Typical treatments of the derivative do not clearly convey the idea that the derivative function represents the original function's rate of change. Revealing the relationship between a function and its rate-of-change function for static values of "x" does not facilitate productive ways of thinking about generating the rate-of-change function or allow students to anticipate the graphical behavior of the rate-of-change function by examining a graph of the original function. Accordingly, the authors propose the calculus triangle approach. This approach builds on Thompson's calculus research (Thompson 1994; Thompson and Silverman 2008), which introduces the derivative in a way that maintains the centrality of rate of change as a conceptual underpinning of derivative. By providing examples of the approach's use in novel and routine settings, the authors will show how it facilitates a mature understanding of the derivative. (Contains 4 figures.)