Math question about borrowing

[cam112198]

How do you guys teach 203-127? My daughter is having trouble understanding borrowing. CLE teaches to make the 3 a 13 and then cross out the 20 and make it a 19. I've never seen it taught that way. Any good resources for teaching subtraction?

[dcjlkplus3]

That how I *personally* would do that problem.

[SquirrellyMama]

I've never thought of doing it that way. I might give that to my kids as an option.

 

Kelly

[persephone43]

That's the way I do it too, except that I was taught to do it one step at a time. For example...I would make the 3 a 13, then the 0 a 9, then the 2 becomes a 1. Same thing just one more step.

[forty-two]

I'd pull out (or make) some base-10 blocks, or use a place value chart to visually show what is going on, and then talk her through it:

 

Let's look at the ones. Can you take 7 away from 3? No?

So what now? We need to regroup. So let's take a ten, and make it ten ones.

Oh, we don't *have* any tens - well, let's go take a hundred and make it ten tens:

 

100s_|_10s_|_1s_

__2__|__0__|_3__

-_1__|__2__|_7__

=>

100s_|_10s_|_1s_

__1__|_10__|_3__

-_1__|__2__|_7__

 

Now we can go, and take a ten, and make it ten ones:

100s_|_10s_|_1s_

__1__|_10__|_3__

-_1__|__2__|_7__

=>

100s_|_10s_|_1s_

__1__|__9__|_13_

-_1__|__2__|_7__

 

And now, can we subtract 7 from 13? Yes:

100s_|_10s_|_1s_

__1__|__9__|_13_

-_1__|__2__|_7__

_____|_____|_6__

 

And now we look at the tens. Can we subtract 2 from 9? Yes:

100s_|_10s_|_1s_

__1__|__9__|_13_

-_1__|__2__|_7__

_____|__7__|_6__

 

And now let's look at the hundreds. Can we subtract 1 from 1? Yes:

100s_|_10s_|_1s_

__1__|_9__|_13__

-_1__|__2__|_7__

__0__|__7__|_6__

 

So our answer is 76.

 

Does that help?

[Dinsfamily]

I'd pull out (or make) some base-10 blocks, or use a place value chart to visually show what is going on, and then talk her through it:

 

 

:iagree: base ten blocks are a great manipulative to show what's going on.

[mom31257]

Does she understand borrowing when you aren't borrowing across zero?

 

If so, then you are really just borrowing 10 from 200 because there is no ten in the tens place to borrow. 200 - 10 would be 190. If you present it that way, would she understand better?

[blessedmom3]

I like to use Maria Miller's video and blocks until my ds gets it. Then we just do it CLE's way but make sure my ds gets why we do it that way first.

 

 

 

By the way , I cannot imagine teaching regrouping without a base ten blocks. You can make these yourself or buy them , they are not too expensive . Also , borrowing is an incorrect term , I'd rather use regrouping .

Edited December 13, 2010 by blessedmom3

[Scarlett]

Does she understand borrowing when you aren't borrowing across zero?

 

If so, then you are really just borrowing 10 from 200 because there is no ten in the tens place to borrow. 200 - 10 would be 190. If you present it that way, would she understand better?

 

:iagree:

 

She needs to understand place value REALLY well.

 

manipulatives are the way to go at this stage.

[IsabelC]

I second the manipulatives suggestions as well. Most kids, even if they can memorize what to do, won't actually *get it* until they've seen it in some concrete form. But once they can understand an example like Forty-Two has set out, it's just a matter of personal preference whether to do the borrowing across the zero in one or two steps.

[Erica in OR]

Saxon uses money to show the borrowing concept, as a previous poster explained it with the base-ten blocks. The child receives money equal to the top number and then is asked to "pay for" the bottom number, as if in a store. They then go through the thought process for each of the places - do I have enough one dollar bills right now to pay what I owe in ones? If not, they start borrowing, changing a ten dollar bill for ones, or if that isn't possible, as in this problem, changing a hundred for ten ones, etc. They then pay the ones, tens, and hundreds owed, and can physically see and count the bills they have left to confirm the answer to the problem in a concrete way. Saxon 3 has students do this method for one or two lessons, then moves them on to doing it with writing the borrowed digits in the problem.

