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# Exponentials and Logarithms: LOUD and CLEAR!

Lesson 9 of 21

## Objective: This lesson will allow the students the opportunity to investigate a real life application of logarithms. Students will be asked to present a portion of their findings to the class on the following day. A brief scaffolding workshop on engaging oral communication might be appropriate, and can be found as an optional addition to this lesson plan. It is important to teach students to communicate mathematics confidently, and in a way that is audience appropriate. Look for sample student presentations when I reflect on this activity in the future! These videos could also make great teaching tools for your students.

#### Roll Out

*6 min*

I start class by welcoming the students with a megaphone that I hide under my podium. I loudly announce “Today we are going to continue in our investigation of exponential functions and logarithms!” (Usually the students are all staring at me and laughing like I am some sort of crazy person… not the first time either!) In addition, I always play music to start my class (as the students enter) because I believe music creates energy. Today, however, I start by playing the music VERY loudly.

In all of this start of class commotion, I pre-plan to have the teacher next door come over within the first several minutes and tell me to “Be Quiet!” and that “Mr. Hammel’s class is 100 times louder than normal!” We then stage a fake argument and I set out to mathematically prove that my class is NOT 100 times louder than normal (it is actually much more). We argue over the decibel readings projected on the screen that stream live from my IPAD through my AppleTV projector. Our staged argument right in front of the decibel meter even adds to the dB numbers shown on the screen!

For a couple of minutes, I argue that a reading of 100 dB’s is only 40 dB’s higher than 60 dB’s (and 60 dB’s = a normal conversation). I tell the other teacher that he doesn’t understand math and that he should go back to English class where he belongs (even though really I know that I am the one who is wrong) and do anything else that I can do to stir the pot! Ultimately we throw it on the students to decide who is right and roll out the entry documents.

DURING ALL OF THIS COMMOTION: It is important to have the Decibel Meter Ap (or decibel meter readings) displayed on a projector screen for the students. I like the Ap because it allows you to monitor and record the average, maximum, and minimum decibel readings. The students can see all of this data the entire time. However, I also recommend taking a screen shot of the image and saving it for a future discussion. It is a great way to pull in real world relevance!

Note: At the end of the class period, the students will understand WHY the logarithmic scale is useful for measuring the intensity of sound. The energy comparisons that the students do will show HUGE differences in relative intensities. Keep this in mind as you engage in conversations with the students! Work hard to allow THEM to make this discovery on their own.

**Summary of Needs:**

1) **http://www.decibelcar.com/menugeneric/87.html**

2) Decibel Meter (check with your physics teacher, or download the free Ap)

3) Stereo/”Boom Box” (optional)

Be sure to get approval from surrounding classrooms. J As you will see, luckily I have great neighbors!

**Resources:** Decibel Meter, Mega-Phone, Entry Document… and a neighboring teacher looking for some fun!

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From the previous day’s lesson, I ask the students to take out their homework. I field clarifying questions from the students over the assignment. Usually, these are over the last several problems, if there are any questions at all. I work VERY hard to answer their questions by rephrasing the original problem, or showing what I am asking in a new way. I never want to just give the students the answer, or show them exactly how to approach it. This defeats the purpose of these extension questions! It is ALL about the productive struggle, and I answer all questions accordingly.

Due to the nature of the period, I allow the students to turn in the assignment on the following day.

Lastly, I ask the students to complete the exit slip attached to this lesson. I re-display the decibel meter data from the start of class and tell the students to provide evidence FOR or AGAINST the opening claim:

“Mr. Hammel, your class is 100 times louder than normal!”

All of this is done independently. The students leave the class period prepared to share out their findings tomorrow!

**Resources: **Exit Slip, Previous Homework Assignment

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Introduction to Exponential Functions - Rational Exponents
- LESSON 2: Real Number Exponents
- LESSON 3: A Conceptual Introduction to Exponential Functions: Collaboration, Questioning, and Financial Advice!
- LESSON 4: Discovering Solutions to Exponential Equations
- LESSON 5: An "Exponentially" Rewarding Battle!
- LESSON 6: Productive Struggle - A Pre-Spring Break Challenge of Exponential Functions
- LESSON 7: Compositions, Inverses & Role Play: Extending Concepts to Exponential Functions
- LESSON 8: Exponential Functions and Logarithms - Connecting the Dots
- LESSON 9: Exponentials and Logarithms: LOUD and CLEAR!
- LESSON 10: A Wrap on Logarithmic dB's and An Extension to Logarithmic Properties
- LESSON 11: Classroom Journey: Exponential and Logarithmic Properties
- LESSON 12: Laws of Logarithms and Real Applications
- LESSON 13: Calculator Boot-Camp and Solving Exponential Equations
- LESSON 14: Logs, Loans, and Life Lessons!
- LESSON 15: "Demystifying e" Day #1
- LESSON 16: Logs, Loans, and Life Lessons Collaboration Day!
- LESSON 17: FInal Discussion - "Demystifying e" PLUS Skills Practice with Logarithms
- LESSON 18: Elephant Tracks!
- LESSON 19: End of Unit Differentiated Problem Set
- LESSON 20: Differentiated Problem Share Out - Unit Review
- LESSON 21: Unit Review