Division is regarded as the most difficult of the four basic operations for students to learn. Yet, there is little research on how teaching can support students learning of methods for multi-digit division. Supporting students’ own construction of methods, rather than letting students imitate given methods, has been shown to result in more sustainable learning for other mathematical topics. However, designing teaching that is contingent to students’ own construction requires knowledge of students’ construction processes for the method in question. In this case study, we provide a detailed example of such a process regarding a method for multi-digit division. The results show that students can construct increasingly sophisticated methods for multi-digit division based on additive partitions of the dividend into multiples of the divisor.