Unless 1984 is on the Common Core reading list, your straw man argument is irrelevant to Common Core.
Maybe not if you're trying to do it in your head. So, you memorized all the way up to 13 x 13. What's 14 x 15?
Here's how I would do it.
14 x 15 = (10 x 15) + (4 x 15) = 150 + 60 = 210.
Or, taking the lesson to it's absurd extreme, maybe it's 150 + 50 + 10 = 200 + 10 = 210.
You want to multiply five times 4, is 20, so zero, carry the 2.
Five times 1 is 5, plus the 2, is 7. That makes 70.
Ten times 14 is is 140, plus 70 is 210.
Same answer, but I'd much rather do it using 10s, 20s, 100s, etc, which is obviously the point of this exercise. Being able to do math in your head, beyond what you've managed to memorize, is a damned good skill to teach kids.
I don’t think referring to 1984 in regards to Common Core is a straw man. The curse of fuzzy math is upon us. If the student ‘thinks’ they got the correct answer, the student is awarded a gold start for thinking they got the right answer. How many fingers do you see? How many oranges do you have is there are 2 in one hand and 2 in the other? How many do you think you have? Sure, teachers aren’t dumping rats on their heads, yet, and telling them how many oranges there are, but who woulda thought it was so close now.