Human social behavior is rhythmic, and synchrony plays an important role in coordinating and regulating our interactions. We are developing technology that allows the robot Keepon to perceive and behave rhythmically, and to synchronize its dancing behaviors to music or to children's movement as perceived using pressure sensors. We present two experiments in which Keepon dances with children to music, and in which the robot's rhythmic attention and role of leader or follower are manipulated in order to examine the effects on engagement and rhythmic synchrony. We found that children can assume the roles of leader or follower in a rhythmic interaction, that followers indeed tend to synchronize with the robot's movements, and that the role of follower causes the children to more closely follow a musical rhythm.