I begin this lesson by reviewing graphing the trigonometric functions and transformations with my students. I tell them we’ve already discussed periodicity and real-world applications using sine and cosine and today we’re going to work with data that is best modeled by a tangent function. I ask them to think back to geometry and when they used the tangent of an angle to solve a problem. Usually a student will come up with something involving the slope of a ramp or road, or maybe the height of something given the angle of elevation. If I don’t get any responses, I draw a right triangle on the board and ask where they might see/use that. Once we’ve identified a couple of examples, I tell them that for today’s challenge they’ll be working in teams of 2, but that each student needs to be able to apply what we’re learning.
The goal for this part of the lesson is for students to be able to see that tangent functions are actually used in real-world situations. In addition, I hope my students become more comfortable using their calculators and also become more confident as problem solvers. You will need copies of the Washington Monument Challenge ready, and students will need their graphing calculators. I ask students to pair up with their front partner (see my strategies folder for grouping tips) and give each student a copy of the Washington Monument Challenge. Some students will struggle with what to do first, which is why I include “make a sketch” in the directions on the Challenge sheet. (MP1, MP4) If a team is still struggling after making a sketch or cannot figure out what to draw I try to talk them through what they would be doing if they were actually standing at the Washington Monument. As the teams work through this challenge I walk around to help as needed and to observe what strategies my students are employing to solve this problem. It’s very informative for me to see how they go about setting things like this up and also how they talk through their reasoning about whether they’ve done it correctly.
When all the teams are done I have each team present their work to the rest of the class using our document camera and projecting on the whiteboard. Each team is given 2-3 minutes to present and 1-2 minutes to answer questions (if necessary). I look for whether or not the students were able to write a tangent equation to model the data and how well their equation fits the data. Some teams will be better at this than others, but since the goal is just to write an equation that fits the data, we don’t judge which are better or worse this time. As each team finishes, I have them write their equation on the front board.
There is also a video narrative to complement this section of the lesson that discusses my pedagogy. To close this lesson, I ask the class to compare all the equations on the front board. We identify as a class what they all have in common and in what ways they differ. I ask each student to write down all of the equations and to make sure they have the data entered into their calculator. Their assignment for tomorrow is either to determine which equation fits best or to use the equations to make an even better one and write both the equation they chose/created and why.