As a geometry teacher, I constantly strive to show students how mathematics is more than just numbers and formulas, it’s a lens through which we can view, analyze, and solve the world’s challenges. One of the most powerful ways to achieve this is by integrating mathematical modeling into the study of geometry. Mathematical modeling connects the abstract concepts of geometry to real-world applications, making learning both meaningful and practical.  In our classroom, mathematical modeling starts with a question: How can we use geometry to make decisions or solve problems? For example, imagine we’re designing a triangular park with a walking path that maximizes space efficiency while staying within specific boundaries. Using modeling, students calculate the optimal dimensions of the park, analyze angles for pathways, and even consider material costs for construction. This process not only reinforces their understanding of geometric principles but also gives them hands-on experience in problem-
solving. 

Why Modeling Matters? 
Mathematical modeling brings geometry to life. It bridges the gap between theory and practice by showing students how geometric shapes, measurements, and relationships play a role in everyday life. Modeling challenges students to think critically and creatively. Unlike textbook problems, which often have one correct answer, real-world problems require assumptions, approximations, and iterations. This process develops critical thinking and resilience.  Moreover, modeling encourages collaboration and teamwork. In our class projects, students work together to design models, critique solutions, and present their findings. For example, we recently explored how to maximize seating arrangements in our rectangular classroom while maintaining aesthetic appeal. Students learned not only about rectangles and area but also about compromise and communication, which are valuable skills in any field. 

As teachers, we have the unique opportunity to show students how math connects to their lives and future careers. Whether it’s designing a park, constructing a building, or planning a garden, mathematical modeling in geometry equips students with the tools to solve real-world problems. It fosters critical thinking, teamwork, and a deeper appreciation for mathematics. By incorporating modeling into our geometry lessons, we not only teach students about shapes and measurements but also inspire them to see the beauty and power of mathematics in the world around them. Geometry becomes more than just a subject, it becomes a tool for understanding and shaping the world.