Past research has identified factors that help maintain the cognitive demand of tasks, including "drawing conceptual connections." We investigated whether teachers who were engaging in the teaching practice of "building"--and thus focusing the class on collaboratively making sense of their peers' high-leverage mathematical contributions--drew conceptual connections at a higher rate than has been found in previous work. The rate was notably higher (54% compared to 14%). By comparing multiple enactments of the same task, we found that this higher rate of drawing conceptual connections seemed to be supported by (1) eliciting student utterances that delve more deeply into the underlying mathematics, (2) giving students more time to explore the underlying math, and (3) using previously learned abstractions to help move the class toward understanding the new abstract concepts underlying a task. [For the complete proceedings, see ED657822.]