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# Laws of Logarithms and Real Applications

Lesson 12 of 21

## Objective: This lesson provides the students with additional support on the properties of logarithms. It concludes with an introductory problem set involving exponential equations.

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After completing the supplemental practice worksheet and addressing any incorrect answers, I have the students pick up the problem solving document. Each of the three problems has a video that corresponds to it and my students can access these videos on our course webpage. Speaking of which, I highly recommend creating a class page to post agendas, documents, and discussion boards! Many college classes are also adopting this tool, so it is a great way to prepare our students.

Each of the videos stars a few brave-hearted teachers in my end of the school building. Although they are light hearted and somewhat goofy, I believe that it is important to occasionally ask the students to solve a problem presented to them orally. I would venture to guess that approximately 95% of the problems that we ask students to analyze and solve in math class are shown to them in written form, and video is a great way for them to be challenged through a new lens. This approach forces students to write down key elements of the problem, and connect it to their existing knowledge. I also think that having other teachers or community members roll out the problem (even if it is “fake” or staged) shows the students that many problems requiring solving transcend the walls of our math classroom!

As another important note, all of these problems can be solved by using a calculator – essentially just “plug and chug”. I created this activity to familiarize the students with several exponential equations that we will be working with in greater detail AND allow them practice with using their calculators. I was shocked at how many of my students needed help using the (or exponent) button on their calculator! In summary, this homework assignment presents the problem in a new way, practices good calculator use, and introduces the students to equations and variables that we will look at more closely in the future. It provides struggling students with the confidence to be successful. Entering Algebra II, many students have never seen equations as complex as those on the worksheet… this can be very intimidating! My philosophy is that if we expect kids to grapple with the complexity of the mathematics, then we must provide them the TIME and the TOOLS to do this. As a teacher, it is sometimes hard to step down from the center stage and let the kids experiment and ask questions. However, these are often the most rewarding activities! I have even had many high achieving students get a lot out of the activity by questioning the validity of the equations, specifically on the automobile purchase problem, and trying to create their own alternate one based research or additional data.

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To wrap up class, I provide the students with a sticky note and ask them to revisit the whiteboard list of mistakes from the start of class activity. Based on the data, I have each student select one problem to offer their advice; which they then write on a sticky note and place directly on the problem. I then take time to quickly go over the most common mistakes. I do this in an effort to promote a classroom culture focused on learning, rather than correct answers. I have found that if I reward and place an equal emphasis on incorrect solutions, then the students are more likely to share out and feel safe participating in the classroom. THIS DOES NOT MEAN THAT I DO NOT CARE ABOUT CORRECT ANSWERS - - allowing them the opportunity to share what NOT to do can be much more impactful than just showing them the right answer.

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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