Stories
Pedals into Proportions
October 21, 2025
At Aspen Country Day School, outdoor education isn’t just a fun excursion. It’s also a chance for students to forge real-life connections between classroom concepts and the world around them. For ACDS Fourth Graders, a sequence of mountain biking expeditions becomes more than just fresh air and trails: It’s a rolling math lab in motion.
The Fourth Grade mountain biking sequence is intentionally structured to build skill, confidence, and understanding over time. At the beginning on the school year, they start on local trails near campus, with students practicing the fundamentals of riding. Then in October they head to Western Colorado and the trails near Fruita. In the spring they explore the red-rock canyonlands near Horsethief, Utah. Along the way they dive into desert ecology, basic bike mechanics and maintenance, and the expedition habits of character, respect, responsibility, and perseverance.
The beauty of the ACDS Outdoor Ed program is how deliberately the classroom feeds the trail and the trail feeds the classroom.
Before hitting the trail for real, ACDS Fourth Grade teacher Rachel Nahirny prepares students with a math lesson inspired by the PBS LearningMedia learning activity on Gears and Proportions. The lesson helps students explore how gear sizes and arrangements affect motion, including how changing the ratio between front chainring and rear cog affects how many times you must pedal to make the wheel turn and thus influences ease, speed, and effort.
With this foundation, students arrived on the trail ready to ask:
- “If I shift into a smaller rear cog, how does that change how hard I have to pedal versus how fast I go?”
- “What gear will make climbing easier? What gear will make flats faster?”
- “How does terrain affect my gear choice and the ratio I’m working with?”
The beauty of the ACDS Outdoor Ed program is how deliberately the classroom feeds the trail and the trail feeds the classroom. Students learn about the engineering concepts that make their bikes work. As they practice their basic riding skills, they discuss how their gear choices make a difference. Then, when they head out to Fruita and Utah, they put their conceptual knowledge to the test with longer rides, varied terrain, and real shifts in elevation.
Why It Matters
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- Authentic connections: The math of gear ratios stops being abstract when you’re mid-trail, pedaling uphill, thinking, “I should have shifted.”
- Skill and thinking: Students don’t just ride; they reason. They choose, they reflect, they adjust.
- Confidence and resilience: Navigating unfamiliar trails and terrain builds character. The math lends another layer of insight and ownership.
- Relevance: Learning about mechanics, ratios, ecology, and expedition behavior connects to life beyond the classroom.
Academics and outdoor learning continue weaving together as the school year progresses. Students debrief after their fall excursion: What gear selections did they make? How did terrain affect those choices? How many pedal revolutions did they require for each wheel revolution?
Next year when these students tackle more advanced trail terrain on Fifth Grade Outdoor Ed, they’ll revisit some of their first routes near Fruita. At that time they’ll also bring more experience, more mathematical insight, and even greater readiness to excel.