Please help my dd with subtraction with borrowing!

[cathmom]

She has had this problem for several years. Let's say the problem is 251-178. In order to solve the problem, you have to borrow from the 5 in 251 and make it a 4, and then the 1 becomes an 11. Subtract 8 from 11, move on to the tens. All well and good.

 

Several years ago, she was having this problem: she wants to do 8-1. I finally got her to memorize that if the bottom number is bigger than the top number you must borrow.

 

Now she is doing MUS Gamma (multiplication), and on a review sheet, there was subtraction with borrowing. She did the problems the way she used to do them. I reminded her that if the bottom number is bigger, you have to borrow. She said, "Why? Why can't you just subtract 1 from 8?" So I got out the MUS blocks and showed her the problem. "I only have one unit here, but I need to subtract 8. I can get 8 by trading in this ten for ten units." I traded the blocks. "Now I only have 4 tens, but 11 units. Now I can take 8 away and I have 3 left."

 

She still doesn't understand. Can anyone think of a way to clearly explain why you cannot subtract up? I actually was trying to figure out if there was a way to do it, and came up with doing it this way: 8-1 is 7, make it a negative 7, add ten, you have 3. But you would still have to remember to take away one of the tens. That method would probably confuse her more, but I was just trying to see if there was some way to go with her natural inclination. I guess her real problem is that she thinks the commutative property should apply to subtraction and it doesn't.

 

BTW, if you have read my other posts about math, this is the child who developed a math phobia from Saxon. She still is pretty fragile with math, although she's much better than she used to be. But this apparently is a real stumbling block for her. Any help would be appreciated!

[EKS]

251 is a number and she is taking 178 away from it. It is not just three columns lined up next to each other that have no relationship to one another. Get out 251 counters and have her take 178 away (not MUS blocks but beans or bears or something that you have 251 of). What does she get? Does her way get the same answer?

 

If she decides to do 8-1 because it is convenient, then she is doing the problem 258-171. If she decides to do 7-5 on the next column then she is doing 278-151. And this isn't the same problem.

 

It isn't about subtracting columns of numbers. It's about subtracting one number from another. We use columns for convenience.

 

I'd make her do these problems mentally until she really internalizes what she's doing. So for the problem we 251-178 here is what you'd do. 251-100 is 151. 151-70 is 81. 81-8 is 73. Start out with numbers that are smaller and easier and work your way up to problems like this. You need to get away from the standard algorithm for a bit because she has completely misunderstood it.

 

She can't just memorize that you have to borrow if the bottom number is bigger. She needs to know why and she needs to internalize that understanding if it is to stick.

[cathmom]

Thank you for those suggestions! I think they will help. You're right - she is seeing the three columns as 3 separate numbers with no relationship to one another.

[TengoFive]

It took my kids quite a while to get this concept. I had them build every problem for a long, long time with the MUS blocks. Have you had her try building the whole problem herself?

[Sasharowan]

I used money to illustrate this to my kids. If you have 1 dollar and the toy is 8 dollars, can you buy it? No, because 1 is less than 8. Therefore, you cannot take 8 out of 1 because it is not there to take. That with a LOT of repetition of "the bottom number comes out of the top one."

[FO4UR]

Base ten blocks would be a good manipulative to use for this problem. I have a blue set and a pink set so I would pull out 251 pink (2 100 boards, 5 10 rods, and 1 one block) and 178 blue (same way). She would then see that she would have to trade the blocks around to make 251 into 100 boards, 14 tens , and 11 ones in order to subtract.

 

I would stress that we aren't borrowing b/c we aren't giving anything back...we are really rearranging the ones, tens, and hundreds in order to be able to subtract easily. We cannot subtract a pink from a blue in the ones and then a blue from a pink in the hundreds...b/c each color is its own number.

 

All the King's Tens in the Sir Cumference series is a good way to hit place value outside of the math book.

[Greta]

Thank you for those suggestions! I think they will help. You're right - she is seeing the three columns as 3 separate numbers with no relationship to one another.

 

Then I would do some activities demonstrating place value. Does she understand, and I mean *really* understand, that one ten is ten ones? And that 71 is seven tens and one unit, OR six tens and eleven units, or five tens and twenty one units, etc? Does she understand that 200 is twenty tens and 2000 is twenty hundreds? An abacus is an excellent tool for this. I'm sure there are others, and maybe other people can chime in here. The abacus is what we've always used, and it has taught this concept very well. (We use the RightStart abacus.)

[2squared]

You could have her count up to check her answer.

