We just switched DD's school. She's in first grade with a reading level of 4.2-6.1. (Not sure how the range was figured on that.)
I do feel that the books she is bringing home are at a higher "level" than than some of the books she was reading from her book box at her old school.
Her new classroom has a lovely library with much more variety and many more chapter books! I don't know if this is typical of all AR classrooms, but I am impressed at what she has to choose from.
I think the biggest thing is understanding words she hasn't read before and how to pronounce them, but that comes with time. You should hear her pronounce Eucerine lotion….Eek urine!!!