An important goal of school mathematics is to enable students to formulate, approach, and refine problems beyond those they have studied, allowing them to organize and consolidate their mathematical thinking. To achieve this goal, students should be encouraged to develop expertise in a variety of areas, such as problem solving, reasoning and proof, communication, representation, and connections, as extolled in the National Council of Teachers of Mathematics (NCTM) Process Standards. In addition, teachers need to support their students' development of adaptive reasoning, mathematical understanding, strategic competence, procedural fluency, and productive dispositions toward mathematics and themselves as mathematics doers. Model eliciting activities (MEAs) are mathematical case studies that involve several variables. Engaging students in MEAs can help develop the skills and dispositions essential for effective mathematical practice and the expertise needed for resourceful problem solving. The choice of the "Aluminum Bat" problem, where students learn that engineers use the size of crystals to determine the strength of the material found in an aluminum bat, elicits thinking about finding the average area of irregularly shaped figures, given a set of micrographic pictures of aluminum crystals. Using the choice of the Aluminum Bat MEA as an example, and chronicling the problem-solving experiences of a group of students, this article shows how engaging students in MEAs supports the goals of STEM education by helping students develop a wide range of mathematical proficiencies.