All Aboard for a Math Adventure!

We suspect many of you out there remember tackling a math question involving two trains traveling in separate directions or racing to a station. Middle School teacher Peter recently turned this classic word problem into a hands-on lesson by bringing a model train set into the classroom. 

The ultimate task? Figure out when to release two model trains traveling at different speeds so that the faster train reaches a 45-degree intersection just before the slower train. Sounds simple, right?

Wrong! As a fly on the wall in Peter’s classroom, we soon realized just how many systems of equations, math facts, and geometrical understanding went into this lesson. Teams of students had to calculate

Throughout the experiment, real-world details caused unexpected results: Do you measure from the front of the engine or to the end of the caboose? How long is each train? Is there any delay between when the ‘go’ button is pushed before the train moves? As they considered each detail, students made quick observations and timely adjustments to achieve their goal, all the while keeping their eyes on the prize: the prospect of setting up the biggest track possible on which to play with the trains once the project was complete. “Only if we have time,” cautioned Peter, causing one 8th grader to stand up and rally his classmates: “Alright everyone, lock in!”

With final calculations in hand, each team got to test their timing in three trials. Peter asked students questions to help them consider what, if anything, was off in their timing and which parts of their calculations could be adjusted. After only one tiny collision, every team was ultimately successful, and the groups finished their project by writing analyses on what worked well and what could be further improved.

In the final trial of the day, one team came down to the wire, deciding the appropriate release delay between trains with only minutes to spare before the bell rang to signal the end of class. They excitedly set up the engines on the branching tracks and focused closely on the stopwatch. The result was one for the record books. The two trains reached the intersection with such perfect timing that the magnet on the rear of train 1’s caboose and the magnet on the nose of train 2’s engine attached, creating one beautiful super train, with all passengers and cargo safely intact. You had to see it to believe it!