In this paper, we describe students' concept images of average and average rate of change and the similarities and differences between those concept images. We do so by describing the students' ways of thinking and ways of understanding average and average rate of change, and how the students' meanings for average influenced their conceptions of average and instantaneous rates of change. We describe the importance of everyday meanings for average in students' conceptions of rate, and propose how instruction might be tailored to address this link. We conclude by discussing implications of this work for teaching average and instantaneous rates of change in single and multivariable calculus, and suggest important directions for future research. [For the complete proceedings, see ED584443.]