The goal of this lesson is for students to develop their skills modeling periodic data. The context in this lesson is the amount of the moon visible in the night sky for each night in January 2018. The minimum, maximum, and midline values here are relatively unambiguous but it is not possible to estimate the period accurately without more data. In addition, regardless of the period chosen, a trigonometric model only approximates the data.

In this lesson, students engage in aspects of mathematical modeling (MP4). The data is provided, and students are prompted to think about the midline, amplitude, and period before choosing their model. The horizontal translation is not directly addressed, however, and the period turns out to be the most interesting part of the story (since an accurate estimate requires more data). As students work, they will need to adjust their model based on its fit to the data.