Computational thinking (CT) activities are increasingly being integrated into early childhood schools. We focus on studying children's learning using an "unplugged" (non-computational) learning unit that considers a teacher's knowledge and classroom space and affords seamless adaptation into the classroom given the objects used in the unit and activities that are reminiscent of classic class activities and games. The gap in research that we address is the focus on unplugged activities, which are less common. A learning unit with card games was developed, focusing on two fundamental sorting algorithms: Linear Sort and Category Sort. Sixteen kindergarten children participated in the study. Their CT skills were assessed using a pretest-intervention-posttest single group research design. An increase in CT skills was observed from an intermediate to a sophisticated level; the number of attempts to completion decreased and the average number of attributes the children could sort with increased. Two children's interactions with the activities were analyzed in depth and compared. It was found that two concepts related to algorithms had to be learned separately and sequentially: multiple repeating actions and a stopping rule for repeating actions. With advanced challenges that involved multiple attributes and more than one sorting algorithm, children needed significant support.