The 2004 reauthorization of the Individuals with Disabilities Education Act (IDEA) approved schools' use of alternative methods for determining student eligibility for special education services. IDEA encourages schools to intervene as soon as there is a valid indication that a student might experience academic difficulties, rather than after performance falls well below grade-level. The Response to Intervention (RtI) framework is an approach for providing instructional support to students at risk for these difficulties. RtI models typically have three tiers of increasing intensity of instruction (Gersten et al. 2008; Gersten et al. 2009). Tier 1 involves research-based core instruction delivered with high fidelity in the classroom by the classroom teacher and universal screening of all students to determine who should receive additional instructional support. Tier 2 involves focused/intensive instruction, often in small groups, for children at risk for failing in the Tier 1 setting. Tier 3 involves even more intensive instruction for students not responding to the Tier 2 interventions and often comprises individual tutoring, referral to a school psychologist, or both. Despite increasing interest, there is little research on the effectiveness of recommended best practices in RtI (Gersten et al. 2008; Gersten et al. 2009). A recent literature review of grades K-3 mathematics interventions suitable for use in Tier 2 revealed just nine relevant studies (Newman-Gonchar, Clarke, and Gersten 2009), with just one that was a rigorous evaluation of an intervention, and that used a randomized controlled trial (RCT) design (Fuchs et al. 2005). The Fuchs et al. (2005) study examined the impact of "Number Rockets", a small-group tutoring intervention for grade 1 students at risk for mathematics difficulties, and found statistically significant positive effects on several measures of mathematics proficiency. But that study was an efficacy trial (one implemented under ideal conditions), involved considerable monitoring and support for experienced tutors, and was conducted in a single district. This study builds on the Fuchs et al. (2005) study and is the first large-scale effectiveness trial (one intended to approximate real-world implementation) of "Number Rockets". The current study addresses the following confirmatory research question: Do grade 1 students at risk in mathematics who participate in "Number Rockets" perform better than at-risk control students on the Test of Early Mathematics Ability-Third Edition (TEMA-3; Ginsburg and Baroody 2003)? The study also investigated three exploratory research questions: (1) Does "Number Rockets" have a differential impact on grade 1 students at risk in mathematics, based on baseline mathematics proficiency?; (2) Do grade 1 students who participate in "Number Rockets" score differently than control students on the Woodcock-Johnson-Third Edition Letter/Word (WJ-III Letter/Word; Woodcock, McGrew, and Mather 2001) subtest?; and (3) Do the impacts of "Number Rockets" vary significantly depending on the average number of lessons delivered within a school? This RCT was implemented in 76 schools in four urban districts across four of the five Regional Educational Laboratory Southwest states. The target student population was grade 1 students at risk for mathematics difficulties who received mathematics instruction in English in a regular education classroom. The main finding of this effectiveness study is that grade 1 students at-risk for difficulties in grade 1 mathematics benefited from participation in the "Number Rockets" intervention. At-risk students in the intervention group showed statistically significant higher performance on the TEMA-3, a broad measure of student proficiency in mathematics, than at-risk students in the control group. This finding was observed in a sample of 994 students from 76 schools in four urban districts across four states. The results of all three exploratory analyses (related to differences in baseline mathematics proficiency, performance on a reading test, and number of tutoring sessions) were not statistically significant. Appended are: (1) Study timeline; (2) Power analysis assumptions; (3) Parent consent form; (4) Screener subtest details and descriptive statistics; (5) Student mobility; (6) Fidelity measures; (7) Models used for confirmatory, exploratory, and sensitivity analyses; (8) Lessons; (9) Complete sample lesson Topic 6, Day 1; (10) Details of tutor training; (11) Tutor background survey; (12) Details of fidelity coder training; and (13) Complete multilevel model results for chapter 4 (confirmatory and sensitivity) and chapter 5 (exploratory and sensitivity) analyses. (Contains 39 tables, 13 figures and 83 footnotes.) [This report was prepared for the National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences by Regional Educational Laboratory Southwest administered by the Edvance Research.]