ABSTRACT
This chapter explores the ways in which classroom activity can promote understand fractions as quotients. The study of rational numbers as a quotient field is well beyond the elementary and middle school child, but the foundations for building a solid understanding are laid in the early years. Partitioning or fair sharing is a process that begins in preschool years, but is no less important during the elementary and middle school years. Some teachers may avoid partitioning activities in the first and second grades because children do not always have good hand—eye coordination at that age, and they have trouble drawing the correct number of parts and making them all the same size. It is important that partitioning be much more than fun drawing and shading. As we have seen children's partitioning work can produce many different results and well-crafted comparisons and discussions of those results can push student thinking to new levels.
