ABSTRACT
In this chapter, the author likes doing the exploration with kids, because they get to draw pictures to make and test their predictions about complex ideas. In the first stage, they use ramps to begin investigating the concept of slope while extending their understanding of ratios. Ratios, rates, and proportions offer wonderfully rich opportunities for students to develop and discuss thinking strategies. As students explore the relationship between rates of change and the steepness of ramps, they are setting the stage for a deeper understanding of slope in algebra courses. The whole idea of proportional relationships that students begin to explore in this activity is foundational for understanding algebra. It will appear in the study of proportions, linear functions, and properties and procedures for working with fractions.
