This is a fun example of common core. (nope I am not going to say it isn't common core) This is in fact a perfect example of common core, it looks very intimidating in this explanation of it though so I will explain all the fun to you guys in a moment.
So many (or at least my teachers taught my classes) of us were taught the "old way" of doing simple subtraction (10-9=) (7-4=) (etc....) two different ways. The "normal" way of starting at the first number and counting down the number of places from the second number.
examples;
(10-9=) start at 10. Go down 9 places. 10,(9,8,7,6,5,4,3,2,1) (leaving you at 1 being the answer)
(7-4=) start at 7. Go down 4 places. 7,(6,5,4,3) (leaving you at 3 being your answer)
Following so far? awesome.
The other way my teachers called the count up method. It's where you would start at the second number and count up the number of places until you made it to the first number.
examples;
(10-9=) start at 9. 9, (10). you only moved up 1 space. Answer = 1 (same as before)
(7-4=) start at 4. 4, (5,6,7). moved up 3 spaces. Answer = 3 (same as before)
With this smaller scale of math the count up method of math is super easy. Sure there would be math problems like (10-1=) which would be easier to start at 10 and count down.
So with a bigger math problems; (examples;)
54-3= (easier to count down from 54, 3 times) 54,(53,52,51) Answer = 51.
54-52= (easier to count up from 52 to get to 54) 52,(53,54) Answer = 2
*Both of these methods are still perfectly correct in common core math.*
Also, the other way of writing out the problems is still correct. Examples;
54 54
-3 -52 (This way your just separating by 1s,10s etc.)
___ ____
51 02
Or if your a visual math person you can take out $0.54 and do these same problems by removing the change that your subtracting.
Lots of different ways already to do / teach/ learn math. These are all the old ways BUT are all still considered "common core math" Whichever way helps you to visualize and do math in your head.
"But Jared! what about when we have to borrow from other places in subtraction problems?"
Happy you asked! The only time the borrowing processes is easy to see is when its written on paper with one number on top of the other number. Otherwise it becomes very difficult to keep track of all those tiny edits to your original number. This is because doing subtraction this way is a very linear process to math. All the numbers are in blocks that you would then have to take from to move around (borrow from) and realistically create an equally annoying number to work with mentally.
EXAMPLE;
TENS ONES
57 5 7
-38 (your basically seeing it like this)--> - 3 8
____ _______________
_______________________________________________________
Yes, that is how I that problem when I write it out that way.
Okay great! So you start doing the problem but right away you notice you need to borrow. You can't take 8 out of 7. It would be like your friend taking away 8 of your 7 pennies when you still have dimes in your other pocket. So you would borrow from the other pocket (in this case trading another friend 10 pennies for your dime)
The problem now is you just dumped all of your pennies into one pile even though you only needed 1 penny from the pile you already had. Giving you 17 pennies. So now you have an entirely different double digit math problem in your math problem.
5 7 (then would become)
-3 8 -3 8
______ ______________
_________________________________________________________
"Yea Jared whats your point?"
My point is that you are now stuck with 17-8. A 2 digit number subtracted by a 1 digit number. When the point of this processes was to separate 10's from the 1's places.
So now your math problem inside your other math problem. You now have to fall back on the other methods of subtraction. The only way said you either counted it up, or counted it down. HOWEVER! if you have read my previous blog on subtraction you know there are other ways to do this problem.
The examples of other ways to do it would be to separate some of the numbers.
"BUT THATS SO MUCH MORE WORK!!!!!! "
On paper yes it does look like more work. BUT mentally (with a little practice) it becomes MUCH less work.
Examples; Parenthesis to show the break down of one number.
[10(+)7] would be more closely understood as [10 AND 7] <---because the combination would be 17.
17-8= 17-8=
[10(+)7]-8= 17-[7(+)1]=
move 1 from 10 -->7 Subtract the 7 first.
