issues.

 

I can't even conceive of how best to present this spatially with c-rods. Ds won't know what he needs to make the 8 into a 10 because he doesn't have his 10 number bonds memorized. So, do I line up the 8 next to a 10 c-rod and ask him to find the difference? Then do I put the 2 next to the 6 and ask him to find the other part of the bond and add them? Do you see how many steps that is? Ds would never figure out (and remember) how to compare all that on his own. Is he supposed to? Because of working memory problems he can't remember that many steps to find an answer.

 

I do not feel confident teaching this way because I don't even feel like my brain gets it. I certainly can't anticipate how to explain and scaffold this for a kid with LDs! So frustrated!

 

Only you know what's best for your child, but I find it to be a very strong way of teaching math. It feels a bit unusual and laborious at the beginning, but soon you will just "see" the actions and the answer in your head. I find it much stronger than straight up memorization of the facts.

 

Here's how I teach it at first:

 

Above the 8, draw eight little dots in two columns (so that it is obvious at first glance that, first of all, there are 8 dots, and second of all, there's a spot at the bottom for 2 more dots to make a 10). Draw a rectangle around the dots, leaving the correct amount of space for exactly 2 more dots.

 

Now draw six dots above the 6, again in columns so yours child can see there are 6 at first glance.

 

Make it a story. Maybe the first number is always trying to have EXACTLY ten dots in his box. The dots might be rubber bouncing balls, and the guy needs ten balls to fit the spots in his box. The second number is always polite, and offers to share some of his balls. Let your son circle the correct number of balls from the polite guy, then draw an arrow from the circled balls to the empty spots.

 

Ask him: How many does the polite guy have left? (4) And 10 plus 4 can be done instantly in his head to come up with 14.

 

If may feel like the long way around at first, but it should pay off. Let him use dots until it becomes easy. Later, when he's really familiar with the process, see if he can picture the dots *in his head* moving over to fill the first guy's box. He will eventually be able to also "see" how many would be left with the polite guy.

 

If you can master this, it virtually does away with finger counting, counting up, counting down, and other inefficient ways of adding and subtracting. It can also be applied to more advanced mental math.

[Farrar]

My kids both got to a point with this in MM where the helper problems were doing more harm than help. For one of my ds, he needed the helper problems when he was doing 8+6 and 9+4 and so forth. It was useful for him to learn to envision the 4 handing one over to 9 because it wanted to be 10 and then seeing the problem as 10+3.

 

However, then he did some other stuff and got to the part where MM was trying to teach things like 39+4 and wanted him to do the helper problem again. It was so ingrained in him at this point that the helper problems actually confused him. He was like, but I already did that! It's 43! What's that there? I had to make him skip around a little and avoid them.

 

I think the value in the MM system is that they teach lots of different ways of seeing the numbers and strategies for solving and thinking about simple problems. I think if a child doesn't get what the "trick" or the strategy is, then it's worth trying to get them to do the helper problems and see the point of the strategy. On the other hand, if the helper problem is getting in the way of the child using the strategy, then I think it's fine to skip it. You just have to evaluate for yourself if you kid gets it or not.

[Trilliums]

Maybe he should just work on math facts that add to 10 and 5. I see this helped my kids tremendously with later math and multiplication facts. Dimes, nickles and pennies could be a good way to go. I also remember using weighted numbers and a balance. Nothing wrong with taking it slowly. :)

[Rivka]

This. And I would be sure not to use terms like "move the two over" because it doesn't accurately reflect what's going on.

 

You also need to be sure he understands that 29 is a number, we are taking 6 away from it, and we want to know how much that is. It is *not* a 3 with the two "moved over." It is 23. Have him count out 29 counters, have him remove 6 of them, and have him count the remaining counters to reinforce this idea.

 

:iagree::iagree::iagree:

 

That number is not a 2, it's a 20. I would banish the practice of calling it a 2 in a problem like this.

 

Dimes and pennies seem like the easiest and most concrete way to cover this. You have 2 dimes and 9 pennies, and you want to buy a piece of candy that costs 6 cents. Do you need to spend any of your dimes? No, you have enough pennies! Cool, you still have both dimes left. You still have 23 cents left after you pay for the candy.

 

You could also draw a long number line on the sidewalk outside and practice moving up and down it to solve addition and subtraction problems.

 

I feel like MEP explains the concepts behind double-digit addition and subtraction really well in 2a. MEP is a free curriculum, so you might take a look and see if you want to supplement with that for a while.

[blondeviolin]

Ack! Looking ahead I'm not even sure I can teach this to ds! Does math have to be taught this way?

 

Giving a problem 8 + 6 = ___ and then asking the student to think that the first number wants to be a 10? Is the student supposed to split the 6 into 4 & 2 in their head? Honestly, thinking about math like that makes my head hurt and I don't think ds has the number bonds memorized well enough to do this in his head. He has serious math fact issues.

 

I can't even conceive of how best to present this spatially with c-rods. Ds won't know what he needs to make the 8 into a 10 because he doesn't have his 10 number bonds memorized. So, do I line up the 8 next to a 10 c-rod and ask him to find the difference? Then do I put the 2 next to the 6 and ask him to find the other part of the bond and add them? Do you see how many steps that is? Ds would never figure out (and remember) how to compare all that on his own. Is he supposed to? Because of working memory problems he can't remember that many steps to find an answer.

 

I do not feel confident teaching this way because I don't even feel like my brain gets it. I certainly can't anticipate how to explain and scaffold this for a kid with LDs! So frustrated!

 

Sounds like he might need more time to just build with the rods. When I do problems like 8+6=8+2+4, we pull out the rods, and I say, "How many to make the 8 a 10?" He should really be able to see that it is 2. Then I would say, "Now how many more do you need to make it the full 6 you'll add?" and she would respond with, "4", thus 10 and 4 is 14.

 

The rods make this easy to "see". When you lay a brown and dark green in a train and place an orange on top of that, you can see that the orange extends into the dark green by the length of a red rod. What else does it take to make the red rod the length of the dark green rod? Why a purple one of course! (The elegance of C rods is so amazing to me.)

 

You might consider trying to work through some Miquon for some confidence with those rods. At the very least, encourage him to build with them and be able to feel and see the relational differences between the rods. Before we did ANY adding or subtracting with them, I made sure my five-year-old could tell me the order up and back without looking or touching. Working through some of the Gattegno Textbook 1 might also help with familiarization.

[peacefully]

.

[Kathleen in LV]

I don't know what materials you are using, but I thought Math Mammoth 2A did a fantastic job explaining double digit addition and subtraction. My son got it right away. She doesn't start out with "moving" or "borrowing," but rather creating or breaking apart groups of tens.

 

In a similar vein, the Liping Ma book describes the approach used in China, where they present the concepts of "composing" a ten (or hundred or thousand) for addition and "decomposing" a ten for subtraction. I think it's much more helpful to describe to the child what is actually happening, rather than using terms like "carrying" or "borrowing".

 

Ma's book also discusses that the Chinese put a lot of effort into children mastering the addition facts to numbers between 10 & 20 as a prerequisite to tackling higher numbers.

 

I agree with other posters that base ten blocks & similar manipulatives can be very valuable in this regard.

[FairProspects]

And after all that, I introduced the "Going over/Making Tens" lesson today, expecting big problems and ds said that this was the most fun technique he had ever learned in math and completed all problems immediately w/o rods, w/o a hitch. :svengo:

 

The kid cannot complete basic addition/subtraction problems, but re-grouping by tens to do them apparently makes complete sense. I should have known that if it throws me, it would instantly click with his brain! :lol: