Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about arguments concerning sums of evens and odds. Data are drawn from classroom lessons of an early algebra instructional sequence and interviews conducted at four timepoints during the implementation of the sequence. Overall, students transitioned from unfamiliarity with the concepts of even or odd prior to instruction in Kindergarten to making valid parity arguments at the conclusion of instruction in Grade 1. Results of this study align with other research that shows young learners can develop viable arguments to justify mathematical generalizations.