It depends on which version of the textbook you have. The “homeschool” line (the two-toned books that have names like Saxon Math 7/6 and 5/4) were created before Common Core existed. The “school line” (the books with the colorful pictures like soccer balls, keyboards, and camera) is essentially the same textbook as the homeschool line, but it has been adapted to meet Common Core Standards. However, the differences are small. Most lessons are exactly the same between the two lines of books, but a few additional practice problems have been added that focus more on word problems and real-life applications (a Common Core requirement.) However, there is no particular “common core way of teaching” in those textbooks. The teaching, for the most part, is exactly the same.