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Harnessing the Power of Primes

place Bulgaria

Game-On for Prime Factors: Making math class a memorable adventure.

"Game-On for Prime Factors" turns math class into an unforgettable experience. The project uses a board game to master prime factorization, linking it to cryptography. Students act as ethical hacking experts deciphering codes. The innovation is already successfully implemented in dozens of schools in Bulgaria, promoting strategic thinking and long-term knowledge retention.

Overview

Information on this page is provided by the innovator and has not been evaluated by HundrED.

Updated May 2026
Web presence

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Countries
All students
Target group
We aim to transform negative attitudes towards mathematics into a positive experience. Our innovation seeks to help students improve their calculation and concentration skills, and crucially, to connect prime factorization to the protection of their digital rights. We want math to be seen as powerful, relevant, and engaging.

About the innovation

Why did you create this innovation?

I created the 'Game-On for Prime Factors' project to solve a significant problem in middle school math: the abstract teaching of Number Theory. The curriculum requires students to master prime factorization, divisibility rules (2, 3, 5), and finding LCM/GCD. I saw that teaching these concepts abstractly led to disengagement and a lack of relevance.

My game’s creation is based on a two-part approach:

1. Connecting Abstraction to Cryptography: I recognized that cryptography is a foreign concept to students. My solution was to have the game bridge this gap, linking the abstract math of prime factorization directly to its essential real-world use in modern security and cryptography. I wanted to fundamentally change the student perspective, showing them why these skills are crucial. I view this connection as vital for improving math education as a whole.

2. Building Context through Play: My design uses a simplified board game environment. I designed this mechanism to allow students to quickly gain the necessary ‘life experience’ or context missing when studying abstract ideas. Through various hands-on scenarios, this acquired context is immediately and effectively used to grasp and solidify the mathematical abstractions, making the learning intuitive, memorable, and highly engaging.

What does your innovation look like in practice?

A game-based math class transforms the traditional lesson into a dynamic and engaging learning scenario.The session begins by dividing students into groups of 6–8, with game tables set up quickly (1–2 minutes), and each table receiving a game set.
Students familiarize themselves with the rules via a pre-prepared online video or the text in the game box (about 5 minutes). Each student then receives their 6 keys, and the game begins, lasting approximately 30 minutes.
After tallying results (2–3 minutes), the class moves to a crucial open discussion of learning outcomes. Key takeaways include:
The uniqueness of prime factorization.
The advantage gained by using divisibility rules.
The concept of asymmetric complexity (easy multiplication vs. hard factorization). The teacher uses this to introduce the application in cryptography and digital signatures.
Students often ask about the "hidden secrets" (number sequences and concepts) depicted on the cards. Teachers can direct students to the game's website for self-study or dedicate another class to these concepts, using the provided short videos to conclude the session. The class finishes with the awarding of "ancient keys" to the winners at each table.

How has it been spreading?

The game is disseminated through several key channels to ensure it reaches its intended audience of educators and the general public:
Firstly, the primary distribution method is through direct sales: schools can purchase the game sets via the official project website. While teachers theoretically have the option to manually create their own card sets, there are no known instances of this occurring, making the commercially produced sets the standard.
Secondly, the project actively engages with educators through promotional events. At least once during the school year, events specifically for teachers are organized to demonstrate the game and its pedagogical use in the classroom. These efforts are significantly bolstered by participation in scientific conferences, specifically to introduce teachers to the advantages of using games in mathematics education.
Furthermore, specialized training courses are offered with a license from the Ministry of Education. These courses are designed to acquaint teachers with the benefits of using games in the classroom, utilizing this specific game as a concrete example.
Finally, the game is spread through public engagement and outreach: We regularly participate in science festivals, allowing visitors to experience and play the game first-hand. We also attend board game-related events, where families and friends can play the game, broadening its visibility beyond the educational sector.

How have you modified or added to your innovation?

We continuously evolve the game experience. This is achieved primarily by introducing new games that utilize the existing components. This approach helps students connect knowledge by applying it to the same set of elements under different rules. We also prepare different, simpler variants of the game using technologies other than the core board game format. Furthermore, we add related classroom activities that build upon the game's concepts. Finally, we maintain a digital library of short videos or texts. These provide supplementary information about the numbers on the doors and their structure, thereby aiming to encourage curiosity in students.

If I want to try it, what should I do?

Here are the options if you wish to try the game:
Purchase and Play: You can buy the game directly from the official website. Once you receive it, you can familiarize yourself with the rules using the information provided in the game box or by watching the instructional video available on the website, and then proceed to play with your class.
DIY Option: Alternatively, you can study the game rules from the video available on the website and create a suitable set of cards yourself to play with your students.
Attend an Event: You can join an event we organize, bringing a group of your students along to participate in the scheduled games.
Invite Us to Your School: You can invite us to your school so that we can conduct a demonstration and run a game session directly with your students.

Implementation steps

Organizational Preparation
The class is divided into groups of 6-8 students. Each group sits in a playing area (for example, around a table) and receives one game set.
Mission
In the world of the game, people collect ancient wisdom. Evil forces hold humanity's secrets hostage behind 36 locked doors. Each group's mission is to free these secrets by unlocking the doors.
Cybersecurity experts, or "white hats," in the hacking world, increase system security by attempting penetration. The good forces, the "White Hat" group, strive to free the secrets. They always have 6 keys. Opening all doors earns the best white hat the ancient key to a human secret.
Game Rules Summary
Students watch a video or read the game rules, and the connection between the game rules and the mathematical concepts being studied is discussed. The key to each door is its prime factorization, based on the Fundamental Theorem of Arithmetic. Players use 6 "keys" (prime factors) to unlock doors by matching the prime combination (multiplication) to the number on the door. The specific role of 0 and 1 in multiplication is highlighted.
Executing the Mission to Liberate the Secrets
Each group plays their game. The teacher acts as a mentor to the groups but does not participate in the game. Each game lasts about 30–40 minutes. Depending on the students' level, the use of calculators may be permitted. This does not significantly change the difficulty of the game.
During the game, players will likely notice that it is much easier to make their move if they know the basic divisibility rules for 2, 3, 5, and 11. This allows them to discover the keys for the corresponding door.
Scoring the Game
When the last door is unlocked, each player counts the doors and keys in their collection, with each door worth 2 points, each key worth 1 point, and each unused "One" or "Zero" key worth 2 points.
The player with the most points is the winner of the group and keeps the key to all the secrets.
Discussion with Answers to Game-Related Questions
Example questions:
Could a door be unlocked in several different ways? Comment the Fundamental Theorem of Arithmetic, every number factors into prime factors uniquely.
Which operation is easier to perform—multiplication when you know the keys, or division when you have to find the keys knowing the door? -Comment the concept of asymmetric complexity of operations can be introduced.
What helps us reduce the difficulty of the task of prime factorization? -Divisibility rules.
Project: Create your own doors and keys (optional)
A worksheet is provided for creating your own door and keys for it. A pencil and possibly coloring materials are required.
The project is for independent implementation.
Using the doors and keys created by the students (optional)
Each student presents his/her door and the keys for it.
A display is made with the doors created and what images the students have chosen for them are discussed.
A game is played with the cards made by the students.