Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2

What is the relationship between addition and subtraction? How do you know whether an algorithm will always work? Can you explain why order matters in subraction 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.