# Teacher Resources

## Modeling With Trigonometric Functions

On this page you will find lesson objectives, standards, instructional notes and UDL opportunities.

Estimated Time:  30 - 40 minutes

### Lesson Objectives:

• Students will be introduced to trigonometric functions that may be used to model a data set.
• Students will apply understanding of residuals and functional behavior to determine whether a trigonometric function model is the best fit for a data set.

Key Common Core State Standards:

S.ID.6 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

1. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Supporting Common Core State Standards:
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Standards for Mathematical Practice Emphasized:

MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.

## Instructional Notes:

In this lesson, students will extend their understanding of regression to trigonometric functions.  Students will be introduced to periodic data, asked to describe the behavior and find a model of best fit.

> Go to Modeling With Trigonometric Functions lesson

## Sample Responses

For sample responses to the Algebra II Journal questions, visit the Algebra II Journal in Teacher Resources.

## Modeling With Trigonometric Functions - Page 5

Consider having students select another city in the U.S. as a potential travel destination.  Have students find either the average monthly low or high temperatures for that city this past year.  Have students calculate the trigonometric curve of best fit and use the curve to make predictions.  As a culminating activity, have the class review the different city temperatures and make recommendations for which city to visit and for what month it would be best to travel.

> Go to lesson, page 5

## Modeling With Trigonometric Functions - Page 6

For sample responses to the Algebra II Journal questions, visit the Algebra II Journal in Teacher Resources.

> Go to lesson, page 6

## UDL Opportunities:

Checkpoint 2.1: Clarify vocabulary and symbols.
Checkpoint 2.3: Support decoding of text, mathematical notation, and symbols.
Checkpoint 3.1: Activate or supply background knowledge.
The Student Resources section includes key vocabulary clarifications that will support the decoding of text and mathematical language.  In particular, students are introduced to a number of key terms, such as periodic, iterations, and sinusoidal data. It may be helpful to introduce some of the key terms prior to the start of this lesson.

Checkpoint 3.3: Guide information processing, visualization, and manipulation.
Checkpoint 9.3: Develop self-assessment and reflection.
In this lesson, students have the opportunity to compare the weather patterns in two cities.  Students have opportunities to investigate the fit of the regression equation, as well as identify differences between the two models.  The lesson reflection provides an opportunity for students to reflect on their understanding and justify conclusions.

Checkpoint 4.1: Vary the methods for response and navigation.
Checkpoint 7.1: Optimize individual choice and autonomy.
Checkpoint 7.2: Optimize relevance, value, and authenticity.

The scenarios in this lesson are based on real-world data in order to optimize relevance and authenticity.  Consider having students research an additional city of their choice to explore more sinusoidal data and determine a model of best fit.  Students may present their findings in various ways.