The Math Behind the Music


Author:

Jake Ohnmeis

Unit Title:

The Math Behind the Music

Grade:

8/9 th

Subject:

Integrated Math 1

Estimated Duration:

10 days of 70 minute periods

Unit Activities:

Activity 1: Let's Talk Music and Math

Activity 2: Box-Plot SmartBoard Notes

Activity 3: Box-Plot Cheerio 

Activity 4: Dot-Plot and Histogram Notes

Activity 5: Dot-Plot, Histogram and Box-Plot

Activity 6: Presenting the Client and Creating Portfolio

Background Knowledge: 

To help make this unit successful, students should have a background knowledge of how to find mean, median, mode, maximum and minimum.  Students also need to be able to create bar graphs.

Date:

July 2014

The Big Idea (including global relevance)

Music is a part of nearly everyone’s life.  We listen to it in the car, at sporting events/shows, and a lot of other places.  While music has been around for many years, what math is behind it?  What trends and data analysis can we use to find patterns in the Top 40 songs over the past decade?  Creating a song takes a lot of time and money, so if students can develop an outline for the next big song then that outline is extremely valuable to artists today.

The Essential Question

Using the Number 1 songs over the past 40 years, what data can we analyze to provide an up-and-coming artist help to create the next big hit?

Justification for Selection of Content

Students have been looking at graphs and analyzing data throughout a lot of their math courses in schools.  Students know how to find the average or the median of a data set, but they do not know how to use that information.  This project helps students conceptualize how analyzing data is much more than just answering a question on a test or creating a graph.  They will have to interpret their results, rank their findings, and present a valuable argument for why they believe the next song should follow certain parameters.  

The Challenge

Students will have to develop a portfolio for their client (an up-and-coming musician) that explains how their song should be structured for it to become a hit.  

The Hook

The hook is Activity 1, Lesson 1 Worksheet A.  It lets the student first collect data about themselves and then collect it about their classmates.  It helps students get engaged in how music is different and how certain parts of music can be interpreted mathematically.

Teacher's Guiding Questions
  • What mathematical ideas do we see in songs?
  • What makes a successful song?
  • What components of a song can I analyze mathematically?
  • Are there any connections between song length and beats per minute?
  • Have songs gotten faster or slower over the years?
  • Can there be “outliers” in music?
  • Does release date of the song matter?
  • Does the genre matter for a hit song?
  • How much does it cost to create a song?
  • How long does it take to create a song?
ACS (Real world applications; career connections; societal impact)

A - Being able to not only notice trends and central tendencies but interpret them is very important.  Analyzing data can be used when trying to predict future pricing of a home, managing money, etc.

C - Engineers use data analysis to improve acoustics in sound proof rooms by examining what materials deliver improved results.

S -  Interpreting graphs and being able to provide valid reasons using math is helpfully for everyone in society.  An example would be to present data to your boss at a local firm explaining how your profits have looked over the past few years.

Engineering Design Process (EDP)
  • Challenge – Students will have to develop a portfolio for their client (an up-and-coming musician) that explains how their song should be structured for it to become a hit. 
  • Research – Use websites to examine trends and previous data analysis on past hit songs.
  • Brainstorm and Essential Questions – Look at what math is actually in music and what aspects of the songs can be analyzed mathematically.
  • Build– Students will create a portfolio given a limited amount of data. 
  • Redesign – Students will improve their portfolio when given more data and see if that affects their findings.
  • Final Conclusion – Students will create a 3-5 minute presentation to give to their client on how he/she can make the next big hit.
Unit Academic Standard

HSS-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

HSS-ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

HSS-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.  

Unit Activities

Day 1:  Pre-test and Hook/Lesson 1 Activity 1

1.     Pre-test students on their prior knowledge of data analysis (Lesson 1, Activity 0).

2.     Present students with the hook using the worksheet “Let’s talk Music” (Lesson 1, Activity 1, Worksheet A).  Students will find data on their favorite song and relay the information to the class.

3.     If they do not get finished, they will need to finish their calculations at home for homework.

Day 2:  Review hook, introduce challenge, and start notes on box plots (Lesson 1 Activity 2 Notes)

1.      Double check all of the students’ data to make sure their numbers match up with the classes.

2.      Talk about the last 2 questions on the hook, and see how student rationale their answers.

3.      This is where we will talk about the challenge of “What does it take to create a top song?”  Students will develop the essential questions needed for the lesson and ultimately the challenge.