[9(+)8]-8= 17-7=10 Then subtract the remaining 1 from the answer
9+8-8=9 10-1=9
On paper it seems like a LOT more work. However if you think about it in your head it is MUCH easier to do. (17-7-1=) VS (17... 16,15,14,13,12,11,10,9)
But I can do that problem in my head just by looking at it!
This small of a question would be something to teach to a 1st or 2nd grader. When you were 6-7 years old could you look at 17-8 and instantly know that it was 9? (a few of you yes. the majority probably not and we would have to utilize some other way other then just memory)
MOVING ON!...... now you know that (
- 3 8 (17...16,15,14,13,12,11,10,9)
__________
1 9
Suddenly this way seems like it would be a lot more work to a kid trying to learn this way. So maybe the written out version of "common core" math isn't as much "extra" work.
Now for (one of many) common core ways of doing this problem
57-38= (same as before but this time we break down numbers)
[50(+)7]-[30(+)7(+)1]=
now the ones and tens are separated in a way that can be subtracted without borrowing.
50-30=20
7-7=0
1=1
turning your annoying math problem into;
20-1=19
(simplified version on paper would look like this)
57-38=
50-30=20
7-7=0
1=1
20-1=19
(or as you develop your mental math skills you downsize the work into)
57-38=
20-1=19
Because mentally removing the 7-7 from the equation is very easy. and 50-30 is easy also. Leaving only that remaining 1 at the end to subtract from 20. BOOM! common core mental math short cut.
"That still never explained the math problem in the picture at the top of this post."
Oh right! back to that. 54-27...... In that picture the "old way" looks like much less work then the new way. BUT as I just finished pointing out, that is because all the shortcuts are added to the "old way" but EVERY thing is written out in the "new way".
OLD WAY NEW WAY
5 4 54-27=
-2 7 from math problem-->27+(3)=30 <-- nice even 10's
______ 30+(20)=50 <-- closest 10's to 54
50+(4)=54 <--from math problem
(borrowing) (20)+(3)+(4)= 27
This can be done very easy in your head
- 2 7
________ -OR-
14...13,12,11,10,9,8,7 54-27=
27+(3)= 30+(20)= 50+(4)=54
- 2 7
________
2 7
Answer:27
Too many different numbers to
keep track of with borrowing
process.
(only very few people can do mentally)
So basically without shortcuts of mental math here and there it all looks like TONS of work. The more mental math the less work it seems like. "Common Core" math promotes the process of mental math therefore in the near future of using it you will pretty much drop most if not ALL of the actual work behind it and just be able to do it mentally.
The old way is not wrong........I REPEAT!
THE OLD WAY IS NOT WRONG!!!!
"But my child's teacher gave my kid a bad grade for not doing it their way."
If your teacher is giving your child a bad grade for not following "the correct path" then the teacher is teaching the way they use to. I use to fail math all the time growing up because my brain processes numbers in the "new way" but that was "unacceptable". "A 7 is a 7. Not a (3+4) or a (6+1) or a (2+5)."<-- read that in a 60 year old math teachers voice. When we all know that it is Technically the same. For instance a 5 year old counting on their fingers can be considered "new math" counting to 7 is (1+1+1+1+1+1+1)
Common core math only ADDs new ways of doing the same math. More paths to the same answer equals more fun in math as well as being able to find a better path for each person. Some people run to a destination while others would rather swim (or fly or dance)
So if you feel more comfortable doing it the "old way" keep doing it that way. If a teacher fails you or your child for not doing it right. Send said teacher to this blog. They can learn what common core is. An guideline of how to add more creative approaches to math. Some people are linear thinkers (old way) while other people are creative thinkers (new ways).
If the understanding of how numbers flow and fit together is there. Then the answer should come out correct. (with the occasional human error here and there.) As long as you are showing your process as to how you got to the correct answer then as far as "common core math" is concerned CONGRATULATIONS your a math wizard.
