Unlocking Math Modeling Through League of Legends: A High School Course Blueprint
This article outlines a 36‑session high‑school curriculum that uses League of Legends to teach mathematical modeling awareness, basic methods, and self‑management, while also presenting real‑life examples, competition insights, and a step‑by‑step modeling process for students.
The course aims to develop awareness of mathematical modeling and basic methods by viewing the online game League of Legends through a mathematical lens, inspiring students to apply mathematics in games and fostering an intrinsic desire for modeling; it also introduces other real‑life examples to broaden students' horizons and uses the game topic to discuss self‑management and discipline.
The curriculum comprises 36 class periods spread over two semesters: the first semester focuses on cultivating modeling awareness, while the second provides deeper mathematical knowledge and training related to modeling.
For the teacher, the main challenges lie in (1) understanding the game, (2) extracting mathematical concepts embedded in the game, and (3) organizing the course; despite extensive playing experience, the instructor must bridge high‑level mathematics such as linear algebra and probability to middle‑school appropriate content and manage pacing with limited resources.
The flexible school‑based format allows trial‑and‑error, giving room for progress in uncovering the game's mathematical content.
Students, familiar with the game, are expected to be motivated by the “cheese” of mathematics in League of Legends, though deeper topics require extra effort; the course seeks to teach a general modeling workflow—problem identification, model construction, solution, and presentation—through independent projects that may demand additional time.
Course introduction: purpose, process, content, assessment, and sample lessons.
Mathematics of League of Legends “level‑up” functions.
Mathematics of attack power, defense, and skill bonuses.
Matching model: why win rates hover around 50%.
Team ranking problem – part 1: using match data to devise a ranking.
Team ranking problem – part 2: introducing an alternative ranking method.
General mathematical modeling process: problem definition, goal setting, variables and assumptions, model selection and construction, solving, and validation.
Overview of modeling competitions (U.S. high‑school, Jin Qiao Cup, Fang Zheng Cup) and university projects.
Student modeling paper – word‑forgetting curve case study.
Student modeling paper – school‑choice problem case study.
Sharing of student‑identified application topics and solution ideas.
Player damage functions: modeling health and mana changes in 1v1 scenarios.
Game theory in League of Legends: team fights, initial equipment design.
Resource allocation problem: distributing limited resources to maximize team strength.
Classroom presentations (session 15).
Classroom presentations (session 16).
Estimation exercise: assessing students' estimation abilities through a competition.
Course summary: reviewing the semester’s outcomes.
Model Perspective
Insights, knowledge, and enjoyment from a mathematical modeling researcher and educator. Hosted by Haihua Wang, a modeling instructor and author of "Clever Use of Chat for Mathematical Modeling", "Modeling: The Mathematics of Thinking", "Mathematical Modeling Practice: A Hands‑On Guide to Competitions", and co‑author of "Mathematical Modeling: Teaching Design and Cases".
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