Model-eliciting activities (MEAs) challenge students to interpret a problem and collaboratively create solutions using the engineering design process. This Innovation to Practice article describes how science, technology, engineering, and mathematics (STEM) teacher educators can use MEAs to build elementary teachers' understanding of computational thinking (CT). Our Countdown Timer MEA is aligned with Grade 2 mathematics and computer science standards. We discuss how this MEA created opportunities for teachers in an online graduate STEM education course to engage as learners in unplugged and plugged CT activities. Teachers used algorithmic design and debugging to model a digital display and to create block-based code for a recess countdown timer. Teachers' reflections on how their learning experiences were different than those offered in step-by-step CT lessons allowed teachers to envision how MEAs can promote important CT dispositions of persistence in open-ended problem solving and tolerance for ambiguity. By aligning MEA design and facilitation with the phases of the engineering design process, teacher educators can use modeling to engage elementary teachers in facets of CT that are transferable to the elementary STEM classroom.