ABSTRACT
This chapter focuses on the importance of students understanding that fractions are numbers, which extend the number system beyond the whole numbers. Developing understanding of fractions as quantities is an explicit goal in the Common Core State Standards for Mathematics (CCSSM) starting at grade 3. The chapter presents some direction for instructional strategies that help to move students away from inappropriate whole number reasoning and toward reasoning about fractions as quantities. Many teachers in the Ongoing Assessment Project (OGAP) studies were surprised at how readily their students inappropriately applied whole number reasoning to all aspects of fractions. Teachers attributed the change from inappropriate whole number reasoning to reasoning with fractions as quantities to their increased instructional emphasis on the use of visual models, comparing and ordering fractions, and the use of the number lines. The chapter also presents case studies of use of inappropriate whole number reasoning in OGAP Grade 4 pre- and post-assessments.
