Many researchers and philosophers recognize the importance of critical thinking and reasoning skills in the life of all students. However, they failed to address the question of how such skills may be incorporated into mathematics lessons or activities. While such skills are often included in mathematics curriculum, they are not always seen in the lesson. This paper presents the integrations of critical thinking and reasoning skills into a sample lesson through block factor game for teaching factors of a number to young learners to play and list factors of a given number. Scholars have agreed that making mathematics practical using concrete materials in the form of game makes it interesting and fun for learners. Two participants in primary 2 and primary 6 were involved in this study through qualitative research design of case study. Data collection was done through audio-and-videotaped. The students’ responses to questions and tasks indicated conceptual understanding and acquisition of critical thinking and reasoning skills. Critical thinking and reasoning skills are incorporated into lesson through critical questions, and games or well constructed tasks in appropriate context. Also, the participants were able to list factors of a given number correctly and also determine the divisibility of a number by another number using block factor game.