SWBAT to decipher basic logarithms and gain a deeper understanding of exponents

To understand exponents, we cask ask students to look at the inverse operation of the logarithm

10 minutes

This **Challenge Lesson **can be done at home or in class, but from an 8th grade perspective I treat these modules as challenges. We tend to avoid logarithms in middle school and as teachers might have forgotten how to work with them (I know I did). But coming back and learning them as a teacher will add amazing depth to your understanding and teaching of exponents.

In general, challenge modules are great opportunities for *all* students. Some students will take on the challenge at hand and others will use the same time to catch up on past content that they found challenging. I always have something set up for all students to work on. I base it on the weekly feedback I get from students and prepare tasks and suggestions based on the standard based grading system. In other words, students and I are very aware of their current struggles and we use that information to help them pick an appropriate task.

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).

I have students start with the intro video and circulate to see how they are doing with the laws of exponents.

**Here is the video for the Evaluating Logarithms module:**

This activity can be incredibly helpful if students slow down and take the time needed to think about what they are doing and *why* it makes sense.

40 minutes

There are currently 3 logarithmic exercise sets on Khan Academy and this is one of the most fundamental in terms of fluency. This is one that I encourage students to even try and get 10 in a row (as opposed to 5 or less on other modules). The key to succeeding with this assessment is to make sure students realize that ** the world of logarithms is based on the world of exponents**.

To begin the module I have my students log in to Khan Academy and then open a second tab and go straight to this link:

http://www.khanacademy.org/math/algebra/logarithms-tutorial/logarithm_basics/e/logarithms_1

As with any challenge, this module is optional, but it is a good lesson that I enjoy leading. So if students want to pass on the logarithms, they can take on review of topics from class. For this purpose I like to print out worksheets from Kuta Software on the laws of exponents:

http://www.kutasoftware.com/free.html

**The guidelines for today's work with logarithms 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 by 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. I circulate during class and help students by asking them reflective questions, like "when you move the decimal, what are you doing to the number? I collect the notes from at least 1 student who has mastered the topic and 1 who is struggling.

10 minutes

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.