The gold-standard for evaluating the effect of an educational intervention on student outcomes is running a randomized controlled trial (RCT). However, RCTs may often be small due to logistical considerations, and resulting treatment effect estimates may lack precision. Recent methods improve experimental precision by incorporating information from large, observational, auxiliary data sets. Specifically, predictions of the outcome of interest from a model fit on the auxiliary data can be used in covariate adjustment. Such auxiliary data, on students or schools not included in an RCT, but with similar characteristics, is often available for educational RCTs. This is the case for a trial evaluating the efficacy of the Cognitive Tutor Algebra I curriculum (CTAI), an alternative algebra curriculum that included a computerized tutoring system. The Texas Education Agency (TEA) provides publicly available data on thousands of schools across Texas, including the 44 schools randomized in the CTAI study as well as nearly 3,000 additional, auxiliary schools. We develop an auxiliary model predicting passing rates for a standardized test in mathematics, which flexibly incorporates the 5,000 covariates available in the TEA data through random forest modeling. We compare our approach, using these auxiliary model predictions, to more standard estimators of the effect of CTAI on schools' mathematics passing rates. We find that leveraging information from the auxiliary data increases precision beyond standard methods that rely on the experimental sample alone, even for this paired trial with a powerful baseline covariate. We additionally demonstrate that working with auxiliary information provides practical benefits for analysis, beyond this increased estimation precision. [This paper was published in: "Proceedings of the 17th International Conference on Educational Data Mining," edited by B. Paaßen and C. D. Epp, International Educational Data Mining Society, 2024, pp. 518-25.]