Despite focused efforts, achievement gaps remain a problem in America's education system, especially those between students from higher and lower income families. Continued work on reducing these gaps benefits from an understanding of students' reading and math growth from typical school instruction and how growth differs based on initial proficiency, grade, and demographic characteristics. Data from 5,900 students in Grades 1-5 tested in math and reading at 6 points across 2 years were analyzed using cohort-sequential latent growth curve models to determine longitudinal growth patterns. Results indicated that students with low initial proficiency grew more quickly than students with higher proficiency. However, after 2 school years their achievement remained below average and well below that of students with higher initial proficiency. Demographic characteristics had small but significant effects on initial score and growth rates. Educational Impact and Implications Statement: The present study determined that students who start out the school year with very low scores on math and reading assessments gain knowledge and skills at a faster pace than students who start with higher scores. However, the lower-scoring students do not grow at a rapid enough pace to catch up to their higher-scoring peers. As a result, achievement gaps are maintained over time. Efforts to raise the achievement of struggling students will need to involve educational interventions that accelerate growth to a much greater degree to make progress in closing achievement gaps.