8+5= (for us adults its easier to do it in our head) BOOM answers 13.
But what about the children just learning?
They think we are just magic guessers of the answer.
The old math VS the new math. There is really no difference to it if you really think about how we teach addition.
example of the old way. We teach kids at first to count on their fingers or dots on paper.
They hold the number 8 in their minds and count up one at a time adding 5 more to it.
On paper that would look like this 8+(1+1+1+1+1)=13.
But silly thing is during this process they make a 10 appear in their heads. 8+1+1=10.
Seeing such stuff on paper makes it easier to understand how numbers flow together. 8+5=13. Not because we are force to memorize it but because it teaches our minds to factor all the numbers into a different form to better understand how they connect.
As you get better at numbers not everyone needs to break numbers into 1's. They can be broken up into anything.
example;
8+5 <-- original math problem.
8+(2+3) <-- Same as original but slightly broken down. And if you did it this way would still have the same answer.
You can then add (8+2) to make 10. leaving your new math problem..
10+3 <-- Same as original only shifted slightly to make it easier to do.
Even though 8+5 is the same as 10+3. If you give kids flash cards of math problems they will add 10+3 much faster.
But why am I telling you that this makes it easier. Well thing about how we first teach our children about numbers. We teach them to count. We start by 1's and even toddlers can grasp it to a specific amount. Then by 2's and 5's and 10's. 1's, 2's and 5's all count into 10's that makes this group of numbers very easy to keep track of mentally.
It is only when we are given weird numbers that math starts to slow down and seem more complicated to kids. 3's, 4's, 6's, 7's, 8's and 9's. It takes longer for these numbers to loop back into an easily tracked number.
3's don't loop to a 10's group until they add up to 30.
4's -->20. 6's -->30, 7's -->70, 8's -->40, 9's -->90.
If you need proof of this idea of how we understand numbers look at money.
We have $1,$5,$10,$20,$50,$100.etc
Same with our coin currency.
pennies(.01),nickles(.05),dimes(.10). Even quarters(.25) are easy numbers to follow because the .20 and the .05 are easily added into .50 so 2 sets of 2 quarters is $1(1.00).
There are lots of ways to break down the question of 8+5 into a way that can be easier for everyone.
you can separate a 5 out of the 8 to add 5's together easily into 10.
8+5=
(3+5)+5=
On paper this seems pretty stupid for an adult but we do stuff like this all the time in our daily lives. If you ever use cash to pay for stuff chances are you do it frequently.
You walk into a store and you have $8 in your right pocket and $5 in your left pocket. You know you have $13 in your pocket. You walk up to the counter and buy a $10 lottery ticket.
When the cashier asks for $10 to pay for said lotto ticket you don't look at him and say "sorry I only have $5 or $8 or $13" and you don't typically dump all of your money on the counter and then have the cashier hand you back $3.
I mean you CAN do these things but the cashier will typically give you a "what in the world is up with this person" look and/or assume you don't understand how money works.
You take $5 from one pocket and $5 from the other to make $10 and pay for your ticket. Leaving $3 left in your one pocket.
However you just bought a lottery ticket so there is a VERY large chance you just wasted $10. Might I suggest buying something else next time? But congrats you just did common core math OR as I like to call it, MATH.
NOW FOR THE BIG STUFF! (because everything in the world is not so small.)
Perhaps your math problem is a bit bigger now.
243+428=
Before anyone starts hyperventilating about doing this any other way then the "normal" way. The new way is pretty much the same.
I will start with the "old" way to solve the problem.
Basically this way to add up numbers means stacking them up and drawing lines separating the 1's 10's and 100's places. (either by actually drawing them or just mentally placing lines down the numbers.)
From there you can pretend there aren't any 10's or 100's. It is now just 3 separate little math problems that are still technically stuck together.
