What she is doing in this video is teaching a concept; breaking down more complex equations into more simple parts in order to solve them mentally. That concept is a part of the common core curriculum. The method used to teach it is not. The method she is using is solving the equation with pencil and paper. She could also use blocks like in my example, or have students count on their fingers, or have 13 kids stand up and split off into smaller groups to see how all those groups of numbers add up to 13. Common core doesn't say "teach the concept this way," it just says "by the end of third grade, kids need to understand this concept."

As an aside, I love that kids are being taught to do math like this now. I struggled with math a lot as a kid, and the way she's solving this problem is exactly how I used to do it, because it's the only way that made sense to me. But it was never formally taught to me and I actually got in trouble for doing it that way because it wasn't how math was "supposed" to be done. I like that kids are being taught that there are different ways to solve the same problem.