ABSTRACT
This chapter focuses on the concept of the density of fractions, and misunderstandings that students have as they are identifying fractions between fraction pairs and developing an understanding of the generalized concept of density. It explains the role that number lines can play in building an understanding of the 'betweenness' of fractions. When studying fractions, students encounter a property of fractions that is very different from properties of whole numbers. One way to mathematically demonstrate the density property of fractions is by looking at averages. The average of any two different numbers will always be another number between the two numbers. The chapter shows how the density of rational numbers property is applied in the design of measurement tools. Students at the Fractional Strategies level are able to explain why there are an infinite number of fractions between any two numbers.
