Programming activities have the potential to provide a rich context for exploring measurement units in early elementary mathematics. This study examines how a small group of young children (ages 5-6) express their emergent conception of a dynamic linear unit and the measurement concepts they found challenging. Video of an introductory programming lesson was analyzed for evidence of preconceptions and conceptions of a dynamic linear unit. Using Artifact-Centric Activity Theory as a lens for the analysis, we found that social context, gesturing, and verbal descriptions influenced the children's understanding of a dynamic linear unit. Challenges that students encountered included developing a constructed conception of a unit, reconciling preconceptions about the meaning of a code, and socially-influenced preconceptions. This study furthers the exploration of computational thinking and mathematics connections and provides a basis for future exploration of dynamic mathematics and programming learning in early elementary education.