Tiffany Dawdy CAMELBACK HIGH SCHOOL, PHOENIX, AZ
12th Grade Math : Unit #9 - Trigonometric Equations : Lesson #10

# Solving Quadratic Trig Equations (Day 1 of 2)

Objective: SWBAT use their knowledge of quadratic equations to solve quadratic trig equations.
Standards: HSA-REI.B.4 HSA-REI.B.4b HSF-TF.B.7 MP1 MP2 MP4 MP5 MP7
Subject(s): Math
60 minutes
1 Warm-Up - 5 minutes

I begin today's class by asking students to solve the equation on slide 2 of  the flipchart - Solving Quadratic Trig Equations. My goal is to get students thinking about how to solve quadratic equations using inverse operations. I am prepared to remind students that:

• They should review having to square root both sides of the equation to solve for x (MP7).
• A quadratic equation can allow 2, 1 or 0 solutions (MP6, MP7).

If possible I will avoid providing assistance to students on this warm-up problem. I want to assess who can and who cannot solve the problem independently. However, I plan to go over the problem with the class.

Same mistake made by majority of students.
Modeling
2 Connecting to Prior Knowledge - 40 minutes

In the middle part of today's lesson, my goal is to have students review solving quadratic equations before we move onto solving quadrtaic trigonometric equations in tomorrow's lesson. After guiding students through part 1 of the Student Activity: Solving Quadratic Trig Equations, I will have students work through exercise 1-5 in part II focusing only on the Algebraic form. then students will present their solutions. Here is more detail on how this went my first year teaching it: Solving Quadratic Trig Equations Day 1, Video Narrative, Quadratic Trig Equations

While students are working through this activity the following mathematical practice standards will be addressed:  MP1MP2, MP3MP5MP6, MP7MP8.

Differentiation Strategies
Intervention and Extension

Struggling students should hopefully be supported in their teams today. If you find that you have teams that hit a wall and are doing nothing, you may want to ask some prompting questions to get students there. For example, many of my students tried to solve the quadratic equations by doing inverses. But then they always get stuck when they can’t combine the variable with the squared variable. So I ask things like:
“Where did you get stuck?”
“Why can’t you do that?”
“What are some strategies from the brainstorming session you could try?”

Most of my students quickly recalled factoring, but many did not recall the quadratic formula. I had it on the board already so some students took that as a hint too and made the connection.

For my students that kept leaving off the negative solutions when directly solving (exercises 3 and 5) I asked them “How many solutions are we supposed to have?” This is one thing they KNOW! I really drilled it in the polynomials unit.

The most challenging problem for my students was exercise 2. For the middle part of the lesson today, give that to your stronger teams. They may even need a hint: FACTOR.

If students are ready for an extension, have them try the trigonometric form of the Algebraic form they were working on. I had one student who got it perfectly! I plan to use him as a tutor tomorrow.

Multiple Strategies Employed and Great Team Learning Environment!
Trust and Respect
Solving Quadratic Trig Eqns Day 1, connecting to prior knoweldge, variety of strategies.MP4