Introductory calculus-based mechanics ("Physics 1") is an important gateway course for students desiring to pursue a science, technology, engineering, and mathematics (STEM) career. A major challenge with this course is the large spread in the students' incoming physics preparation. This level of preparation is strongly predictive of a students' performance because of the overlap between Physics 1 and high school physics courses. Because the level of students' incoming preparation is largely determined by the quality of their high school physics courses, Physics 1 can amplify K-12 educational inequities and be a barrier for marginalized students wishing to pursue a STEM career. Here, we present a novel introductory course design to address this equity challenge. The design and implementation are based on the concept of deliberate practice as applied to learning real-world problem solving. Students explicitly practice research-identified decision-based skills required for problem solving in the context of solving real-world problems. The problems used in the course and their solutions have little resemblance to what students encounter in high school physics, thereby reducing the dependence of course performance on the high school physics preparation. Versions of this course were taught at a highly selective private and a lightly selective public university. The students who took the course learned the physics content knowledge they needed for future courses, particularly in engineering, and their problem-solving skills improved substantially. Furthermore, their course performance had much less correlation with their incoming physics preparation than was the case for the outcomes from the traditional Physics 1 courses at both institutions: in one case the correlation dropped from r = 0.62 to 0.14, and on the other case the correlation dropped from r = 0.56 to 0.26. These findings suggest this course design can be a more equitable version of the traditional Physics 1 course, and hence particularly beneficial for marginalized students.