Common Core Subtraction

[RobDownSouth]

Hmmm, if the WRONG answer is acceptable as long as the right procedure is used then it stands to reason that the RIGHT answer is acceptable even if the non-officially accepted method is used.

Ishmael

Classic Denying the antecedent logical fallacy.

 

[4est_4est_Gump]

If you all weren't so dead against common core, you'd notice that the method being taught is how we perform subtractions in our head. Following this technique does not require the use of paper and pencil and is of more practical use.

I've said this before when someone else- it may have been Julybaby- posted an example of common core mathematics and complained that they found it too complicated for young kids.

From the examples I seen posted in threads on Lit so far I have yet to see cause for concern.

No it's not.

I use recursion going from L to R using a peek to see if I will have to borrow. You can't keep all that adding straight in your head in a efficient manner especially at that age.

 

[4est_4est_Gump]

And you whiffed on the last paragraph. 4est's kid goes to a private school and uses four methods - which isn't a terrible idea. Public school kids? From what I understand, they're stuck with the bullshit method.

Nope.

That passage is by the author.

My remarks are not in a quote box.

 

[4est_4est_Gump]

WHen Throb cannot get my attention with race-baiting, he goes to sexualizing my daughter.

He is a sick, twisted puppy and should never be quoted or acknowledged.

 

[JAMESBJOHNSON]

No it's not.

I use recursion going from L to R using a peek to see if I will have to borrow. You can't keep all that adding straight in your head in a efficient manner especially at that age.

Youre right. Plus people use calculators
most of the time, and no pencil-paper computation can beat a calculator. So if youre checking the calculator result any process is as good as another.

 

[Late_Sleeper]

Always calculate these with grid paper, it avoids silly mistakes for even the best calculators.


"Left-to-right method" and "old granny method" aka "old American method" are similar things, except that you calculate from the wrong way, compared to the granny method.

The granny method seems to be easier with pen and paper though. Also it might be easier to do the granny method first, and only then proceed to the other method such as left-to-right method.

Granny method is also known as American method.

Wikipedia has a good comparison about the two methods. Scroll down to subtraction by hand. http://en.wikipedia.org/wiki/Subtraction


In the left-to-right method, you start from the hundreds, you proceed to tens, you proceed to ones...

In the old granny method, you start from the ones, you proceed to tens, you proceeds to hundreds...


Left-to-right method you have to remember that the sum of subtrahend and difference, cannot exceed the original minuend. Sum of the final result and subtrahend must be equal to, to the minuend

An example... 753 - 491 = x
753= x +491
x +491 = 753

x= difference, which we must calculate

You compare how many hundreds do I have to add, to 400 in order to get 700. You write three, into the hundreds bracket.

Then you proceed to tens. How many tens do I have to add to 90, in order to get 50. Obviously the question doesn't seem sensible, you have to add negative number. Wikipedia states, that if the number in the minuend, is smaller than the number of the subtrahend, then you must backtrack into previous bracket (in this case the hundreds bracket is the previous one)

Now you have to backtrack into the hundreds bracket. You erase three, and write two instead.

Then you carry over 10, into the tens bracket. The child calculates 15 -9 = 6. When you add 9+6 =15.

In reality though, the child is calculating 150-90 = 60, at this stage. Remember that 10, which you carried over from the hundreds bracket?

This become the following calculation 5x10 (already exists in the tens bracket because 50=5x10) + 10x10 (carried over from hundreds bracket into tens bracket) - 9x10 = 6x10. Once again, to validate 60+90=150.

