Standards-based grading, in which grading should be designed to communicate to students their current level of mastery with regards to well-articulated standards, is becoming popular at the K-12 level. As yet, the literature addressing standards-based grading at the university level is scarce. In this paper, I document my attempts to put into practice the principles of standards-based grading in a lower-level undergraduate mathematics course that aims to introduce mathematical proof and the basic definitions of sets, logic, and functions.