Within STEM (Science, Technology, Engineering, and Mathematics) education, integrating real-world problem scenarios is paramount. Within interdisciplinary education, modeling is an approach to fostering student learning and skill development in a student-centered learning environment. This study focuses on an integrated physics and mathematics course in STEM education based on modeling for first-year engineering students. The main objectives of this study are to analyze students' models, assess the effectiveness of the pedagogical approach, and evaluate the benefits of integrative education. This study uses a Model-Application Activity as a closure for the quadratic model and extends the models built to a two-dimensional motion situation. The core activity involves a real-world experiment where students attempt to roll a ball down a ramp into a cup. While most groups successfully constructed theoretical models, only a few hit the target, highlighting the complexities of applying theoretical knowledge to real-world scenarios. The study also emphasizes the seamless integration of physics and mathematics, enriching the learning experience and making the models more robust and versatile. Despite the promising results, the study identifies a gap between theoretical understanding and practical application, suggesting the need for more hands-on activities in the curriculum. In conclusion, this study underlines the value of integrating physics and mathematics through modeling and a student-centered approach, setting the stage for future research to enhance the effectiveness of STEM education.