4.     Once this is all finished, you will begin the notes on box plots (Lesson 1 Activity 2).

Day 3:  Cheerio Activity (Lesson 1 Activity 3)

1.     Once box plots notes are completed, you will begin the next activity.

2.     Students will be put into small groups and will begin work on the Cheerio Activity (Lesson 1, Activity 3, Worksheet B).

3.     This activity will let students be engaged as they use the “handfuls of Cheerio” data to create box and whisker plots.

4.     Give students the homework (Lesson 1, Activity 3, Worksheet C).

Day 4: Dot Plots and Histogram notes (Lesson 2 Activity 1)

1.     In the second lesson, we will be creating dot plots and histograms.  At times we will be looking at some of our hook data so remind students they need to keep bring worksheet to class everyday (Lesson 2, Activity 1).

Day 5: Graphing Activity (Lesson 2 Activity 2)

1.     Students will begin the activity that uses dot plots, histograms, and box plots (Lesson 2, Activity 2) and the worksheet that goes with it (Lesson 2, Activity 2, Worksheet D).

Day 6:  Begin Creating Portfolio (Lesson 2 Activity 3)

1.     Review challenge and start the Engineering Design Process.

2.     Provide students will the data and have the students start creating their portfolio (Lesson 2, Activity 3, Worksheet E).

Day 7-8:  Redesign and evaluate

1.     Look at current portfolios and introduce the larger data set (Lesson 2, Activity 3, Worksheet F)

2.     Have students evaluate their current portfolio and redesign what they think is necessary for success.

Day 9Finish final portfolio and begin creating presentation for client.

1.     As portfolios are finished, give the groups a tri-fold presentation board so they can create their “pitch” to the client. 

Day 10:  Presentation to their client        

1.     Students will present their finalized portfolio with poster during 3-5 minute presentation.

2.     Rubric (Lesson 2, Activity 3, Worksheet G).

Where the CBL and EDP appear in the Unit

CBL - (Activity 4)

EDP - (Activity 4)

           (Activity 5)

Misconceptions

Students will believe that “their” way is the right way.  You must remind them that there might be more than one correct answer, as long as they can provide mathematical reasoning behind their choices

Additional Resources

Box-and-Whisker Plot Activity:  http://www.regentsprep.org/regents/math/algebra/ad3/datateacher.htm

Box-and-Whisker Overview:  http://www.purplemath.com/modules/boxwhisk.htm

Outliers:  http://www.mathsisfun.com/data/outliers.html

All 3 types of graphs:  http://ccgps.weebly.com/uploads/9/7/1/5/9715761/s.id.1-3_utah.pdf

Box-Plot Homework: http://learn.bcbe.org/pluginfile.php/408786/mod_resource/content/0/Day%2038%20-%207.3-7.4%20Homework.pdf

Pre-Unit Assessment Instrument

Pre Test Worksheet

Post-Unit Assessment Instrument

Post Test Worksheet

Results: Evidence of Growth in Student Learning

Below are the results “Math Behind the Music” Pre-Test vs. Post-Test results

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With all three of my classes, Block 1, 2 and 3, the overall results are as follows:

Pre-test: 81%

Post-test: 89.5%

An increase of 8.5%

How to Make This a Hierarchical Unit

In order to make this a middle school unit, I would bring the entire project focus on mean, median and mode.  6th grade math introduces these topics and they could analyze a smaller set of data and find its central tendencies.  They then could create 3 portfolios, one that uses on mean values, one that uses only median, and then one that is a combination.  They then must example which one is better and why they would use that.

Reflection

This unit went very well with all 3 of my Integrated Math 1 classes.  Having the students breakdown their favorite songs using the hook was very nice.  It kept them engaged from the beginning of the lesson to the end because they were researching songs they enjoyed listening to.

The reason I selected the standards listed above for this unit is because in the past, data collecting is boring to students.  While they can understand the concepts, students seem to be disengaged because they are always given the data to analyze.  In this unit, students not only analyze data but they are the ones who find it.  They have to create different graphs to model the data and be able to explain why they created such a graph.  The thing loved most about this lesson was hearing students talk about why they did what they did.  Usually in math there is only one correct answer or way of going about a problem.  In my unit “Math Behind the Music” this is not the case.  Students have to think critically onto why they are creating certain models for their data.  By doing this, I believe students understood the material better than years past and the assessment results proves this.  All 3 of my Integrated Math 1 classes improved from the pre-assessment to the post-assessment which can be seen on my unit poster.