In this paper, we explore the following research questions: How do first-grade students define even and odd numbers? What types of justifications do they use to support their generalizations using these definitions? We report the ways in which first-grade students define even and odd numbers and how they justify generalizations that use their definitions. While we focus on definitions and explanations of those definitions, the targeted underlying thinking practices at hand are generalizing and justifying. The instruction used in this study was aimed at supporting students in providing definitions, and then reasoning with their definitions by using them in new problem contexts in which they were asked to generalize a relationship about sums of evens and odds or justify that relationship. Our study shows that students shifted from using pattern-based definitions of parity to using structure-based definitions of parity. When justifying the parity of sums of even and odd numbers, students shifted away from using examples through empirical arguments towards using generic examples and in some cases a general argument.