DGD's grade at school recently had a "Multiplication Bee" (like a Spelling Bee, but w/ times tables). Apparently, they have learned the multiplication tables, by heart, all the way through the 12s. She asked me to study w/ her, one day, while I was watching her and DGS (flash cards - 1st straight through each table, then mixing it up). And I'm proud to say she knows it all very well (though the 7s, 8s and 12s give her a little trouble ).
What I was especially glad to see, however, is that they are learning the tables this way, at all. As I recall, my DDs didn't though, no doubt, they did learn to multiply. Ok, I guess the fact that my DDs got to know their multiplication facts, anyhow, shows that doing "tables" isn't exactly necessary. But, IMO, it's good for their basic foundation in math. At any given moment now, I can ask DGD, say, "What's 5 x 6" and she'll answer "30," just like that, etc. IMO, that's a good thing.
Is this part of Common Core now? I don't think so. To my knowledge, CC provides a set of standards for math and English/language arts, not any specific methods of teaching them. So it may just be my state, city, school district or the school, itself, that decided to teach multiplication this way. IDK.
I'm just glad the times tables are "back." But, no doubt, I'm wondering if other people are seeing the same in other schools, states, etc....