Equivalence of algebraic expressions is at the heart of transformational work in algebra. However, we know very little about students' understanding of equivalence. This study is part of a larger project that explores the use of CAS as a didactical tool for promoting both technical and conceptual growth in high school algebra with tasks specially designed by the research team. We report on a class of 10th graders coming to grips with the underlying theoretical ideas related to algebraic equivalence and on the role that the CAS played in the shaping of these newly emerging notions. Two different notions of equivalence of expressions were found to emerge: one was purely numerical and entailed reasoning about expressions for which some but not necessarily all numerical substitutions would yield equal values; the other entailed both numerical and common-form reasoning. Interpretation of CAS outputs (the equality test, in particular) played a role in occasioning discussions that don't normally occur in algebra classrooms and led to clarifying distinctions about equivalence for many. (Contains 3 figures.) [For complete proceedings, see ED496848.]