Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the topic of limits before introducing the limit definition of the deriative and using it to prove derivative formulas. This introduction to the derivative is rigorous and mathematically sound, so it presents only one problem: students generally do not understand it (Davis and Vinner 1986). In this article, the author proposes an alternative approach to teach this. It begins with a graphical introduction to the derivative. This creates, the author surmises, the possibility for students to observe the main ideas in a less formal way and to engage in sense making that is more natural.