Rendezvous on the River
“Two trains leave stations 180 miles apart on the same track heading towards one another. One is traveling 40 mph, the other 30 mph. When will they meet? Where will they meet?…”
Challenging American high school sophomores with this type of question has prevailed through the decades. Last week at OA, our students explored it in full experimental mode and answered these questions: Do textbook systems of equations actually work out in real life? Can we apply the properties of substitution and linear combination to our local river with OA students paddling as our variables?
In OA fashion, instead of trains, we took to the French Broad in canoes. The problem we focused on was this… If two boats start a certain distance apart, one team paddling upstream and the other downstream, how long will it take them to meet? How far will each boat travel before they meet?
The day opened with students creating their own hypothesis of this rendezvous location by observing the river current, staring and ending locations, and standing where they thought two boats, traveling towards one another would meet. This hypothesis forming was followed by lots of practice of fractions using physical objects: boats, paddles, humans, and whistles. This prepped students for figuring out the average rate of downstream travel and upstream travel for the student body of Semester 39. It was quite exciting to watch pairs students use their strength, calm minds, and determination to paddle tandem whitewater canoes upstream against the current with an audience timing them. The current was so strong that a few pairs even found negative rates of upstream travel, which only made our calculations more exciting! At lunch, Jess taught the community a very fun, upbeat rowing song from South Africa and another equally beautiful sailing song. A small group of students bravely stepped into the middle of the circle to lead the whole community in song.
Then, we were all back into the math problem at hand. Students broke out into class groups and used matrices, substitution, and graphing to solve the system of equations we had derived earlier in the day. The students discovered that the distance and time that would pass before the two boats met found with all three of these methods of math was only one second off from when they ran the experiment on the river themselves! Their accuracy in data collection and their consistency in paddling was incredible.
While celebrating the students’ tenacity in working almost an entire day on solving a single problem, we readily discussed the different variables that can influence data collection. Some of these variables include: student energy levels changing the strength of their stroke, river currents changing over the course of the day, or a boat taking a curved versus straight path up the river! Despite these possible variations, Semester 39 was extraordinarily close to their calculations as they paddled towards one another in real time, and surprised both themselves and faculty with both their paddling and mathematical skills. It was a rendezvous worth the trip!
Math Teacher, Wilderness Leader