 Welcome to our unit on recursion. Our plan with this video and this unit is to empower you to enter your classroom ready to motivate and teach your students about the rich topic of recursion. You and your students may be asking why should we be interested in recursion? How would we use this in the real world? What are the most important elements that students should take from this unit? What kind of problems will recursion help us solve? To what other results or mathematics will our studies lead us? Recursion provides us with a method for creating models that capture phenomena that change at fixed time periods. Many of the mathematical models we create are continuous models. That is, they well model phenomena that are constantly changing. For example, a continuous model would be very appropriate for determining how many bacteria are left in a certain sample after different time periods, given the bacteria's doubling time. Suppose, however, we are modeling the amount of color left in a pair of genes after different numbers of washings. Since the decrease in color happens only at each washing, a discrete model is the more appropriate choice. In this case, the recursive model would be more useful than a continuous model. Studying recursive equations opens up a whole host of real world applications. In this unit, we explore questions such as how pollution spreads through the network of interconnected Great Lakes, and how two investment strategies can differ over time. The ideas we develop in these lessons could be further applied to problems, such as investigating the spread of a disease through a closed population, or determining how lead builds up in different areas of the body. Another motivation for studying recursion is to gain a better understanding of exponential functions. By deriving explicit exponential functions from recursive equations, students will get to actually see that exponential functions are the result of repeated multiplication. Along with gaining a better understanding of how basic exponential functions behave, this will allow students to understand when and why exponential functions will be appropriate models for phenomena. The following set of lessons on recursion helps us address many of the common core standards related to recursion, sequences, function interpretation, and exponential functions. A list of the relevant standards is provided at the end of each lesson. We hope you found the materials and lessons we provided here useful. We encourage you to send us any comments and feedback on other materials you would find helpful. Thank you.