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 9**: **Finish 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