# How would you do this subtraction problem?

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Ok so I want to know if I'm crazy or not. Math is not my strong subject at all so I thought I would ask all of you how you would do it.

81,327

-45,189

Would you start in the ones column and regroup each column as you come to it or would you start with the 10,000's column and regroup starting there?

I would start in the ones column and regroup each column as I come to it but there is another person in my house that would start with the 10,000's column.

What say you hive?

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I think starting with ones is the typical way Americans have been taught to do math. Starting anywhere else seems very backwards to me unless you are trying to do it mentally with regrouping "tricks."

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Standard algorithm starts at the ones column, but it's perfectly valid to start at the other end.

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I think RightStart teaches both ways of doing it, and then says the child should use whichever way makes sense to him or her. But it's been a couple of years since I've looked at that level (was it Level C?), so I may have this muddled.

I go right to left, but I know that isn't the only way to do it. I think if you do a lot of mental math, going left to right works better.

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All the Americans I know go right to left, but I know a couple dozen Brits and they seem to all do left to right. My DD does left to right sometimes, she says it's 'easier for mental math' although I don't see HOW since you have to keep track of all the carrying AFTER the fact....

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The Constructivist way would be to start at the left with the 10,000. It's easier if you think about real life. Example:

"I want to buy a house that costs \$81,327. I have a down payment of \$45,189 saved. How much will money to I need to borrow?" If you were driving home from the Open House you would probably be thinking mentally "81,000-45,000 = 36,000. So I need to borrow about \$36,000." You probably wouldn't be thinking "7-9, can't do that, got to borrow from the 2 so put down a 1...."

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I think starting with ones is the typical way Americans have been taught to do math. Starting anywhere else seems very backwards to me unless you are trying to do it mentally with regrouping "tricks."

:iagree:

Or unless you're working specifically on estimation.

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Not just Americans.

In Germany, students are taught to begin with the ones.

I don't see how you could possibly start anywhere else without having to go back at some later point and fix your calculation: if you started 81,000-45,000 from the left, you'd do 8-4=4, but oops, because 5 is larger than 1 it's actually 3 and you'd have to go back and erase it... makes no sense to me.

If you start with the ones and work towards the larger places, , you do not have to erase anything

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Liping Ma explains this method in her book:

..81,327

-45,189

--------

..4

..362

..3614

..36148

Whereas the standard algorithm has you do this:

..7...21

..81,327

-45,189

--------

36,138

And looky there... I got the wrong answer in the top one AND it took longer to do. :D In Liping Ma, she mentions that starting from the left may be easier for smaller numbers and is certainly easier for mental math, but when doing larger numbers with pencil and paper, the standard algorithm is easier. This was actually a story about a teacher whose class didn't see the point in the standard algorithm. It's on pages 20-21 if you have the book.

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If it's a child wanting to do it that way, I'd have them show you that they know how to do it the other way a few times to make sure they understand. After that I would say that they can do it in a way that they can explain and produces the correct answer.

I usually go from the right, but sometimes it is easier when you look at the problem to do it from the left.

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Hm. Without a pencil I'd start from the 10,000. If I had a pencil and paper, I'd start at the ones.

That may seem wierd, but honestly, if I had to do it mentally starting from the ones, I'd forget what I had figured out already. If I start from the 10,000 and work towards the ones, it's easy enough to quickly look to the next lowest place value and see if regrouping is going to be necessary. I say the answer as I calculate it in my head, so I don't have to try to remember digits in the opposite order.

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Hm. Without a pencil I'd start from the 10,000. If I had a pencil and paper, I'd start at the ones.

Same here. I'm very good at mental math but with large numbers like this it usually is quicker (depending on how much distraction is around me) to work from the ones with paper and pencil.

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Liping Ma explains this method in her book:

..81,327

-45,189

--------

..4

..362

..3614

..36148

------ Ok see this is how much I know about math. I see where the 4 comes in but I'm lost on how one got the 362, 3614, or 36148 LOL

Whereas the standard algorithm has you do this:

..7...21

..81,327

-45,189

--------

36,138

And looky there... I got the wrong answer in the top one AND it took longer to do. :D In Liping Ma, she mentions that starting from the left may be easier for smaller numbers and is certainly easier for mental math, but when doing larger numbers with pencil and paper, the standard algorithm is easier. This was actually a story about a teacher whose class didn't see the point in the standard algorithm. It's on pages 20-21 if you have the book.

