Cara, a seventh-grade student with learning disabilities (LD) in mathematics, believes that the ratio 2:3 is equivalent to 4:5 because there is a difference of one between the two numbers in each ratio and there is a difference of two between corresponding numbers in the two ratios (2 + 2 = 4 and 3 + 2 = 5). This misconception affects her ability to find equivalent ratios as well as to work with ratios and proportions in multiple contexts, including determining rates of change with functions and other contextual situations. Why are ratios and proportions important for students' success in mathematics? What are common misconceptions that challenge students with persistent mathematics difficulties? What lesson components for intensive interventions are necessary to address the instructional needs and misconceptions of students with persistent mathematical difficulties? How can progress-monitoring results inform instruction and address misconceptions? Cara's teacher seeks to find the answers to these questions in order to identify ways to support Cara's understanding of ratios and proportions.