Students learning the skills of science benefit from opportunities to move between the scientific problems and questions they confront and the mathematical tools available to answer the questions and solve the problems. Indeed, students learn science best when they are actively engaged in pursuing answers to authentic and relevant questions. We present an activity teachers can use in the classroom to introduce the concepts of species richness and diversity. We break down the history and logic behind the two primary statistical tools ecologists use to quantify species diversity: Simpson's and Shannon's diversity indices. With hypothetical data, we show how students can learn about and practice the calculations. We then describe an activity where students collect authentic ecological data with pitfall traps while learning some arthropod systematics and practicing their newly acquired quantitative reasoning skills, all within the context of edge effect ecology and habitat conservation. The entire activity reinforces for students how interesting and helpful mathematical models and quantitative reasoning in science can be for understanding biological phenomena, but also for generating more questions, and for designing additional data-collection techniques and experiments.