ABSTRACT
This chapter focuses on understanding partitive and quotative division, interpreting remainders, and the different levels on the OGAP Division Progression. The foundations of understanding of division as a concept come from equal sharing experiences during preschool years. For example, children share with their peers by partitioning food portions into equal parts or dealing out equal shares of discrete objects before they even enter formal schooling situations. The progression levels represent the continuum of evidence from Nonmultiplicative to Multiplicative Strategies that is visible in student work as students develop their understanding and fluency for whole number division. The design of the OGAP Division Progression is to provide a learning path based on mathematics education research that develops procedural fluency with understanding. The Transitional Level in both progressions is the bridge between additive reasoning and strategies that reflect procedural fluency with understanding at the multiplicative level.
