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# Sinusoidal Functions and Climate Changes

Lesson 10 of 13

## Objective: SWBAT analyze text to determine the key features of a sinusoidal functions.

*40 minutes*

#### Bell Work

*5 min*

Today I am preparing students for the project that ends the unit. Students will also work on how to read text to find a model for a situation. I begin with a problem that requires students to explain the meaning of some of the key features in context of the problem.

Students discuss the meaning of the 50 and 13. Most students know that the 50 is the midline of the graph and 13 is the amplitude. I ask **"If the 50 is the midline what is that in terms of the temperature of the city? What does the amplitude tell you. So how would you state the meaning in terms of the situation?"**The students need to realize that the 50 represent the average yearly temperature. The 13 is the fluctuation from the average yearly temperature.

This problem will help students as the read the problem for today.

#### Resources

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#### The Problem

*30 min*

Today students will work on one problem from "Mathematics Teacher," Media Clips, November 2012. I have formatted the questions to make it easier for the students to read.

I have the students work in groups since this is a complex problem. The questions are designed to help students determine the key features for the graph and then the equation that will model the situation.

As student work I question students about what they read to that can help them answer the questions.

For question #2:** Does the article give you anything that can help you find the period? What is meant by "11 cycles in 800,000 years?" Can you use this to help you find the period?**"

When students try to write the model some struggle with identifying the amplitude. **"What is the meaning of the amplitude? Do you know the maximum temperature? How about the minimum temperature? Can you use these to determine the amplitude? What else will the maximum and minimum temperature help you find?**

Question 3- **When did the last maximum or minimum occur? How long will it take for the next maximum or minimum to occur? Where in the cycle are we right now between a minimum and maximum or a maximum to a minimum?** Many students will begin making a number line as they process this problem.

#### Resources

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#### Closure

*5 min*

With 5 minutes left, I ask students to tell me what they found interesting. This will usually begin a conversation on Global Warming. Which could be a long discussion. Some see this article as a reason to argue that Global Warming does not exist. We discuss how this information is used by scientist. Even though the ice core data shows that the average Earth temperature is increasing the question we need to look at is whether the temperature is rising faster than it did in the previous cycle. If we use this model now are we seeing the data moving away from the predicted value from the model.

*expand content*

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- UNIT 1: Introduction to Learning Mathematics
- UNIT 2: Functions and Piecewise Functions
- UNIT 3: Exponential and Logarithmic functions
- UNIT 4: Matrices
- UNIT 5: Conics
- UNIT 6: Solving Problems Involving Triangles
- UNIT 7: Trigonometry as a Real-Valued Functions
- UNIT 8: Graphing Trigonometric Functions
- UNIT 9: Trigonometric Identities
- UNIT 10: Solving Equations
- UNIT 11: Vectors and Complex Numbers
- UNIT 12: Parametric and Polar graphs and equations

- LESSON 1: Trigonometric Graphs (Day 1 of 3)
- LESSON 2: Trigonometric Graphs (Day 2 of 3)
- LESSON 3: Trigonometric Graphs (Day 3 of 3)
- LESSON 4: Frequency versus Period
- LESSON 5: Graphing Sine and Cosine Functions (Day 1 of 2)
- LESSON 6: Graphing Sine and Cosine Functions (Day 2 of 2)
- LESSON 7: Graphing the nonsinusoidal trigonometric functions Day 1 of 2
- LESSON 8: Graphing the nonsinusoidal trigonometric functions Day 2 of 2
- LESSON 9: Writing Sinusoidal Models
- LESSON 10: Sinusoidal Functions and Climate Changes
- LESSON 11: Sinusodial Project Day 1 of 3
- LESSON 12: Sinusodial Project Day 2 of 3
- LESSON 13: Sinusoidal Project Day 3 or 3