Since the 1950s, the understanding of how the base 10 system works has been encouraged through alternative base systems (Price 1995; Woodward 2004). If high school students are given opportunities to learn other base systems and analyze what they denote, we believe that they will better understand the structure of base 10 and its operations (Verschaffel and De Corte 1996). Special pedagogical knowledge is needed to teach numbers and operations (Ball and Bass 2000). In the primary grades, teachers focus on base 10 and often use base 10 blocks to support the development of operations and number structure. Learning other base systems forces the students to deconstruct a system that they do not always structurally conceptualize (Anderson, Reder, and Simon 1996). For example, students must critically analyze regrouping and scrutinize place values and digits (Woodward 2004). The activities presented in this article, for students grades 8-10, focus on two alternative base systems: base 5 and a student-selected base system beyond 11. Polynomial operations are also presented as they relate to alternative base systems. A bibliography is included.