Math 10 Students Use Trigonometry to Solve a Crime


A newscaster (very much resembling math teacher Mr. Steve Bates) comes on the television to deliver breaking news.

“At precisely 7:47 this morning, Mr. Andy Rodford, Director of the Senior School at St. Michaels University School, was shot with a foam dart. While standing in front of an open east-facing window in his office, taking in the morning sun, he was struck with a dart from a high-powered child’s foam dart rotary cannon. Police officials have re-enacted the scene based upon forensic evidence and discovered that the dart impacted his neck at an angle of 4.5 degrees. Mr. Rodford was uninjured.”

Armed with this information (plus the knowledge that Mr. Rodford stands 6-foot-2 and his office is 10 feet above the ground), Steve and Mr. Evan Fryer’s Grade 10 math and pre-calculus students were put to work solving the imaginary crime.

“They weren’t using forensic evidence or detective skills. We structure the questions and clues such that they have the necessary data to work with, and only trigonometry can help them the rest of the way,” Steve says.

Once students used math to find the exact spot from which the dart was shot, there they’d find a series of clues – three trigonometry puzzles – the fictitious shooter left behind to ultimately reveal their identity. Solve those, and students would be led straight to the perp.

The clues all corresponded with the assailant’s getaway, first calculating the length of wire needed to zipline from one building to another on campus, at an angle of depression of 6.8. The second had students using a clinometer to calculate the horizontal distance the shooter travelled on a slip and slide downhill to their final escape route. The last clue saw the perpetrator charter a hot air balloon from campus to the top of the Space Needle in Seattle, and students needed to determine the horizontal distance between the two locations to uncover their last clue.

“First of all, they’re making the math meaningful for them. These kind of activities, getting outside, getting students engaged in the math, it gives students the desire for the instruction, as opposed to just giving them the instruction and giving them problems to do. It changes the way we teach,” Evan says. “It’s designed so there’s this optimal flow of learning, they don’t pay attention to anything other than the fact they want to finish this math problem. The clue is motivating to them to get the answer; it doesn’t matter to them that they’re doing trigonometry, they’re just solving a problem with what they know.”

The two teachers concocted this idea with the goal of giving students an opportunity to learn in a meaningful way that doesn’t simply involve them absorbing instruction in-class.

“A couple of weeks ago they wouldn’t have had the knowledge of how to figure it out. Grade 10 is their first introduction to trig, so they don’t have that background. We had to go through and give them the base skill set and all the algebraic skill to go with it, so then we’re now just looking for them to apply it in a greater sense,” Steve says.

“All of this is in our effort to really be intentional about how we teach, not just what we teach, and starting to align ourselves with the new B.C. curriculum that focuses more on the competencies; the communication and critical thinking, not just the content in the classroom,” Evan says. It’s also intentionally aligning with the school’s Grade 10 experiential program, which aims to connect in-class lessons with real-world experiences.

So who was the shooter? Well, we can’t say. Both teachers hope to run hands-on problems like this more often in class, and will likely use this problem again in future years. Students in all three Grade 10 classes managed to work together to solve the crime, so unless you know trigonometry, you may need their assistance to help you ID the shooter.

(photo by Kyle Slavin)



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