Trigonometry as a team sport

How do you measure something taller than you—especially if you don’t have a ladder? As Lori Reardon’s 8th graders will explain, you simply pull out your trusty clinometer, a tape measure, and a calculator, and get to work.

Today’s math class started with a review of a trigonometry formula that required students to practice with the tangent button on their calculators. These calculators are not the kitchen drawer variety; nearly as big as a loaf of bread, they are like calculators on steroids that serve as a tool in the problem-solving kit. “Calculators are handy, but they aren’t going to tell you what ‘x’ is,” Lori reminded the students.

After kids worked through warm-up problems, Lori brought out the clinometer. To the untrained eye, the device looks like a protractor with a straw on top and a weight hanging from the bottom. Similar equipment enables professionals to do complex calculations that ensure buildings are constructed correctly, roads are laid down evenly, and airport runways are accurate and safe. In fact, Lori told the class that her students from last year used the clinometer and trigonometry to build theater sets for one of the school plays.

Students took turns practicing with the clinometer to measure a ceiling corner in the room. Then it was time to team up and head outside to the deck. Kids formed four groups. The groups had an assigned resource manager who was charged with gathering the measuring equipment; a facilitator who was responsible for reading all the measurements; and a recorder/reporter, who kept a log of all the data.

Math teacher Lori Reardon shows a student how to use a clinometer.

Lori created four measuring stations: the basketball hoop, a light post, the corner of the building, and a ladder on the side of the building that led to the roof. Each team circulated among the stations, measuring twice to make sure their numbers were good. Students worked collaboratively with both their teammates and the other teams, sharing information and challenging assumptions. Lori bounced from group to group, coaching the kids and asking them questions that forced them to check their understanding.

Students take measurements of the light post using the clinometer.

Before I go into what came next, I have to point out that this is not the way I learned trig. In those dark days, I sweated it out in a classroom with 30 other kids while a bird-like woman lectured about formulas and rules that made no sense to my right-brain mind. My experience was the polar opposite of what was happening today in Lori’s classroom. Her students were actively solving real problems using real tools. And they were working in teams to do it.

After they gathered all their data, the students went back to the classroom to plug the numbers into equations. The teams wrote their findings on the whiteboard, and they took averages and ranges of the results. The results weren’t exact, but that was OK. The class talked about what factors influenced the outcomes, like eye height and precision in measurements.

In the end, each student had a solid understanding of the core principle. And while they may not have realized it, those kids also got a lesson in teamwork.

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