The author discusses the problem of creating a game playing situation in a kindergarten math class. Incorrect organization of game playing, with the teacher mainly concerned about "merry" presentation of the material, not only destroys the very essence of the developmental effect of mathematical content, but forms in a child distorted mathematical notions and kills interest in autonomous cognitive activity in math which alone is the appropriate cognitive and educational motivation. The author argues that the child's taking on the part of a character in a game helps to overcome the child's self-centeredness and solves the conflict brought about by transition from game playing as leading activity to the leading learning activity.