ABSTRACT
Additive reasoning is comprised of various mathematical skills, concepts, and abilities that contribute to number sense. The mathematical foundations of additive reasoning include concepts of early number, specifically part–whole relationships, and two important properties: commutativity and the inverse relationship between addition and subtraction. There is a concurrent and mutually reinforcing relationship between the development of base-ten understanding and additive reasoning. Understanding of part–whole relationships supports base-ten understanding of multi-digit quantities, and base-ten understanding supports more sophisticated strategies for addition and subtraction. The OGAP Additive Framework contains learning progressions for base-ten number, addition, and subtraction that provide instructional guidance for ensuring that all students can access the important concepts and strategies that lead to additive reasoning
