Lesson #1: 2-3 days
Complete unit: 4 weeks

Imagine yourself swimming in the ocean. Based on the photo in Figure 1, take a moment to make a conjecture for the graph of the light intensity as a function of depth. Before continuing to read this lesson plan, look at the graphs in Figure 2. For most students, the fact that the light intensity decreases as the depth increases is intuitive. All of their conjectures illustrate this fact (Figure 2). However, students frequently disagree on the shape of the curve. These differences are a result of two informal yet incorrect observations. One belief is that if you go deep enough in the ocean, then there is no light and so the graph must reach zero. A second belief is that near the surface of the water, there is little change in the light intensity and so the curve must have an initial gradual change. This simple question of how the light intensity changes as a function of depth provides an excellent catalyst and center for the following light activity.

Fig.1 An underwater snapshot is used to launch the activity

In this activity, students develop exponential models, difference equations, derivative, integrals and procedures for analyzing exponential data. Students explore concepts and methods which have become fundamental in mathematics, chemistry, physics and biology. The rich context and hands-on experiments provide a strong foundation from which students can make sense of the principles and procedures involved. Some equipment needs to be gathered and prepared, but these materials are easily available. The experiments have the added features of being fast, simple, inexpensive and reliable which make their use in the classroom feasible.

Fig. 2