It was my son that started regrouping at the 8. He got the right answer but I also think there is more of a chance to make mistakes doing it that way. He says he learned it in BJU math. I don't know if it's regrouping tricks they taught him or something else. I'm with Liping Ma on this one. I think it would be fine for smaller numbers but a problem this size is asking for mistakes. But I am phobic of math so what do I know :lol:

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And without pen and paper I would be estimating until I found paper or wrote on my hand. :001_huh:

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Hm. Without a pencil I'd start from the 10,000. If I had a pencil and paper, I'd start at the ones.

That may seem wierd, but honestly, if I had to do it mentally starting from the ones, I'd forget what I had figured out already. If I start from the 10,000 and work towards the ones, it's easy enough to quickly look to the next lowest place value and see if regrouping is going to be necessary. I say the answer as I calculate it in my head, so I don't have to try to remember digits in the opposite order.

:iagree:

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I did some weird method mentally, based loosely on the RightStart math re-grouping I have been teaching my ds (which I never learned in school, so I've never been very good at mental math!:D) -

I saw that the 189 could be subtracted from the 327 pretty easily, so I skipped straight to the 81 - 45.

81-45 = 36 (figured mentally by saying 45 + 5 = 50 and I need 31 more to get to 81, so 31 + 5 = 36).

Then I went back to 327 - 189 and decided that 189 + 11 = 200, which means I would need 127 more to get to 327. 127 + 11 = 138.

36,138

If given something like that IRL, though, I likely would have pulled out pencil & paper and subtracted starting at the ones & carrying. That is definitely how I was taught in school In fact, this time last year (pre-RS math) even my "mental math" would have been basically doing the ones & carrying in my head - and I'd probably have messed it up along the way.

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I'd go left to right. It makes more sense to me that way.

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Ok so I want to know if I'm crazy or not. Math is not my strong subject at all so I thought I would ask all of you how you would do it.

81,327

-45,189

I would add the sum of 11 and 127 to 36,000 to get 36,138.
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Ohhh, ohhh, ohhh... I'm not alone. :D

I did some weird method mentally, based loosely on the RightStart math re-grouping I have been teaching my ds (which I never learned in school, so I've never been very good at mental math!:D) -

I saw that the 189 could be subtracted from the 327 pretty easily, so I skipped straight to the 81 - 45.

81-45 = 36 (figured mentally by saying 45 + 5 = 50 and I need 31 more to get to 81, so 31 + 5 = 36).

Then I went back to 327 - 189 and decided that 189 + 11 = 200, which means I would need 127 more to get to 327. 127 + 11 = 138.

36,138

If given something like that IRL, though, I likely would have pulled out pencil & paper and subtracted starting at the ones & carrying. That is definitely how I was taught in school In fact, this time last year (pre-RS math) even my "mental math" would have been basically doing the ones & carrying in my head - and I'd probably have messed it up along the way.

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I would REGROUP starting at the first digit that wouldn't have to be regrouped again... In this case the 3 in the hundreds place. But once I borrowed, I would do my actual subtracting from right to left.

Ex. 3 becomes 2, (1)2 becomes 11; and 7 becomes 17. Then I would subtract 9 from 17, 8 from 11, and 1 from 2. Then I would borrow from the 8 (becomes 7) to make the 1 an 11. Then subtract 5 from 11 and finally 4 from the 7.

Make sense?

Oh, and I don't think I could pull that off mentally. :D

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All the Americans I know go right to left, but I know a couple dozen Brits and they seem to all do left to right. My DD does left to right sometimes, she says it's 'easier for mental math' although I don't see HOW since you have to keep track of all the carrying AFTER the fact....

I'm a Brit and I start with the ones. That was how I was taught in the late sixties/seventies.

Laura

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I did some weird method mentally, based loosely on the RightStart math re-grouping I have been teaching my ds (which I never learned in school, so I've never been very good at mental math!:D) -

I saw that the 189 could be subtracted from the 327 pretty easily, so I skipped straight to the 81 - 45.

81-45 = 36 (figured mentally by saying 45 + 5 = 50 and I need 31 more to get to 81, so 31 + 5 = 36).

Then I went back to 327 - 189 and decided that 189 + 11 = 200, which means I would need 127 more to get to 327. 127 + 11 = 138.

36,138

If given something like that IRL, though, I likely would have pulled out pencil & paper and subtracted starting at the ones & carrying. That is definitely how I was taught in school In fact, this time last year (pre-RS math) even my "mental math" would have been basically doing the ones & carrying in my head - and I'd probably have messed it up along the way.

:iagree: Mentally I would do this.

Pen and paper, I'd start at the ones and regroup as necessary.

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I would add the sum of 11 and 127 to 36,000 to get 36,138.

We call this method "difference with tails" at our house.

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