In the third grade, children integrated math into their representations of Wisconsin Fast Plants in a variety of ways. They developed “pressed plant” silhouettes that recorded changes in plant morphology over time, coordinate graphs that related plant height and time, sequences of rectangles representing the relationship between plant height and canopy “width,” and various three-dimensional forms to capture changes in plant volume.

As the diversity in types of students’ representations increased, a new question emerged: Was the growth of roots and shoots the same or different? Comparing the height and depth of roots and shoots, students noticed that, at any point in a plant’s life cycle, the differences in measurement were apparent. However, they also noted that graphs displaying the growth of roots and shoots were characterized by similar shapes: an S-shaped logistic curve (see Figure 6-5).

Finding similarities in the shape of data describing roots and shoots but not the measurements of roots and shoots, students began to wonder about the significance of the similarity they observed. Why would the growth of two different

FIGURE 6-5 A display of plant height over time depicted in an S-shaped curve.