The Common Core Mathematics Companion: The Standards Decoded, High Schoo

Frederick L. Dillon is an author and national mathematics curriculum and professional learning consultant based near Cleveland, Ohio. He is a retired teacher with 35 years of classroom experience, having taught grades 7 through college. Fred is a frequent speaker at national, state, and local conferences and institutes. He is active at the local, state, and national level in professional organizations, including serving on the board of directors for the National Council of Teachers of Mathematics (NCTM). Fred was a recipient of the Presidential Award for Excellence in Science and Mathematics Teaching and the Christopherson-Fawcett Award from OCTM for Lifetime Contributions to Mathematics Education. W. Gary Martin is Emily R. and Gerald S. Leischuck Endowed Professor in the Department of Curriculum and Teaching at Auburn University, where he teaches undergraduate and graduate courses in mathematics education and serves as co-director of the Mathematics Teacher Education Partnership (www.MTE-Partnership.org), a national coalition of universities seeking to improve the preparation of secondary mathematics teachers. He has been a writer on multiple standards documents, including Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 2000), Focus in High School Mathematics: Reasoning and Sense Making (NCTM, 2009), and Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014). Most recently, he was the lead writer for high school on the Standards for Preparing Teachers of Mathematics (Association of Mathematics Teacher Educators, 2017). He has presented extensively on mathematics education, particularly the teaching and learning of geometry, mathematics curriculum and standards, and mathematics teacher preparation. Previously, Martin served as the director of research for NCTM and has also held positions at the University of Hawai?i and Northern Illinois University. He began his career as a high school mathematics teacher, a role that remains central to his professional identity. Basil Conway IV is an associate professor of mathematics education in the College of Education and Health Professions at Columbus State University and serves as the mathematics education graduate programs director. He serves on numerous doctoral committees as both a chair and methodologist. He earned his BS, MS, and PhD. in mathematics education from Auburn University in 2005, 2012, and 2015, respectively. He also completed his MS in statistical science at Colorado State University in 2010. Basil previously spent 10 years teaching in public middle and high schools before he became a teacher educator. During this time, he also worked as an instructor at a local junior college. Over the past 17 years of service in teaching mathematics and future teachers of mathematics, he has served in various local mathematics education leadership positions and organizations including Transforming East Alabama Mathematics (TEAM-Math), Auburn University's Teacher Leader Academy, East Alabama Council for Teachers of Mathematics, Woodrow Wilson Fellow, National Mathematics and Science Initiative, and A+ College Ready. He has published works related to teaching mathematics for social justice in numerous books and journals and has a special interest in statistics education. Basil's lens for teaching and student learning draws heavily from Vygotsky's theory of social constructivism in which language and culture play essential roles in human intellectual development. Thus, he believes the co-construction of knowledge is paramount in the development of students' social, religious, and mathematical identities. He believes teachers, parents, other students, cultural norms, and other cultural communicative devices play a critical role in shaping students' knowledge of themselves, faith, and mathematics. Marilyn E. Strutchens is the Emily R. and Gerald S. Leischuck Endowed Professor for Critical Needs and the Mildred Cheshire Fraley Distinguished Professor of Mathematics Education in the Department of Curriculum and Teaching at Auburn University and coordinator of secondary mathematics education. She is also the Director of the Professional Mathematics Learning Communities Project between TEAM-Math and the Alabama Mathematics, Science, and Technology Initiative. She teaches courses in mathematics education. Strutchens is a member of the Board of Directors for the National Council of Teachers of Mathematics and serves on the Advisory Committee for the Education and Human Resource Directorate for the National Science Foundation. She has held positions at the University of Maryland at College Park and the University of Kentucky. Her research interests include mathematics teacher preparation, equity issues in mathematics education, and teacher leader development. Recently, she was one of the writers for the Standards for Preparing Teachers of Mathematics (Association of Mathematics Teacher Educators [AMTE], 2017). She was the series editor for AMTE's Second Monograph Series, editor for the special equity issue of the Journal of Mathematics Teacher Education published in February 2012, and has co-edited several National Council of Teachers of Mathematics (NCTM) books including, Focus on High School Mathematics: Fostering Reasoning and Sense Making for All Students, The Learning of Mathematics: 69th NCTM Yearbook, and Changing the Faces of Mathematics: Perspectives on African Americans. She has also authored and co-author several book chapters and journal articles. In addition, she has given numerous presentations. In addition, she was the AMTE 2017 Judith Jacob's Lecturer.

Acknowledgments Letter to High School Mathematics Teachers Letter to High School Principals Introduction A Brief History of the Common Core The Common Core State Standards for Mathematics Instructional Shifts Major Work of High School Common Core Word Wall The Common Core Standards for Mathematical Practice Effective Teaching Practices How to Use This Book Reflection Questions 1. Modeling Conceptual Category Overview Sample Unit Planning Page Reflection Questions: Modeling 2. Number and Quantity Conceptual Category Overview Suggested Materials Number and Quantity - Overarching Key Vocabulary Domain: The Real Number System (N.RN) Domain: Quantities (N.Q) Domain: The Complex Number System (N.CN) Domain: Vector & Matrix Quantities 3. Algebra Conceptual Category Overview Suggested Materials Algebra - Overarching Key Vocabulary Domain: Seeing Structure in Expressions (A.SSE) Domain: Arithmetic with Polynomials and Rational Expressions (A.APR) Domain: Arithmetic Creating Equations (A.CED) Domain: Reasoning with Equations and Inequalities (A.REI) 4. Functions Conceptual Category Overview Suggested Materials Functions - Overarching Key Vocabulary Domain: Interpreting Functions (F.IF) Domain: Building Functions (F.BF) Domain: Linear, Quadratic, and Exponential Models (F.LE) Domain: Trigonometric Functions (F.TF) 5. Geometry Conceptual Category Overview Suggested Materials Geometry - Overarching Key Vocabulary Domain: Congruence (G.CO) Domain: Similarity, Right Traingles, and Trigonometry (G.SRT) Domain: Circles (G.C) Domain: Expressing Geometric Properties with Equations (G.GPE) Domain: Geometric Measurement and Dimension (G.GMD) Domain: Modeling with Geometry (G.MG) 6. Statistics and Probability Conceptual Category Overview Suggested Materials Statistics and Probability - Overarching Key Vocabulary Domain: Interpreting Categorical and Quantitative Data (S.ID) Domain: Making Inferences and Justifying Conclusions (S.IC) Domain: Conditional Probability and the Rules of Probability (S.CP) Domain: Using Probability to make Decisions (S.MD) Resources Reproducibles Additional Resources About the Authors