We are increasingly seeing an emphasis on STEM integration in high school classrooms such that students will learn and apply relevant math and science content while simultaneously developing engineering habits of mind. However, research in both science education and engineering education suggests that this goal of truly integrating STEM is rife with challenges. As such, this paper reports upon the efforts of an NSF-funded project to translate the lessons learned in science classrooms--in which the science learning goals are contextualized within engineering challenges--to engineering classrooms--in which the engineering practices are an additional, and important, learning goal. In particular, this paper identifies design principles for facilitating student application of math and science concepts while they engage in the practices of engineering. We explain the intent and learning theories behind each principle. In addition, we reify each goal by illustrating its application in our yearlong engineering course.