No this is a valid mathematical technique. It appears silly in this example because the teacher is using single digit numbers. And yes the student should have been taught from rote memory that 9+6 = 15.
But what about 9886 + 318?
You can solve this using the long hand method, or you can solve it faster by recognizing that you need 114 to get to 10,000. And 318 = 114 + 204. So 9886 + 318 = 9886 + 114 + 204 = 10,000 + 204 = 10204. And you can do that in your head faster than long hand.
It’s an important skill for business. I use it all the time. It shouldn’t instead of long hand arithmetic but in addition to long hand.
This is not a reason to oppose common core unless long hand addition is not being taught. There are valid reasons to oppose common core, including opposing federal control of education, and the introduction of alternative agendas such as gay rights that have nothing to do with reading and writing.
“No this is a valid mathematical technique. It appears silly in this example because the teacher is using single digit numbers. And yes the student should have been taught from rote memory that 9+6 = 15.”
But the way the teacher demonstrated it was nothing like this. She was either intentionally or unintentionally making it more complicated than necessary and ignored the meaning of base-10 numbers.
I maintain that this is deliberately done to bog down the smarter kids.
if kids just learn addition, subtraction, multipication and division by simple memorization, they will come to these shortcuts by themselves. .... Teaching the shortcuts too early will just confuse them...
I agree with teaching children why nine plus six equals 15. But, young children will be slowed down if they're forced to use these concepts for basic math. Sure, we can introduce the concepts to them, talk about the concepts, etc. But requiring children to demonstrate those concepts on a test, rather than letting them just give the answer, is going to slow many children down and frustrate them.
I taught my kids by rote memorization, then the long way for larger numbers, then the ‘cheats’. They picked it up all very fast and had a great grasp on the concepts. (They actually took their Saxon math books and left me in the dust.)
9886+318 I do in my head by adding 300 and then 18. Don’t know if that’s normal or not. Works for me on larger numbers.
add 114 to 9886, subtract 114 from318 add 204 to 10,000...something about the distributive and associative properties of addition and subtraction with a simple bit of algebra.
“...by recognizing that you need 114 to get to 10,000.”
How is that ‘recognized’? Only by doing a subtraction problem, right? Along with the other subtraction you throw into that solution.
Not buying it. Are you a teacher? Public school?
I was thinking the same thing. The difference, however, is that CC teaches this as a primary problem solving technique before teaching the basics and letting the students develop these concepts on their own as they advance.
No I can't. I can either do it in long hand on a piece of paper which might take 3 or 4 seconds or use a calculator..the same goes for subtraction, multiplication and long division.
But I cannot solve it in my head. All of the extra numbers clutter my brain. By the time I get to the first 10,000, all of the other numbers you posted might as well be hieroglyphics. I am not exaggerating. Each time I go through the numbers you posted, I end up scratching my head & saying "Huh?
When my youngest son was in high school, he needed help with Algebra. My brain is not wired for numbers, but I had an excellent Algebra teacher in high school. At 60, I can still do equations because I was taught how to solve and why each step was necessary. I was of no use to my son. They were using something called the Diamond Method which made absolutely no sense.
Nonsense. You “recognize” that 114 = 10000-9886 by doing a subtraction, no matter what you call it. Now you subtract that from 314 to get the 204; two subtractions replacing one addition, which is always the easier operation anyway.
This case didn’t even have any “borrows” in the subtractions, there’s a second level of inevitable and avoidable complexity.
Using that method, you can easily add even longer numbers together, such as 17,493,735 + 14,388,923.
By memorizing the addition, subtraction and multiplication of all combinations of single digits (a second grade activity), you can do any basic mathematical function on a piece of paper without having to "decompose" numbers and "anchor" them to 10s.