Common Core teaches our kids different methods than we learned to get to the same answers. To help my 2nd grader, and I, with her Common Core skills I use these Carson-Dellosa workbooks for Math and Language.
Common Core Math introduces methods of counting like base ten blocks and other math mechanisms that were not used in my "new math." The method seems to be a highly visual approach to skills. Equations are often represented by pictures. Language skills are more in tune with what I expect. Nevertheless, these workbooks help me understand what my daughter needs to learn and provide a framework she and I can work on together.
Organized into exercises by Day and by Week, there are 40 weeks of exercises to roughly match her school year. The instructions are pretty clear and rarely do I have to puzzle out what the heck they want her to learn. We use them as time permits, and I find that regular work makes a clear difference in her at school performance.