As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of instructional videos and live rehearsal to teach children how to decompose and accurately solve complex addition problems using only "mental math." Six first graders who did not use decomposition strategies at baseline participated in a single-subject, multiple-probe across participants design. Participants first learned component decomposition skills to identify ones and tens place digits, add tens place values, and retrieve simple addition facts. However, despite mastery of these skills, participants did not use the composite decomposition skill spontaneously when presented with complex addition problems. The primary investigator then provided training on how to apply the component skills to the composite skill. Following training, participants immediately used the composite skill to solve random, complex addition problems with sums up to 198. Results suggest that, through explicit instruction informed by skill hierarchies, children who do not use broadly applicable and efficient methods of solving math problems may come to match their peers in more challenging, mathematics-related activities.