This work presents a proposal for teaching binary numbers in the basic education level through playful and motivating activities based on: a trick to perform a (magic) of guessing, a secret message that needs to be unveiled and a game called Nim, which has a winning strategy developed and demonstrated by the mathematician Charles L. Bouton. We begin with a conceptual approach on the positional numeral system and the base 10, and then we will talk about the binary numeral system and its relevant aspects. We introduce the theory that underlies the binary magic cards and analyze Boutons winning strategy for Nim, including a fresh view on that strategy. Subsequently, we describe the three proposed activities that can be applied in classes of Elementary II and High School. We conclude presenting the methodology and considerations about the application of these activities in the ninth grade classes at a public school in the municipality of Guapimirim, in the state of Rio de Janeiro.