A few things about Common Core should be clarified. Every state has a core curriculum. Utah's current and previous core can be found at www.uen.org/core/. The Common Core program is simply math and English standards that are the same for all states that have adopted them instead of different states having varying standards.
This means that if Sally moves from Maine to Colorado after second grade, then she will start third grade with the same math and language arts knowledge as her classmates.
From the Common Core website: "The standards themselves do not dictate curriculum, pedagogy, or delivery of content. In particular, states may handle the transition to high school in different ways."
This means that when fourth graders should "use place value understanding to round multi-digit whole numbers to any place," then the teacher is the one who gets to decide how they want to teach that lesson.
Core curricula have never supplied text books. Publishers produce broad textbooks to try to cover all states' standards. Teachers must match chapters in the text books to their state's core. Core curriculum may lead to better textbooks because they no longer have such a varying array of standards to cover.