The Common Core State Standards for Mathematics (CCSSM) presents new challenges and opportunities for local school districts and teachers to focus on curriculum as a means of improving what students understand and can do in their study of mathematics. In response, the Center for the Study of Mathematics Curriculum (CSMC) leaders have developed this volume to further the goal of teachers having opportunities to interact across grades in ways that help both teachers and their students see connections in schooling as they progress through the grades. Each section of this volume contains three companion chapters appropriate to the three grade bands-K-5, 6-8, and 9-12-focusing on important curriculum issues related to understanding and implementing the CCSSM. To promote a deeper understanding of CCSSM-related ideas and their implications for district policy and practice, an Introduction and a series of Questions for Reflection and Collective Discussion accompany each set of three grade-band chapters in Sections II-VII. The questions and the prompted collegial discussions, curriculum and related resource audits, CCSSM implementation planning, and reports of classroom trials of new ideas are the core of this volume. The book encourages groups of teachers to work together, within and across grades in professional development settings, to accomplish this work. Such interactions around practice can help start conversations within and across buildings that change the culture and underscore the importance of teachers having time to learn, plan, and work together. The book's goal is to foster educative and empowering interactions between teachers as they work to both interpret and implement the CCSSM effectively