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# Khan Academy on Operations with Logarithms

Lesson 12 of 15

## Objective: SWBAT to perform basic operations with logarithms and deepen their understanding of the laws of exponents

*60 minutes*

#### Assessment Overview

*10 min*

These logarithmic modules are challenging because they heavy on notation. The word logarithm in itself scares most students. Here we are getting them some brief exposure to the concept. If nothing else, they will be easier to process the logarithmic content in high school. There are only 3 modules dealing with logarithms on Khan academy (although that is sure to expand). But students enjoy trying this new material (in many cases they have never even heard of a logarithm).

This module is the toughest to work with because it requires a mastery of the laws of exponents. Although I can't stress enough how rewarding it is for the students who get this far. For those who don't, they really enjoy mastering other topics from the unit.

#### Resources

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#### The Assessment

*40 min*

The structure of the site is overwhelming to many students. To simplify the process, I have them log in to Khan Academy and then open a second tab and go straight to this link to get started today:

http://www.khanacademy.org/math/algebra/logarithms-tutorial/logarithm_properties/e/logarithms_2

**The guidelines for today are as follows:**

- Finish the module until you reach "mastery." We encourage you at least 10 problems in a row.
- As you work, write the questions and answers in your notebook.
- When you are finished, annotate your notes and explain some general observations you made as you worked. Identify the laws you used to solve each problem.
- Create solve and explain a challenge problem that would fit nicely in each module.
- Write several numbers in exponential and logarithmic form. Explain how they are talking about the same numbers but from different perspectives.

I usually ask for part 5 in email and ask for *very* detailed explanations. Since all students have set me up as a coach I can easily monitor their progress after class.

#### Resources

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#### Assessment Review

*10 min*

I finish this assessment by reviewing questions with the class. I log into Khan Academy and project for the whole class to see. I popcorn around the room and ask students to solve and explain. For each question I get at least 2 algorithms, since students love to hear other strategies. I have noticed that many students use one strategy throughout all the problems and are usually so tired of it by the end that they *crave* a more efficient strategy. I wait until the end to share all strategies because I believe that process of struggling helps them process the importance of a more efficient strategy. If we just shared at the start, I think many students would blindly plug in the more efficient strategy without understanding why or how it is efficient.

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- UNIT 1: Starting Right
- UNIT 2: Scale of the Universe: Making Sense of Numbers
- UNIT 3: Scale of the Universe: Fluency and Applications
- UNIT 4: Chrome in the Classroom
- UNIT 5: Lines, Angles, and Algebraic Reasoning
- UNIT 6: Math Exploratorium
- UNIT 7: A Year in Review
- UNIT 8: Linear Regression
- UNIT 9: Sets, Subsets and the Universe
- UNIT 10: Probability
- UNIT 11: Law and Order: Special Exponents Unit
- UNIT 12: Gimme the Base: More with Exponents
- UNIT 13: Statistical Spirals
- UNIT 14: Algebra Spirals

- LESSON 1: Chess and the Monsters
- LESSON 2: Homework and Exponents
- LESSON 3: Fluency Check In
- LESSON 4: Games with Paper
- LESSON 5: Khan Academy and Simplifying Radicals
- LESSON 6: Khan Challenge Adding and Subtracting Radicals
- LESSON 7: Khan Cube Roots
- LESSON 8: Strings of Exponents
- LESSON 9: Measuring the Laws of Exponents
- LESSON 10: Khan Academy on Evaluating Logarithms
- LESSON 11: Khan Academy on Evaluating Logarithms (Part 2)
- LESSON 12: Khan Academy on Operations with Logarithms
- LESSON 13: Khan Exponent Challenges
- LESSON 14: Patterns in the Digits of Powers
- LESSON 15: The Digital Exponent Worksheet