SMALL-GROUP ENRICHMENT • REACH@LYCEUM
From Questions to Models
An eight-week group enrichment program in mathematical modeling and research thinking.
How do we turn an interesting question into something we can study? In this professor-guided modeling lab, students explore five investigations across different domains and learn to move from curiosity to assumptions, variables, mathematical models, and the mathematical questions that can deepen our understanding of the original problem.
A first step into research thinking
The central idea is to understand how a mathematical model is created—and how to judge what it can tell us. Students practice asking sharper questions, making their reasoning explicit, and connecting mathematics to problems beyond the classroom.
Format: Live online group enrichment • Duration: 8 weeks • Cohort: 10 students, brought together by a school or community organization.
How it works
Across five investigations, students return to the same essential habits of research:
1. Ask a precise question
Turn a broad curiosity into a question that can be investigated.
2. Make the assumptions
Choose the variables, identify the relationships, and decide what to simplify.
3. Build and explore a model
Use mathematics to express the assumptions and relationships underlying the original question.
4. Identify the mathematical questions
Identify the mathematical questions arising from the model that can help us understand the original problem.
What students learn to do
• Formulate a clear question about a problem.
• Identify useful variables and explain simplifying assumptions.
• Translate relationships into a mathematical model.
• Identify relevant mathematical questions arising from the model.
• Explain how those questions can help us understand the original problem.
Who is it for?
This program is designed for organized cohorts of 10 advanced high-school students through schools, homeschool associations, parent associations, math circles, and STEM organizations. Participation is arranged through the cohort organizer; individual enrollment is not offered.
Organize a Group Program
Schools and group organizers can contact REACH@Lyceum to discuss hosting a cohort and receive program details.
What comes next?
From Questions to Models is a separate group enrichment offering alongside our three individual mentorship tracks: Foundations, Topical Review, and Research Fellowship. Students interested in individual mentorship can discuss their preparation, interests, and goals with REACH@Lyceum.
Organize a Group Program
Representing a school, homeschool association, parent association, math circle, or STEM organization? Contact REACH@Lyceum to discuss an eight-week online program for your cohort of 10 students.