As education seeks to mold itself to fit the demands of the 21st century, STEM education will continue to be an important consideration. The integrated and crosscutting nature of STEM is incorporated into the "Next Generation Science Standards" in which engineering design is raised to the same level as scientific inquiry and is expected to be taught in science classrooms. This report analyzes a 2014 Utah survey of science teachers to understand how prepared Utah science teachers are to teach engineering design and the relationship between their preparedness and beliefs about whether building prototypes, computer modeling, and mathematical modeling belong in the instruction of engineering design. Ordinary least squares (OLS) regression results indicate that physics teachers are the most prepared to teach engineering design and that science teachers are significantly more prepared to teach an integrated STEM curriculum, such as engineering design, when they agree that modeling techniques from each STEM discipline should be used in instruction. It is recommended that teachers in STEM classrooms be comfortable and fluid in each STEM discipline, instead of representing one single subject expertise with some familiarity with the other three.