For this lesson I changed things a bit from what I’d been doing with this trigonometry unit and returned to a more traditional format because I know that is what they are most likely to experience in college. I begin this lesson with the following equation and question on the board: sin2Θ + cos2Θ = 1 and “What familiar equation does this resemble?” Many of my students will begin discussing this before class begins, so if you want it to be an independent activity, be sure to state that on the board and/or wait to post the question and equation until after your class begins. As the bell rings I ask my students to think-pair-share about the post on the front board and give them 2-3 minutes to complete the task. This question is really about helping my students learn to apply prior knowledge when introduced to a new concept, in this case recognizing the similarity between the structure of the posted equation and the Pythagorean Theorem (MP7). I walk around during this time making note of which students/pairs are on track and which ones seem lost. When I call time, I either share comments I’ve heard or ask students to share their comments with the class. As they share, I also prompt them to explain how they’ve arrived at their conclusions. (MP2) If this is the first time you’ve asked your students to explain their thinking, you may have to be more specific in your questions. For example, if a student responds with “I thought it was like the Pythagorean theorem because they look the same” you might follow up with “In what way(s) does this look like the Pythagorean?” When I’ve gotten responses from all the groups, I put the Pythagorean equation under my original equation, lining up the respective components. You can see a picture of my whiteboard entitled “Pythagorean Identity” in my resources. Then I tell my students that the first equation is called a “trigonometric identity” and that today we are going to walk through a proof of the equation, using our understanding of the Pythagorean Theorem.
When I’ve completed the example and answered any questions from my students I tell them that for their homework, they will be practicing applying what they’ve just learned. I assign problems that specifically work with the Pythagorean Identities and finding values. I tell students that I need to see their mathematics, but that I also need them to write about the problems to explain why they chose to solve each one as they did. (MP2) A copy of the problems assigned is in my resources as Homework and the second page is an answer key.