There have been several strong attempts at keeping parents informed about the Common Core including resources from the PTA (here) and the Council of Great City Schools (here). Stand for Children, an organization dedicated to promoting educational outcomes for K-12 students, has created a new resource to help parents better understand the CCSS.
By visiting http://get2core.org/ and clicking on “Common Core in Your State” visitors can learn more about implementation and impetus for adoption in the state they live. In addition, parents can learn about specific grade level outcomes, in parent friendly language, by following additional prompts. The interactive tool is free and allows you to navigate through the site without giving away any personal information.