This study compares various approaches for incorporating family risk factors in explanatory models of children's achievement over the first 4 years of school. Living in poverty, in a single-parent household, in a household whose primary home language is non-English, and having a mother with less than a high school diploma are well-known risk factors related to lower achievement in reading and mathematics. This study examined three analytic approaches for describing children's level of family risk factors: 1) a cumulative risk index; 2) the four individual risk factor variables; and 3) unique combinations of the four risk factors, represented by a set of dummy-coded variables. Findings are based on a nationally representative sample of 10,345 children from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 (ECLS-K) who were first-time kindergartners in the fall of 1998. Data come from parent interviews in the fall of kindergarten and individual child assessments in reading and mathematics in the fall and spring of kindergarten, spring of first grade, and spring of third grade. A series of hierarchical linear models (HLM) were conducted to compare the relationships between each of the three risk factor approaches and children's initial achievement status and growth over the first 4 years of school in reading and mathematics. Results indicate that the unique combinations of risk factors present at kindergarten entry yielded more specific information on the relationship between family risks and achievement outcomes than the other approaches of using a cumulative risk index or using the individual risk factors as predictors. Children from single-parent households and those whose primary home language was non-English began school, on average, with lower achievement than children with no risks; however, if they had no other risk factors they tended to have higher initial scores and make greater growth over the first 4 years of school than children who's mothers did not complete high school. This study also found that children whose only risk factor was living in a home where English was not the primary home language had lower initial scores in mathematics but made greater growth over the first 4 years, in essence narrowing the achievement gap. Furthermore, increases in the number of risk factors were not always associated with greater achievement differences. Findings indicate that researchers should account for the specific combinations of risk factors present when exploring relationships between family background and student outcomes. (Contains 5 tables and 16 footnotes.).