Here's what you are actually doing at the calculation.

original calculation 753-491= X

X+ 491 = 753

To calculate X here's what we're doing:
How many hundreds do I add into 400, to make it 700= 3 into the hundreds bracket

How many tens do I add into 90, to make it 50 (in order to avoid negative number we do the following mental gymnastic... we are backtracking into the hundreds bracket, also an important reason is simply that 300+491 is already too big, when you compare it to 753, so the hundreds bracket must be less than 3. The difference, cannot begin with 3 in the hundreds bracket

hundreds bracket (3x100 -1x100) = 2x100

tens bracket (10x10 +5x10) -(9x10) = 6x10

ones bracket, how many ones do I add into 1, in order to make it into 3? The answer is 2x1 = 2


At the Final stage, the brackets combine into the final answer.
two hundreds + six tens + two ones

You had 2 in the hundreds bracket, you had 6 in the tens bracket, and you had 2 in the ones bracket.

The Final result 262 can be added into the subtrahend, to check if you calculated correctly.

If the sum of the result and the subtrahend is equal to, to the minuend, then you know that the correct difference has been achieved.

Of course, even with the granny method, you can check the validity of the result. Even in the granny method, the sum of the difference and subtrahend, must equal to, to the minuend.


Sometimes I calculate with granny method, sometimes I calculate with left-to-right method... I think both are nice in a way...

 

[RobDownSouth]

WHen Throb cannot get my attention with race-baiting, he goes to sexualizing my daughter.

He is a sick, twisted puppy and should never be quoted or acknowledged.

Pfft. Everyone knows you read each and every one of my posts.

You can't help it. You NEED to be teh victim.

 

[Boxlicker101]

If you all weren't so dead against common core, you'd notice that the method being taught is how we perform subtractions in our head. Following this technique does not require the use of paper and pencil and is of more practical use.

I've said this before when someone else- it may have been Julybaby- posted an example of common core mathematics and complained that they found it too complicated for young kids.

From the examples I seen posted in threads on Lit so far I have yet to see cause for concern.

I'm pretty good at doing math mentally, and I don't do it that way, and I doubt if anybody else does. There are just too many steps involved. I would start by saying "15 minus 8 is 7," then continue to "38 minus 3 is 28," then combine the two results so the difference would be 287. Of course, by just looking at the two numbers involved, I would have a good idea of the difference.

 

[Aquagal]

Talk about confusing, here's how the Chinese multiply.

http://m.youtube.com/watch?v=SO-qULaAwMY

 

[about_average]

That passage is by the author.

My remarks are not in a quote box.

I know, that was the reason for my post.

 

[sigh]

Hmmm, if the WRONG answer is acceptable as long as the right procedure is used then it stands to reason that the RIGHT answer is acceptable even if the non-officially accepted method is used.

Ishmael

Partial credit has long been a part of grading in both science and math, right up through college in even the most demanding fields. If you demonstrate an understanding of the process, that should be worth something. And how many times have students been penalized for getting the right answer, but not showing their work? It's long been accepted that you must show you understand the process. There's nothing new about that part of it at all.

Of course, once real life arrives, it's only the right answer that counts, and sometimes the wrong answer that kills. That's why I think it's also vital to teach kids how to estimate, so they'll know right away if their answer is way off. After a while you can do that subconsciously and just know when your answer can't be right. They never stressed estimation nearly enough when I was in school. That's something I taught myself.

As for the demonstrated problem in the OP, it wasn't intuitive to me. I found it difficult to understand the directions, though once I got it, it was okay. But I can't imagine doing math that way other than as an interesting game, though maybe that's just because I'm too ingrained in another method. They taught my kid a way of doing basic math by somehow using the knuckles of one hand and the fingertips of the other. That's not intuitive to me either, but he's a whiz at it. It's like some kind of unholy morphing of sign language and abacus, as best I can tell, and he never uses paper.

 

[4est_4est_Gump]

Do they add by subtraction?

What's worse is how they try to teach division for fractions. There's no such freaking thing, you multiply by the inverse. They try and teach Algebra as if you were doing sums. It's nothing more than a side-effect of degree inflation and the publish-or-perish mentality that permeates our top-heavy bloated government-educational complex.

 

[Ishmael]

Partial credit has long been a part of grading in both science and math, right up through college in even the most demanding fields. If you demonstrate an understanding of the process, that should be worth something. And how many times have students been penalized for getting the right answer, but not showing their work? It's long been accepted that you must show you understand the process. There's nothing new about that part of it at all.

