Quite a bit of the arithmetic in elementary school contains elements of algebraic reasoning. After researching and testing a number of instructional strategies with Irish third graders, these authors found effective methods for cultivating a relational concept of equality in third-grade students. Understanding equality is fundamental to algebraic understanding. Although we introduce the equals sign to children as young as five or six, equality is not simple. The notion of equal is "complex and difficult for students to comprehend" (RAND Mathematics Study Panel 2003, p. 53). Overcoming such difficulty is essential because an understanding of equality supports the transition from arithmetic to algebra and forms the basis for comprehension of equations and inequalities. The huge impact that understanding equality has on later algebraic understanding draws attention to the importance of identifying and tackling misconceptions that are related to equality when they arise in elementary school classrooms. This article describes ways the authors worked with school children in Ireland to refine nine approaches to developing notions of equality.