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Middle School Math Department | Beyond the Ruler Indirect Methods in Mathematical

June 6, 2025

“Math is more than equations—it’s a way of seeing the world.”

When rulers and tape measures can’t reach, ancient wisdom steps in. From Egyptians using knotted ropes to measure land, to Eratosthenes estimating Earth’s circumference with just a stick and a shadow, people have long used creativity to extend the limits of measurement. Today, our 7th graders carry on this tradition with a hands-on “Geometry Challenge” across the school campus.


The journey began with students becoming historical investigators, tracing the evolution of indirect measurement. How did medieval architects scale towering spires? How do astronomers measure distant stars? These stories sparked their curiosity—math, they realized, is a tool for solving real-world problems.


Stepping outside the classroom, students worked in small teams using homemade clinometers, mirrors, and even their own shadows to tackle real-world challenges: How tall is that tree? How high is the flagpole? How wide is the pond? They experimented with different methods—mirror reflection, shadow ratios, angle measurements—and adapted their approaches with creativity and precision.







Their curiosity drove deeper thinking: “What happens if the sun goes behind a cloud?” “Can eye level replace full height in calculations?” One team even developed a “double-angle method” to calculate river width, demonstrating impressive mathematical thinking.







In the final showcase, students presented their work through hand-drawn diagrams, dynamic videos, and detailed data analysis. One group even used LEGO bricks to build scale models, turning complex math into something visual and hands-on. These creative formats reflected not just their understanding, but their ability to apply and express it.








This indirect measurement project was more than a math lesson—it was an exploration of how math connects to life. It sharpened students’ observation, reasoning, and collaboration skills, and helped them see the world through a mathematical lens. Through this experience, they are growing into thoughtful, curious, and capable learners for the future.

Written by Wei Xu

Pictures by Grade 7 Math Teachers

Edited by Cong Luo

Reviewed by Zheng Wenyin, Chenli Shen, Cong Luo, Judah Kuhn