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# Discovering Log Rules (because logs rule!)

Lesson 3 of 11

## Objective: SWBAT discover the properties of logarithms and apply these properties to condense expressions.

*40 minutes*

#### What is a slide rule?

*10 min*

As an introduction to today’s lesson, we are going to be talking about the old-school slide rule: Discovering Log Rules, Video Narrative, slide rules intro.

Here are the links to the videos I mentioned in the narrative above (they are also linked on the flipchart):

Demonstration of Slide Rule Multiplication:

The Joy of Slide Rules:

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For the rest of today’s lesson and tomorrow’s, I will be following the NCTM lesson *Logarithms Demystified.*

Students are now going to make log slide rules and use these to explore the properties of logs. Students first need to complete Questions 1-3 on the Student Worksheet - LogarithmsDemystified. They will use their findings here and the *Slide Rules Template* to make the slide rules. Here's what the Completed Logarithmic Slide Rules should look like. Basically students will be plotting the values of the logarithms evaluated at each value of x and marking it with the x value. For example, log 1 = 0 so students would mark a 1 at the 0 location on the ruler. log 2 is approximately .301 so students should write a 2 at the .30 mark. Note that the major ticks on the ruler are counting by tenths, while the minor marks are counting by thousandths.

See the Lesson Information on the NCTM site for more specific details about creating the slide rules.

As students complete the first three questions they will be reinforcing their ability to identify and articulate patterns. I plan to help my students with **MP6: Attending to precision **by collecting and providing feedback of their written explanation of these patterns tonight and returning this before tomorrow’s lesson. Students will also be demonstrating **MP8****: Look for and express regularity in repeated reasoning** so I will also be able to get a quick assessment of their current abilities with this practice by doing a quick read of students’ response to these questions.

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Encourage students to help each other to finish their slide rules when they are done with the student worksheet. After all students have finished making their slide rules demonstrate how to use them to do some basic operations. Here's a quick video demonstrating addition and subtraction with the logarithmic rulers: Discovering Log Rules, How to use the logarithmic rulers.

(Check out the lesson link above for more details.)

As you demonstrate the use of the slide rule, try not to give away any of the log properties. It is important that students discover those on their own. If there is more time in the period I plan to have my students start exploring the properties by completing the Logarithms Demystified worksheet. We will pick up on this tomorrow so I plan to really let my students work at their own pace.

*expand content*

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: What Is A Log?
- LESSON 2: Graphing and Shifting Logs
- LESSON 3: Discovering Log Rules (because logs rule!)
- LESSON 4: Applying Log Rules
- LESSON 5: Puzzling Log Equations
- LESSON 6: Solving Exponential Equations Using Logs
- LESSON 7: Experts on Exponential Equations
- LESSON 8: Modeling Exponentials Using Logarithms
- LESSON 9: Speed Dating with Logarithms
- LESSON 10: Logarithmic Equations Test Review
- LESSON 11: Logarithmic Equations Unit Test