178+2=180, 180+20=200, 200+51=251

 

51+20=71, 71+2=73

 

We are doing Level C in RightStart, and they introduce subtraction by having the kids count up.

 

I do think the mental math is a great idea. Does she truly understand place value?

[Ray]

I cannot get the 70 + 3 = 73 to line up... should be under the tens/ones to the right side.

 

251 = 100 + 140 + 11

-178= 100 + 70 + 8

70 + 3 = 73

 

Another example:

 

34 = 20 + 14

- 15 = 10 + 5

10 + 9 = 19

[cathmom]

Thank you! I believe she does understand place value. She always seems to get it when it applies to money - maybe I will make a bunch of money problems.

[kalanamak]

Any help would be appreciated!

 

My son got this with coins. I'd lay out dimes and pennies and ask to him subtract some amount. If he needed to "deconstruct a 10" (yes, I'm reading Liping Ma again), he had to pick up a dime and trade it for a pair of 5-stacked pennies. (I prestacked so we didn't spend all day counting).

Later, using a stamp for making dimes and pennies, he learned to cross a dime out and just "know" that there were now, e.g. 14 pennies instead of 4 in the penny area.

 

What we are working on now, to solidify this is something like

74-56. Son does 74-50=24, and then he does 24-6 to get the answer. Oddly (it seems odd to me) he has no trouble with the 24-6, but is having trouble getting back by 10s. One darned thing after another, as my mother used to say.

[ElizabethB]

The RS abacus with exchanging beads was helpful for my daughter.

 

When she gets the order wrong, I inform her, "no, that would be negative 3." Money examples are also helpful. Talking about the negative numbers is helpful, and also expands her math knowledge while explaining her mistakes. She has a fairly sound understanding of negative numbers now, my husband asked about something and she correctly answered that the answer was a negative number!

[sagira]

I believe if you go on Youtube and type in Math Mammoth, you can find Maria Miller explaining subtraction with regrouping on a whiteboard.

[Dana]

She has had this problem for several years. Let's say the problem is 251-178. In order to solve the problem, you have to borrow from the 5 in 251 and make it a 4, and then the 1 becomes an 11. Subtract 8 from 11, move on to the tens. All well and good.

 

Several years ago, she was having this problem: she wants to do 8-1. I finally got her to memorize that if the bottom number is bigger than the top number you must borrow.

 

I am glad to hear that my son isn't the only one who has done this.

He does seem to understand place value. I think with him it was more that he's trying to get the problem done quickly and he wasn't wanting to show much work.

 

When I saw him do a problem incorrectly, we pulled out the base-10 blocks and I'd have him rework the problem using the blocks, then write it out with the "borrowing" shortcuts. I think he finally figured out that doing it correctly the first time took less time. He's been making the error less often.

 

We also did the "four sentences" to help him see all possibilities (so for 7-3=4, you also have 7-4=3, 3+4=7, and 4+3=7). I'd have him check his work by doing the corresponding addition problem. Sometimes he'd see that faster than by using the blocks.

[DarlaS]

Base ten blocks would be a good manipulative to use for this problem.

 

:iagree:

 

I finally bought a set and I don't know how I taught place value without them. When they come out for my youngest, even my older kids will watch and "help". They're just really neat to have.

 

I don't have two sets though, so we'd just make 2 hundreds, 5 tens and a 1 unit and she would have to trade the tens for ones etc. until she could show me the separate pile of blocks that equaled 178. Then we'd see what was left. Over and over if necessary.

[MerryAtHope]

When we went through this, I went totally away from paper for a few days & just used Base 10 blocks. You could do it with MUS blocks but I'd just use the 100's, 10's & 1's for now. We did all kinds of problems with just the blocks. When they consistently did them correctly, then I started writing the problem on a white board. They still did the blocks, and I showed how to write that down. Then I had them talk me through writing it down. My next step was to let them write on the white board, but I talked them through if needed and we still did each step with the blocks. Then finally they could do it all by themselves.

 

One final thing that helped here--I had my kids draw a down arrow on the right side of the problem to remind them that they couldn't reverse the way they subtract--they have to start with the top number and go down. If the problem is written horizontally, I had them rewrite it vertically if needed.

 

Hang in there! Merry :-)

[Guest Cheryl in SoCal]

Is there any way you could get your hands on the Alpha DVD and Decimal Street?

[cathmom]

I believe that she understands place value and borrowing - it's understanding the convention of subtracting down. Thank you for all the suggestions!