In this specific problem there is only one issue with doing all the different parts separately and that is the 8+3 part. In this part of it we teach kids they need to just already know that 8+3=11; but then they need to break the answer they just figured out back up into 10+1 so they can move (carry) the 10(which gets its 0 cut off and moved to the 10's row) and the 1 stays in the 1's row. Then now they have to add 3 numbers together in their heads. In this math problem its easy but sometimes its not so easy for mental math.
The 10's row is (1+2+4=7) pretty easy for us adults that add 2 numbers then add the 3rd to the answer. If you were 4-6 would that be so easy of a process? or if instead the numbers were say 1+7+9=17 only to do more carrying over to the next line of numbers?
So basically this way we teach kids that the 4 of the top number is a 4 in the hundreds spot because 4s are easier then 400. When in reality its still 400. so when your adding the 4 and the 2 your actually adding 400+200.
And now we move forward to the dreaded COMMON CORE MATH!. DUN DUN DUN.
I know it looks terrifying and like it has WAAAAY to much effort to figure out the same thing, but like any good relationship lets talk it out first, Okay?
243+428 looks kind of big for those of us who can't just automatically piece numbers together. However like any other common core question lets break up the easy parts first.
At first I broke down both of the two numbers.
(100+100+10+10+10+10+3)=243 + (100+100+100+100+10+10+8) =428
Still following? good. So we went over numbers that are easy peasy lemon squeezy. So we are just going to leave all the 100's and 10's where they are. We will get back to them later. That literally only leaves us (3+8).
"but how is this any different then the other way then?" you may say.
Exactly it's very similar.
Doing the same process as our little 5+8 question earlier we know that if we take 3+8 we can find a 10 to get out of our way same as all the other 10's.
3+8=
(1+2)+8=
Then by adding the 2 into the 8 you make 10. TADA! now you only have 1 in our annoying number section. Instead of 3 and 8.
Then you throw the numbers back up. Thus the circled 10 has an arrow pointed back up to the 8 showing that the 8 was separated from that group. shifted with the 3 and then put back as a 10.
Now if we write it all down with it being slightly adjusted for easier comprehention.
(100+100+10+10+10+10+1)+(100+100+100+100+10+10+10)=
Then we add ALL the 100's and 10's back together as easily as counting 1,2,3.
600+70+1=671 -BOOM!- we just did some math!
"But wait I don't understand how this makes any sense for practical use in the real world."
Funny you should ask that. On paper this process seems very silly and drawn out and otherwise a large waste of time. But what if we do this ALL the time. In fact we do.
*RIDDLE TIME!*
What do we do more with money when we have less of it?
.
..
...
..
.
COUNT IT!
What if instead of the numbers being 243+428 the numbers were converted into money.
"Yea cause I totally carry around $671 right?" Nope but close.
$2.43 + $4.28
So instead of 100's they are actually $1(aka 100 pennies)
and instead of 10's they are Dimes(aka 10 pennies)
So $2.43 is more likely 2($1), 4(Dimes) and 3(pennies)
And $4.28 is more likely 4($1), 2(Dimes) and 8(pennies)
So if you mix it all up on the table you unintentionally seperated everything the way we did earlier that seemed like a waste of effort.
Anyway moving on...
So when I count change. In this case the pennies I typically group them. so instead of a pile of a weird number 11 pennies but adding all the pennies together I would have grouped them into a group of 10 and then kept the other one separate. Thus creating the 10+1. Then when I add up all the $1's i would have $6's in ones. $0.70 in dimes (and the group of 10 pennies). Then one remaining penny. Thus giving me $6.71
We end up doing all this entirely without thinking about it when we get good at math. However Common core math is not "new math" that makes the old one wrong. It is just an easier way of explaining it to kids/people who just aren't able to do it in their heads yet. After learning it this way it because more of an understanding on WHY the numbers become what they do with adding/subtracting/multiplying/dividing instead of just memorizing them as they are with flash cards because everyone told you that 8+5 is 13.
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