 

Erica in OR

[FO4UR]

Base ten blocks:iagree:

 

I start by seeing what the numbers look like in blocks. Which is greater? So we can subtract? (w/o going into neg numbers)

 

OK - but I can't take 7 ones away from 3 ones? What can I do?

 

dc: trade in a 10 rod for 10 ones.

 

OK - but we dont' have any 10 rods...what can we do?

 

dc: trade a hundred for 10 10 rods....good.

 

So lets move the rods around to make this work.

 

Then it's a matter of showing how to notate that on paper, which the way you described works...it's just a matter of your dc understanding how and why.

 

I use the manips on concepts until ds balks "I know, I KNOW!";)

[walkermamaof4]

Liping Ma's book would be very helpful to you: http://www.amazon.com/Knowing-Teaching-Elementary-Mathematics-Understanding/dp/0415873843/ref=sr_1_1?ie=UTF8&qid=1292298326&sr=8-1

 

She has great explanations for why it matters how you teach this, and all of math. I gleaned so much from that! if your library has it, you'll get a lot from it.

[MerryAtHope]

I see Base 10 blocks mentioned & just want to say that really helped here too! Teach the concept with the blocks first, have her trade a 10 for 10 ones & etc... to really see what needs to be done. Then show her how to write that process on paper after she can talk through what to do and show what to do with the blocks. We did this over a week--don't expect to do it all in one day.

 

Merry :-)

[susankenny]

I also use & teach the CLE way.

 

Susan

[katilac]

How do you guys teach 203-127? My daughter is having trouble understanding borrowing. CLE teaches to make the 3 a 13 and then cross out the 20 and make it a 19. I've never seen it taught that way. Any good resources for teaching subtraction?

 

How have you seen it taught? :confused:

 

I don't know any other way to do it; enlighten me!

[melmichigan]

We did this with CLE and SM. We made place value discs from markers, you need 20 for each number, a different color for each, 1's, 10's and 100's, (we have tried MUS blocks but the discs are easier to manipulate). We then just took the place value chart at the back of the LU and worked the problem out. My DD's will still pull them out on a difficult problem. I do teach with the middle step so that each row is addressed in each problem. Manipulatives are definately the way to go with large numbers for addition with carrying and subtraction with borrowing. :)

 

Eventually this is taught as a mental math problem and can be taught by making tens and ones, but that is later down the line. (There are three ones between 127 and 130, then 7 tens to 200, then 3 ones.)

Edited December 14, 2010 by melmichigan

[SquirrellyMama]

How have you seen it taught? :confused:

 

I don't know any other way to do it; enlighten me!

 

The way I understand it is that instead of saying "make the 3 into a thirteen, the 0 into a 9 and the 2 into a one" you would say "make the 3 into a thirteen and the 20 into a 19". Making this a two step instead of a three step.

 

My son was unimpressed. I'm always trying to make things easier and they never find them impressive.

 

Kelly

[katilac]

The way I understand it is that instead of saying "make the 3 into a thirteen, the 0 into a 9 and the 2 into a one" you would say "make the 3 into a thirteen and the 20 into a 19". Making this a two step instead of a three step.

 

My son was unimpressed. I'm always trying to make things easier and they never find them impressive.

 

Kelly

 

Oh. That's disappointing. I thought there was some whole new way I wasn't aware of :D

[NicksMama-Zack's Mama Too]

The way I understand it is that instead of saying "make the 3 into a thirteen, the 0 into a 9 and the 2 into a one" you would say "make the 3 into a thirteen and the 20 into a 19". Making this a two step instead of a three step.

 

My son was unimpressed. I'm always trying to make things easier and they never find them impressive.

 

Kelly

 

I would stress that you are taking 10 from 200 and now you have 13 and 190 on the top. I actually have my student cross out 203 and write 190 and 13 (sideways so it fits) above the number you are subtracting. I restate that 190 and 13 equal 203. You are not making 20 into 19, you are taking (borrowing implies that you are giving it back!) 10 from 200 and redistributing it to the "ones place". You are skipping an opportunity to emphasis place value with your student.

 

 

 

IMHO, the two most important concepts in elementary mathematics understanding place value and knowing that the fraction bar is really a division bar!

