ABSTRACT
This chapter presents an overview of the expectations in the Common Core State Standards for Mathematics (CCSSM) for the development of understanding and fluency when multiplying and dividing with fractions. The two most widely used algorithms for division of fractions are the common denominator algorithm and the invert and multiply algorithm. The chapter shows how the use of visual models, unit fraction understanding, use of contexts, estimation, and properties of operations can build fluency with conceptual understanding. It explains students' experiences with the division of whole numbers sometime lead them to believe that the operation of division always makes something smaller. The chapter examines the need for students to interact with a variety of situations and contexts that include both partitive and quotative division requiring different interpretations of remainders. It also presents case studies of Tania's response, Toby's hike, Justina's response, Troy's response, Corey's response, Alejandro's response, and Abigail's response.