Of course, once real life arrives, it's only the right answer that counts, and sometimes the wrong answer that kills. That's why I think it's also vital to teach kids how to estimate, so they'll know right away if their answer is way off. After a while you can do that subconsciously and just know when your answer can't be right. They never stressed estimation nearly enough when I was in school. That's something I taught myself.

As for the demonstrated problem in the OP, it wasn't intuitive to me. I found it difficult to understand the directions, though once I got it, it was okay. But I can't imagine doing math that way other than as an interesting game, though maybe that's just because I'm too ingrained in another method. They taught my kid a way of doing basic math by somehow using the knuckles of one hand and the fingertips of the other. That's not intuitive to me either, but he's a whiz at it. It's like some kind of unholy morphing of sign language and abacus, as best I can tell, and he never uses paper.

Sweetie, international testing shows that the US is weak in math and science. Obviously no one believes that to be a harbinger of good things to come. But this whole new technique of teaching math seems to me to be nothing more than "new math", round two.

Is this method being used by any of the nations that are out performing us? As far as I've been able to research they most decidedly are not!!!! OK, we can assume that this is a profound leap forward, but we've heard that song and dance before. Why hasn't this methodology been approached like any other scientific experiment? A study group and a control group to determine whether this methodology truly is the panacea its being held out to be? Again, to my knowledge this is NOT the case. It is the case of an attempt to use the entire school age population of the nation as lab rats to test an unproven methodology. And if it doesn't work an entire generation of school children is lost.

I'd like to see some empirical results BEFORE this is foisted on an entire generation of students.

Ishmael

 

[4est_4est_Gump]

The only thing they are learning is how to use a calculator and Google...



What constitutes thinking is how they feel about things.

 

[Ishmael]

The only thing they are learning is how to use a calculator and Google...



What constitutes thinking is how they feel about things.

If the battery industry ever collapsed we'd be back to stone tablets.

Ishmael

 

[4est_4est_Gump]

Our educated society no longer knows chisel from hammer.



Well, some do..., in theory; the "historical" school.

 

[Que]

The only thing they are learning is how to use a calculator and Google...



What constitutes thinking is how they feel about things.

Church.

The academic industrial complex removes critical thinking skills while claiming they are installing them. To them "critical thinking" is arriving at concurrence with liberal thinking.

 

[Ishmael]

Our educated society no longer knows chisel from hammer.



Well, some do..., in theory; the "historical" school.

*chuckle*

After all is said and done I have to admit that I do use a similar method to mentally calculate addition, subtraction, multiplication, etc. However I came to my shorthand technique after having mastered the traditional method.

Ishmael

 

[4est_4est_Gump]

Exactly.



Social Justice, the ever moving target which forces them to stay focused on Social Media to pick up on the clues to success.

 

[4est_4est_Gump]

*chuckle*

After all is said and done I have to admit that I do use a similar method to mentally calculate addition, subtraction, multiplication, etc. However I came to my shorthand technique after having mastered the traditional method.

Ishmael

The traditional method being tablet, chisel and Roman Numerals?

 

[Ishmael]

The traditional method being tablet, chisel and Roman Numerals?

I learned the Inca knotted string method.

Ishmael

 

[about_average]

The academic industrial complex removes critical thinking skills while claiming they are installing them. To them "critical thinking" is arriving at concurrence with liberal thinking.

It's interesting that the Republican party platform actually identified "critical thinking skills" as something that should be avoided in education and that students shouldn't have their beliefs challenged.
It's hard to teach critical thinking without challenging "fixed beliefs".

 

[4est_4est_Gump]

I learned the Inca knotted string method.

Ishmael

We counted corn kernels.

 

[Ishmael]

We counted corn kernels.

Sorted by color of course.

Ishmael

 

[4est_4est_Gump]

yellows were ones,

blues were tens,




and blacks were "many."