The Common Core State Standards for Mathematics (CCSSM) require students with learning disabilities in mathematics to use a range of cognitive, skills, and foundational numerical competencies to learn and understand complex standards. Students with learning disabilities in mathematics experience deficits in cognitive processes skills and foundational numerical competencies which have emerged as underlying barriers associated with mastering CCSSM. Examining the impact of high-stakes assessments on readiness for college and careers and student achievement may provide evidence that deficits in cognitive processing skills and numerical competencies can impact achievement levels. Using the cognitive theoretical frameworks of Bandura and Gagné, along with the concepts of cognitive learning, instructional interventions, and inclusion, the relationship between students' scores in the algebraic foundations (AF) intervention inclusion method and the regular algebra (RA) nonintervention inclusion method, as measured on the end of the year assessments were examined in this study. An ANCOVA design was used to test the statistical significance of the relationship between the two intervention methods and the use of cognitive and numerical competencies for the two groups and to analyze the disparity in achievement scores between the AF intervention inclusion method and RA nonintervention inclusion method. The results revealed a statistically significant relationship between cognitive processing skills and foundational numerical competencies as measured on the final exam for both methods. The intended audience include academic communities using evidence-based inventions to improve college and career readiness results, leading to positive social change.