Hello. I'm a math teacher, licensed to teach in two states, currently teaching algebra 2 and AP calculus. What are you talking about? I'm familiar with the common core state standards (CCSS). I've never heard of a "common core addition method." Care to enlighten me?
Please give a link to the online version of the CCSS that describes this algorithm. If, instead, you're seeing this algorithm described in some crap textbook your school district got from the lowest bidder, well, that's too bad. The publishers don't have their books vetted by common core. They are completely independent.