Never having done CC I'll give it a shot..Fail. You said only use a CC method that does not apply to determining area under a curve. You were supposed to only use equivalent math tables as per your own defined rules. You had to go off and use a formula that has nothing to do with the math table memorization technique. Why is that?Try to calculate the area underneath a curve using only memorization, post your results.Why can't there be room for both? When children start to add, then they need to fool around with the process of putting things together. They need to play with numbers, see what happens when you add two positive numbers, what happens when you add two negatives, discover the patterns. Then, they are better equipped to memorize. Because when you memorize with a solid foundation, it's easier to know if the answer that popped into your head makes sense, or if you've memorized wrong.
You'd have a point if the current CC method was one of many ways to learn basic arithmetic, but it's not. It is being used as the only way which is not good.
I learned the number line method, memorization, estimation (similar to the process described in the OP), binary, base 6, and hex in grade school. It was done quite well. There are no Common Core lessons for different methods in grade school, just this one foreign and inefficient method. That's why this is a problem. It's not intuitive and it doesn't actually help later.
Try to calculate the area underneath a curve using the Common Core arithmetic method. Post your results.
That's a false premise because I never said that memorization only was correct. But I can do it using only memorization.
The area under the curve y=10-x^2 between the x axis on x=-3 and x=5:
Solve for x=5 minus x=-3 using (10x-1/3x^3)
((10*5) - ((5^3/)3) - (10*-3)-((-3^3)/3))
((50-(125/3)) - ((-30)-(-27/3)))
8 +1/3 - (-21)
29 +1/3
I used memorization only to solve the problem as you demanded. You did not demand that I only use equivalent math tables, and I didn't define any rules. You are correct that I worded my initial demand incorrectly so I'll try again:
Try to calculate the area underneath a curve using the Common Core method for the arithmetic portion. Post your results.
Your arithmetic starts here:
((50-(125/3)) - ((-30)-(-27/3)))
You simplified -27/3 to -9 ... without showing your math cc would do it the same way... you then reduced -30+9 to get -21 without showing you math, cc would have the same result and do it the same way. You then simplified 125/3 to get 41 2/3 without showing your math, cc would have the same result and do it the same way you did 120/3 = 40, 3/3 = 1, 2/3 or 41 2/3. You then subtracted 41 2/3 from 50 without showing your math; cc would have the same results 50-40 = 10, 10- 1 = 9, 9 - 2/3 = 8 1/3.
8 +1/3 - (-21)
You then added 21 to 8 1/3 to get 29 1/3, cc would have the same results and do it the same way.
29 +1/3