 

hth,

K

[RootAnn]

uses money

 

:iagree: I was teaching the concept of regrouping in subtraction (ten's place) to my dd#2 today. We used money. She *hates* the base ten blocks, but I do "force" her to use them sometimes. She much prefers money and it is easier to teach a reluctant child with something she likes.

 

That said, she could do the problem every time with money (while writing down on paper or the white board what she was doing and using the terms "tens" and "ones"). When we did it that way seven times, I asked her to do the final problem without the money (manipulatives). After much whining and "freaking out," she indicated that she couldn't do it because she didn't know how. :001_huh:

 

Anyway, manipulatives are only a start. Make sure your child understands place value and *I* found it was helpful to use the proper place value terms when teaching it rather than single digit numbers. I.e., the "20" is 20-tens or the "2" is 2-hundreds. Zero tens. Three ones. Etc.

[SquirrellyMama]

I would stress that you are taking 10 from 200 and now you have 13 and 190 on the top. I actually have my student cross out 203 and write 190 and 13 (sideways so it fits) above the number you are subtracting. I restate that 190 and 13 equal 203. You are not making 20 into 19' date=' you are taking (borrowing implies that you are giving it back!) 10 from 200 and redistributing it to the "ones place". You are skipping an opportunity to emphasis place value with your student.

 

 

 

IMHO, the two most important concepts in elementary mathematics understanding place value and knowing that the fraction bar is really a division bar!

 

hth,

K[/quote']

 

I was explaining it quickly on here. I actually tell a story when I explain borrowing that goes into place value and all that. I rarely miss an opportunity to get more words our of my mouth :001_smile:

[Ray]

Be aware of increased difficulty of carrying or regrouping across zero.

Expanded notation makes a good transition from Place-value discs to algorithm example (200 + 3) – (100 + 20 + 7)

 

Some mental arithmetic could be used to by giving 127, three fake ones to make 130 , crunch the numbers than add back the 3 extra you took away.

200 – 130 + 3 = 73

73 + 3 = 76

 

The attachment shows the 'dot' method that reduces clutter but ...Remembrall :glare:

 

We generally use mental math tricks for oral problems.

Edited December 14, 2010 by Ray

[hsbaby]

I would do it the way done in the OP. That's how I was taught.

[bairnmama]

I don't know if this will help, but I recently found instructions for a game that really reinforces place value and the reasons for regrouping. I made 3 columns on poster board and labled them "red", "blue", and "green". (Every player gets their own board.) You then need 1 red marker for each player, 30 blue markers, 30 green markers, and a deck of playing cards. You only use the Ace through 9 cards. You can use anything for the markers from construction paper squares to poker chips to counting tiles or figures. And I suppose even M&Ms would work if you were doing subtraction, lol!

 

To work on subraction and "borrowing", everyone starts out with 1 red marker on their board. Each player then draws a card on their turn and removes that many green markers from their board. If they don't have enough green, they must exchange a blue for 10 green. If they don't have any blue markers, they must exchange 1 red for 10 blue. The person who empties their board first wins.

 

To work on addition and "carrying", just play the opposite way. Everyone starts with an empty board and the goal is to be the first to get a red tile in the far left column by adding the number of green tiles shown on the card they drew and exchanging 10 green for one blue, etc.

 

My kids enjoyed playing it and it has really helped my dd with her understanding!

[s.z.ichigo]

How do you guys teach 203-127? My daughter is having trouble understanding borrowing. CLE teaches to make the 3 a 13 and then cross out the 20 and make it a 19. I've never seen it taught that way. Any good resources for teaching subtraction?

 

Saxon teaches this as well. I had been taught to borrow from the hundreds, then the tens. Seeing it done this was was a real revelation. It makes so much sense!

 

To really reinforce the concept, try frequently reffering to 200 as "twenty tens", or 203 as "twenty tens and three ones", etc.. It really helps my daughter see how all those number groups fit together..

[Susie in MS]

I like to use rubber banded bundles of Popsicle sticks in place of base 10 blocks. Just make bundles of 10, and for each 100 make 10 bundles of 10.

[cam112198]

Thanks so much for all of your wonderful suggestions!! We pulled out our base 10 blocks and I think she is understanding much better.