Technology is an increasingly important component of education. Children’s mathematical interactions with technology have become a focus of mathematics education research, but less research has investigated constructs that contribute to these mathematical interactions. Attributes of children and technology play a key role in mathematical interactions and both children and technology can modify attributes during these interactions. Grounded in the Artifact-Centric Activity Theory and linked to recent developments in research on technology in mathematics education, this qualitative study extended an earlier exploratory study to investigate attribute modification. In particular, this study examined patterns of attribute modification evident during fifth grade students’ mathematical interactions with two mathematics virtual manipulative touchscreen tablet apps. Results included three categories related to attribute modification: (1) reactive attribute modification (linear progression or repeated repetition); (2) unperceived attributes and opportunities for proactive modification; and (3) proactive modification (seeking equilibrium, seeking disequilibrium, or seeking equilibrium and disequilibrium). Findings have implications for designers, teachers, and researchers of educational technology.