What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining an understanding about addition and subtraction is essential as they are the foundation for students' later learning of multiplication and division. This book contains three chapters: (1) Addition and Subtraction: The Big Ideas and Essential Understandings; (2) Connections: Looking Back and Ahead in Learning; and (3) Challenges: Learning, Teaching, and Assessing.