ABSTRACT
The number line—the translation (mapping) of number to linear distance—is one of the most powerful tools in the numeracy toolbox and in the classroom. This spatial numerical analog efficiently illustrates both the relative cardinal values of numbers and their ordinal relations. It also serves as a mental template (mental number line) for numerical (arithmetic) transformations, while reducing the burden on working memory. This chapter discusses the cultural influences on the mental number line’s spatial direction and describes several methods for using children’s number line placements as a window into their developing view of numerical relations. The difficulties encountered in understanding negative numbers are also addressed, along with the idea of introducing the bidirectional number line early in the curriculum. Finally, with its standard units, the number line is also a model for linear measurement. The chapter discusses the most common difficulties encountered in learning to measure, including beginning at 0, the need to count unit lengths rather than divisions, and the scaling of nested units. Classroom activities provide children with a concrete introduction to the number line and tackle the difficulties with measurement head on.
