State-mandated tests have taken center stage for assessing student learning and for holding teachers and students accountable for achieving adequate progress. What types of early knowledge predict performance on these tests, especially among low-income children who are at risk for poor performance? We report on a longitudinal study of 519 low-income American children ages 5-12, with a focus on mathematics performance. We found that nonsymbolic quantity knowledge and repeating pattern knowledge at the end of preschool were reliable predictors of performance on standards-based high-stakes tests across three different grade levels (4th-6th grade), over and above other math and academic skills. Further, these effects of preschool math knowledge were partially mediated through symbolic mapping and calculation knowledge at the end of 1st grade. These findings suggest that nonsymbolic quantity knowledge and repeating pattern knowledge prior to formal schooling are valuable indicators of low-income children's performance on high-stakes state math tests in the middle grades. [For the corresponding grantee submission, see ED600991.]