Background: Since students' success in their first-semester college mathematics course is a key factor in their success in engineering, many summer bridge programs for underrepresented students focus on their preparation in mathematics. However, research on the design and efficacy of such programs is limited. We examine the design and effectiveness of a modeling-based approach to mathematics for entering freshmen engineering students. Purpose: The study addresses two questions: Does a modeling-based mathematics course in a bridge program positively affect students' performance in their first-semester college mathematics course? To what extent does a sequence of modeling tasks support the development of students' concepts of average rates of change? Design/Method: This quasi-experimental study compared two cohorts of bridge program students over six years to examine the effectiveness of a modeling-based mathematics course on first-semester mathematics course grades. Pre- and post--tests measured changes in students' concepts of average rates of change. Results: The modeling-based mathematics course closed the previous letter grade gap between bridge program participants and non-participants in the first mathematics course. We also found significant course grade gains for students who took the modeling-based mathematics course compared with a previous cohort who took a traditional summer mathematics course. Conclusions: These results suggest that the modeling-based mathematics course, with its focus on the development of engineering students' abilities to model changing phenomena, was effective in improving students' concepts of average rate of change and their first-semester mathematics course grade.