COMMON CORE DOES NOT SPECIFY PEDAGOGICAL METHODS!
It is, essentially. a list of topics that should be mastered at each grade level.
At some point the idea came about that for things like addition, subtraction or multiplication, we should teach multiple different ways of viewing the same concept (like addition) in the hopes that even if students don't really understand the classic approach one of the other approaches makes sense. So perhaps the classic explanation of borrowing in subtraction does not make sense to some students, but one of a few other equivalent ways of handling it does make sense.
But then it got turned into a system where all students need to learn all these different different methods, and apply them in both homework and on tests. Which totally defeats the point. The who idea was that some students may find some methods useful and intuitive, and others find different methods useful and intuitive, and as long as every student finds some method can can work with we are better off than only teaching the classic method of the concept.
My little cousin goes to the same elementary school as I did. When I looked over his homework, I saw none of what I was taught. A glance at his textbook showed they had switched back to the old method of teaching by rote. Apparently school board members who had run in part based on their skepticism of the new techniques had voted in a change in curriculum. One funeral at a time indeed.