Interventions to support children with mathematical learning difficulties typically address deficits in domain-specific knowledge. However, not all students benefit from these instructional programs. In this case, some authors suggest an even more intensive instructional program combined with other factors assumed to be relevant for learning. Previous research has demonstrated that working memory is such a factor. It underpins a range of cognitive abilities, including arithmetic and mathematical development. For this reason, we developed an integrated approach, a working memory sensitive math intervention. This new approach aims at domain-specific knowledge, while a) taking poor working memory into account and b) stimulating learners to invest cognitive resources in mental confrontation with the learning content. The present multiple baseline study was designed to investigate its effects. On the basis of their low performance in a standardized test of mathematical precursors, we identified 13 first graders (mean age 6.8 years) to take part in our study. Over a period of four weeks, the children participated in 12 half-hour sessions of our program. Results show small to large positive training effects on competencies that are near to the training, though not for all participants. We discuss why the intervention works well for some children, only moderately for others, or fails to work.