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# Modeling Real World Data (Day 3 of 4)

Lesson 10 of 15

## Objective: Students will be able to use trigonometric functions to model real world data.

## Big Idea: Students use data they collect to see how trigonometry exists in their world by modeling the data on posters.

*50 minutes*

#### Warm Up

*5 min*

Students should finish their work on their Real World Data Trig Poster. The primary goal for today is for students to create a great problem they can ask regarding their data.

As a warm-up for today's work, I will present page 2 on the flipchart, Flipchart-Day 3 of 4 - Real World Trig Project. Students will again be asked to write the equation of this sine curve which has a horizontal shift. Since the period of the graph in this problem is not 2*pi radians students will need to be aware of the phase shift occurring with the change in period. I elected to review this concept again today on the warm-up just to reinforce all the work done yesterday with the real world data and to be sure that any students who didn’t find their equations could see another example modeled.

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#### Application

*45 min*

Today, students continue to work on their Projects. Today, I will be helping them to write a question they can ask their classmates about their data. This question will be an important element on their poster. They will also produce a detailed answer to the question, but on a separate piece of paper **(MP3, *** ***MP6)**. I encouraged students to be as creative as they’d like with this question. The only requirement is that students must be able to solve the question themselves.

**Teacher's Note: **Although students are working on an individual project, I will structure the classroom to support collaboration today. I will encourage students to help each other create a question that can be answered using their models.

Students will also have some time today to make their posters more visually appealing. I will use Page 3 of Real World Trig Project to briefly review the expectations for today's lesson.

For students struggling to create a question to ask, I will remind them of the importance of providing their audience with enough information to understand the data, and, to be interested in finding the answer to the question. I will also help students think about the functions to describe their data.

- What is the input?
- What is the output?
- What is the relationship between these two variables?

Then I will ask students if they are more interested in determining the output for a given input, or, the input for a given output? I find that this approach helps most students come up with something.

For students who are finding it easy (or taking it easy) to write a question, I will push for more challenging questions. Can you stump the class? Can you stump the teacher? Remember that you need to be able to solve the problem yourself.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Making Waves... with pasta! (Day 1 of 2)
- LESSON 2: Making Waves... with pasta! (Day 2 of 2)
- LESSON 3: Calculator Activity: Transformations of Trig Functions (Day 1 of 2)
- LESSON 4: Calculator Activity: Transformations of Trig Functions (Day 2 of 2)
- LESSON 5: Graphing Trigonometric Functions
- LESSON 6: One of Those Days
- LESSON 7: Modeling Using Trig Functions
- LESSON 8: Modeling Real World Data (Day 1 of 4)
- LESSON 9: Modeling Real World Data (Day 2 of 4)
- LESSON 10: Modeling Real World Data (Day 3 of 4)
- LESSON 11: Modeling Real World Data (Day 4 of 4)
- LESSON 12: Trig Millionaire Game
- LESSON 13: More Trig Functions
- LESSON 14: Trigonometric Functions Review
- LESSON 15: Trigonometric Functions Unit Assessment