# Digital Age Skill: Trigonometry Sinusoidal Modeling

## Description of the Lesson

### Overview

After collecting data, students will develop a sinusoidal model for a real-life phenomenon that follows a “wavelike” pattern.

### ISTE Standard

5b, 9-12 Grade Level Expectation:  Students collect data or identify relevant data sets, use digital tools to analyze them, and represent data in various ways to facilitate problem-solving and decision-making.
1d, 9-12 Grade Level Expectation:  Students understand the fundamental concepts of technology operations, demonstrate the ability to choose, use and troubleshoot current technologies and are able to transfer their knowledge to explore emerging technologies.

### NE Standard

MA 12.2.3.a (AT) Model periodic events with specified amplitude, frequency, and shifts.
MA 12.2.3.b (AT) Solve real-world problems using trigonometric and inverse trigonometric functions.

## Rubric Used for Assessment

Example Student Artifact(s)

NA

## Lesson Design Reflection

Lesson Design:

HOOK/ATTENTION GETTER:  Music and Math: The Genius of Beethoven video

Teacher Instructions:  Show video then ask, “What do music, daylight hours, temperatures, ferris wheels, and tides have in common?”

DIRECT INSTRUCTION:

Teacher Instructions:  You will need to teach the concepts of sinusoidal functions (amplitude, period, phase shift, and vertical shift) and give students a chance to practice those concepts before assigning this project.

GUIDED PRACTICE:

Teacher Instructions:  As an example to show my students, I used my own Black Hills Energy bills from 2017 and 2018, so I had 24 data points.  I plotted the (month, amount) data points on Desmos along with the sinusoidal function that fit my data points.  I reviewed the formulas for amplitude, vertical shift, period, and phase shift with my students using my data.  See Google Slides.

INDEPENDENT PRACTICE:

Teacher Instructions:  Students were allowed to work individually or with one or two other people.  I gave them three days to complete the project with very little in-class time.

STUDENT INSTRUCTIONS/ASSESSMENT:

Instructions and Rubric

NA