12th Grade Math : Unit #8 - Cyclical Patterns and Periodic Functions : Lesson #7

Modeling Using Trig Functions

Objective: SWBAT to model a situation using sinusoidal curves.
Standards: HSF-TF.B.5 MP1 MP2 MP4 MP5 MP6
Subject(s): Math
60 minutes
1 Modeling Using Trig - 40 minutes

For the majority of the class period today, students will work together to complete the Modeling with Trig Functions worksheet. The goal today is for students to get a solid understanding of some cyclic real world problems, and, an understanding for how functions can be used to represent them. Toward the end of class, students will work toward being able to model a situation using a trigonometric equation.  

I really want students working together today. I think that this lesson offers a great opportunity to engage in Mathematical Practice 3.  Students should have enough prior knowledge to be successful in this activity without much help from me. So, I will also be implementing a strategy, such as Question Cubes, to limit the questions that are asked of me.


Improving Today's Lesson
Adjustments to Practice

-  One common error that students were making was in question 2, part b. Many students were answering that they would be at a height of 40 feet. They often forgot to add in the 5 feet that they were off the ground before the ride even started. When I would see student’s mistakes I would let them know they were wrong, but would leave it to them and their team to figure out why.

-  I also found it helpful to have graph paper on hand for students to complete question 5. Many students didn’t feel there was enough room on the paper to successfully graph this and using graph paper of course leads to much more precise graphs.

- Students will need to know how to calculate the circumference of circle in questions 7 and 8.

- I would recommend chunking this lesson by giving students set time limits for each problem. I gave my students 15 minutes for the Ferris wheel problem, 10 minutes for the breathing problem, and 5 minutes for the swing problem. Then I spent the additional 10 minutes in between reviewing selected answers.

2 Closure: Can you write the equation? - 10 minutes

With about 10 minutes remaining in the period, I am going to have them start to work on writing an equation to model the Ferris Wheel problem from their worksheet today, Modeling with Trig Functions. I will collect their answer as their ticket-out-the-door. I want each student to submit their own answer. I plan to review correct answers at the beginning of the next class period.

3 Homework - 0 minutes

Students should complete Homework 9- Trigonometric Functions tonight.