There is a notable shift towards prioritizing the teaching of engineering design within K-12 education, coupled with a strong recommendation for engineering design-based integrated STEM education. This approach underscores the sharing of science and engineering practices as a means to facilitate the learning of various STEM disciplines. Nonetheless, the implementation of integrated STEM education in rural schools poses challenges due to constrained resources and a shortage of high-quality programs. To present a tangible instance of design-based integrated STEM education within a rural setting, this study presents a model lesson that showcases the integration of interdisciplinary problem-solving skills within a genuine real-world context. This study examined how teacher collaboration for engineering and science shared practices influenced students' design process. Concurrent Think-Aloud (CTA) protocol data and design sketches produced by the student design teams during the protocol sessions display how they elicited their design thinking skills and STEM domain knowledge acquired from the integrated STEM lesson in an engineering design task. This study found that the students learned the model lesson through the fully integrated instruction between students and teachers utilized more balanced design cognitions than the silo approach of integration. The findings highlight that the utilization of engineering design in K-12 education to cultivate integrated problem-solving skills should be accompanied by domain-integrated instructions for effective implementation.