Harnessing the power of primes: An educational game approach to prime numbers in middle school

Abstract

This study introduces an innovative, game-based approach to teaching specific abstract concepts in Number Theory (prime numbers, the Fundamental Theorem of Arithmetic, and divisibility rule) to middle school students by immersing them in a simplified cryptographic world. The author developed two original educational board games: "The White Hat and the Ancient Key" and "Hacker Duel," which use custom components (cards representing "doors" with composite numbers and "keys" with prime factors) to make the principles tangible. The first game is a cooperative and strategic exercise in prime factorization that models the concept of asymmetric complexity which is central to cryptography, while the second is a competitive duel focusing on distinguishing between common and different prime factors to understand the least common multiple (LCM) and greatest common divisor (GCD). Preliminary observations from implementation in Bulgarian schools suggest that this method effectively improves students' computational skills, encourages active use of divisibility rules, and fosters proactive mathematical thinking about fundamental concepts such as the uniqueness of factorization, demonstrating that educational board games offer a promising, innovative enrichment to traditional mathematics instruction.