A lot of you are confusing Common Core Standards with the method of teaching being used in your district.
Common Core is a set of standards. That's it. A list of things a child must be able to know and do at the end of a certain grade level. It does come with things like a list of approved books, etc., but that's all Common Core is. In concept, it's no different than list of standards your state had last year or two years ago, etc.
What everyone here is having a problem with is the implementation of a curriculum used by your district to teach the Common Store Standards. That's a completely different kettle of fish.
For example, "cross teaching" is a concept going back to early 1990's (and earlier) and is not related to Common Core. Some districts might find using cross teaching is helpful so students can apply concepts from one class in another class (I certainly found Calculus made more sense when I was in Physics class). What jodifla is describing (teams of 4 students where each student has a role) is called
cooperative learning, and this is a style that also existing before the Common Core Standards.
Here's a quote:
Please don't confuse the standards with your district's implementation. Some people don't like Common Core because of the amount of testing involved, or because they feel different states should have their own standards, or they think it's some kind of federal takeover. Whether those beliefs are fair is certainly up for debate. But what most of you are talking about isn't even about the actual standards.