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 from ages 5-12 with a focus on mathematics performance. We found that nonsymbolic quantity knowledge and repeating patterning 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 first grade. These findings suggest that nonsymbolic quantity knowledge and repeating patterning knowledge prior to formal schooling are valuable indicators of low-income children's performance on high-stakes state math tests in the middle grades. [The paper was published in "Journal of Educational Psychology" v111 n3 p402-413 2019.]