Patterns in Music


Halla  Shteiwi

Unit Title:

Patterns in Music




Algebra II

Unit Activities:

Activity 1: PP, Hook, EQ, GQ Challenge, Act. 2

Activity 2: Music Track Creation


July 2015

Anticipated Guiding Questions
  • What is a sine function?
  • What does a cosine function look like?
  • How do faster beats look graphically?
  • How do slower beats look graphically?
  • What is periodicity?

Unit Academic Standard

(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.


Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*

The Big Idea (including global relevance)

Patterns in music

The Essential Question

How can patterns in music be shown graphically?

How can we use mathematical equations to perfect the music we create?

What patterns can we use to predict the next period of a track?

The Hook

The video will show the students how the looper app works. I think that the students will be able to connect and find interest in the topic very quickly. 

The Challenge and Constraints

Description of Challenge (Either Product or Process is clearly explained below):

List the Constraints Applied

Create a musical track using sine and cosine equations.

  • Must use only sine and cosine functions
  • Must use school approved music
  • Must use Looper App


What the coefficients within a sine and cosine function really do to the graph. 

  • How does periodicity connect to music?
  • What is high frequency?
  • What is low frequency?
Engineering Design Process (EDP)

How will students test or implement the solution? What is the evidence that the solution worked? Describe how the iterative process from the EDP applies to your Challenge.

Give students an option of working alone or with one other person.

The problems students have encountered is created a music beat with sine and cosine functions. Students must figure out the changes in the graph as the numbers (being coefficients or constants) do to the graph. Their graphs/functions must match the beat they create using the Loopy app. This process is going to require multiple refine and redesign steps.

The research students must do is research frequency waves, high and low to determine what sine and cosine functions to use.  Research will also need to include music videos of waves, in addition to sine and cosine wave functions. Students must learn to be creative while creating their music beats. 

How will students present or defend the solution?  Describe if any formal training or resource guides will be provided to the students for best practices (e.g., poster, flyer, video, advertisement, etc.) used to present work.

Students will create a music video with images of their sine and cosine functions, as well as their music beats they created. Students will create this video in our Multimedia Management course. They have already learned to use iMovie to create their music videos for their History project.

What academic content is being taught through this Challenge?

Students will learn how to graph sine and cosine functions. Students will also learn how to model periodic phenomena with specified frequency. Students will decide what numbers make changes in the graph’s frequency. 

Unit Activities

Day 1: 50 minutes in Algebra II: Do Hook

In addition to the hook show students this link or have student play with it and decipher how changing the variables change the graph.

PowerPoint and Pre-Assessment

Day 2: 110 minutes Activity on Sine and cosine waves. Graph on excel and determine what makes the wave faster or slower. Be sure students are doing enough research and gather enough data on music, frequency and patterns so they understand what type of beat they want to do.

Before having students complete the sine and cosine worksheet have them work in partners on this pitch and frequency piece. The students will get a better handle on the topic instead of jumping straight into the sine and cosine content.

Complete the graphing sine and cosine functions worksheet

If time allows that day, students will use the looper app and start designing their music track using their beatboxing skills.

Day 3: Continue creating beat using Looper. Now with the app and your cosine and sine waves, figure out what waves will match the sound waves of your music.

**Be Prepared: Teachers keep in mind that all students cannot record their sound track in the same classroom. Have different areas set aside ahead of time so students are able to record alone with their partner.  

Day 4: Post-Assessment and discussion of findings

Additional Resources

iPads with Looper app installed.

Laptop using excel

Graphing calculators

Teach Engineering - Making Music