# How to I teach borrowing ( subtraction) to

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one of my 1st grade twins. They are halfway through CLE maths 2 and they are doing great. But now we are doing borrowing, one of them keeps putting negative numbers for some of the questions. He has just finished arguing with me that in the problem 51-17 , 1-7 is -6, and 5-1 is 4, so the answer is -46. He refuses to consider borrowing because according to him that is 'stealing' and since he is not giving back the 1 ten again, he is not going to take it in the first place. Talk about twisted logic.

OH, well. Back to the table!

Elmeryl :confused:

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Do you use manipulatives to give him a visual? Or maybe make up a story about how the 10's column is very generous and doesn't care if the 1's column uses some of his units. He knows his reward is in heaven? LOL I've found that making up goofy stories sometimes helps.

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Do you have any manipulatives you can use? We have ones, tens, and hundreds blocks, but you could toothpicks or something else that would be fairly easy to "bundle" with a rubber band into tens. Then you could show him how you have to "unbundle" one of the tens to be able to take away the 7 ones. That might help him see the logic behind it.

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The curriculum we use (MCP) talks about "trading" rather than "borrowing." I also refer to "making a ten" or "breaking a ten." I used toothpicks wound in dental floss to "make a ten" and then unwound the floss to show how to "break" a ten, all the while emphasizing that it was still the same total number of toothpicks.

Would any of that help?

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regrouping. It sound so much less "sinful" than stealing. :-)

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Our math program also calls it trading. We use dimes and pennies for a visual and practiced each problem using the dimes and pennies before writing.

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Check out this site for some interesting algorithms.
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he seems to be getting it now, but he still feels sorry for the 'poor 10'.

Elmeryl:D

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Now I get why R&S 2 calls it "borrowing back" versus just borrowing. Maybe they thought of the same thing. And in this case the one is just borrowing back the ten that it originally had?

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You know, your ds is actually right when he says "1-7 = -6 and 5-1 = 4." The tricky part is to take his method to the next level. The "4" is really "forty" so when you take the forty that you have left and then subtract 6 (the -6 from the 1-7) you will have 34, which is the right answer.

Do you see what I mean? He's really quite brilliant! :)

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You know, your ds is actually right when he says "1-7 = -6 and 5-1 = 4." The tricky part is to take his method to the next level. The "4" is really "forty" so when you take the forty that you have left and then subtract 6 (the -6 from the 1-7) you will have 34, which is the right answer.

Do you see what I mean? He's really quite brilliant! :)

My oldest discovered this method. He did it for months.

We used dimes and pennies to show borrowing. Money really helps the child understand.

k

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On the Professor B Math site, there are some sample lessons for the level 1 CD. I think one of these lessons provides his "teaching story" about how to solve this kind of problem.

The gist of it is that there aren't enough ones in the ones place to subtract the number beneath them; they call out for "Help!" and the tens, living next door in the tens place, offer to send over one of their guys. The only problem is that "only ones can live in the ones place", so the ten rushes to the bank, exchanges one ten for ten ones, and runs back to the ones place. With enough ones in the ones place, subtraction can now proceed as usual.

The lessons are entertaining, and easily recalled, because they are presented as engaging stories.

When my ds 8 forgets how to do these problems, I need only say "Help!" and he recalls the sequence to solve the problem. He loves to act out the rushing off to the bank scene. I echo the suggestion of others; using money helped cement this concept for my ds.

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The child might see that nothing is being lost, just called something different that means the same thing (one 10 is renamed as 10 ones). You can still add up all the ones and tens and get the same number, 51.

I agree he is partially correct in his method, but the -6 would have to be added to the 4 tens (a positive 4 tens), and then you would get the correct answer, 36. Never thought about it that way before!:)

You might be able to show him on a number line, by counting backwards by 17 ("subtracting") that you don't go way past zero to the negative numbers, so his answer, though well thought out, can't be correct.

We use chalk on the driveway to draw dots in a place value chart, a la Singapore 2. Redraw a ten-dot as ten dots in the ones column. You might have to wait for the snow to go away.:rolleyes:

We also used dime-to-pennies trick.

That's cool that he has a reason for his method, and is really thinking.:D

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I taught my ds with beans. And the terminology is important...when I was a kid it was 'borrowing', but I think regrouping, makes much more sense.

I honestly believe that understanding place value is the basis for all math.

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I just played around with this and easily subtracted 4 digit numbers in my head this way. It makes left to right subtraction really simple. RightStart tried to teach up left to right sub. but I just couldn't get it and it was confusing my daughter--I wonder if this is what they were getting at.

Now I am wondering if I should teach this to my second grader who just started learning to borrow last week--or wait until the pencil and paper method is solidified.

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That's really very cute and quite clever.

We use poker chips and a home made place value chart. Perhaps that's another way, if tou need a change. But "unbundling" toothpicks is really excellent.

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I like the idea they have on the Serendipity blog to teach about place value using a rainbow. Ones are red, tens are orange, 100s are yellow, etc. and there are only 9 allowed in a column.

Now when it comes to subtraction I like the idea of telling the child that we are giving away to those who have less than we do.

So when we learn about re-grouping I tell a story like this: let us say that we are trying to do this problem 437-269. I will tell my children that 437 wants to give 269 away. But when we get to the ones place the poor 7 has a very giving heart and wants to give away 9 but just doesn't have it so she goes to her brother 3 to see if he will give her a ten. He has a generous heart and gives her a 10 so she becomes 17 and after she gives 9 away becomes 8.

Now the 3 is a 2 and he wants to give away 6 tens but does not have enough so he asks his older sister 4 for one of her 100s. She gives him one so that he now has 12 tens and is able to give away 6 of them to become 6.

Then the 4 who is now a 3 has her chance to give away 2 100s and becomes 1.

So the answer to 437-269 is 168.

My girls like all this generosity in subtraction and it makes it a lot more pleasant.

I also like to use the abacus for teaching subtraction.

Good luck and I hope this helps.:)

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This is how I teach my sons. I printed some fake money online.

I say to my son to put out \$32. So, he gets three tens and two ones. Then, I tell him to take \$7 from \$32.

He looks at the three tens and then he takes one ten. He changes that ten into ten ones. He moves it to the two. I tell him that he had to borrow that ten from the thirty in order help you take away seven. They totally understand borrowing with that concept. I do that with my younger son once a week.

I hope that helps.

Blessings,

Karen

http://www.homeschoolblogger.com/testimony

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