Computation competence (CC) with non-counting (NC) strategies is an important aim of Grade 1 mathematics education, but studies have shown that many students struggle to acquire these skills and continue to rely on counting strategies in later years. Therefore, even though counting is an important first strategy for young children, it is vital to support the development of CC with NC strategies from the earliest stages of mathematics education. This study examined the success of an intervention to promote the use of CC and NC strategies and conceptual subitizing (CS). The study was conducted with a sample of N = 1017 Grade 1 students, and investigated whether the achievement gain was affected by the intervention setting: cooperative learning, individual support for low achievers, a combination of the two settings, and a control group. Students in the combined setting had greater achievement gains in CC with NC strategy use and CS than the control group and outperformed those in the other intervention groups in CS. The combined setting also benefitted low achievers in mathematics for CS, but not for CC and strategy use. A combination of cooperative learning and individual support seems to be the best option for improving the CS and CC and NC strategy use of first graders, especially low achievers in mathematics.