In this action research, first-graders were challenged to cope with a sequence of modelling tasks involving an analysis of given situations and choices of mathematical tools. In the course of the sequence, they underwent a change in the nature of their problem-solving processes and developed modelling competencies. Moreover, during the task sequence, the first-graders spontaneously discovered the power of organizing problem data in a table. They did not merely use their existing mathematical knowledge, but also "reinvented" tables as a new mathematical tool. This paper describes the gradual development of this tool as the children moved along the task sequence. Notably, the first-graders exhibited this progress in spite of having relatively little mathematical knowledge.