# Logarithms (Lesson 5.5)

###### Unit 1: Sequences and Linear Functions

**Day 1:**Recursive Sequences**Day 2:**Applications of Arithmetic Sequences**Day 3:**Sum of an Arithmetic Sequence**Day 4:**Applications of Geometric Sequences**Day 5:**Sequences Review**Day 6:**Quiz 1.1 to 1.4**Day 7:**Linear Relationships**Day 8:**Point-Slope Form of a Line**Day 9:**Standard Form of a Linear Equation**Day 10:**Quiz 1.5 to 1.7**Day 11:**Unit 1 Review**Day 12:**Unit 1 Test

###### Unit 2: Linear Systems

**Day 1:**Linear Systems**Day 2:**Number of Solutions**Day 3:**Elimination**Day 4:**Larger Systems of Equations**Day 5:**Quiz 2.1 to 2.4**Day 6:**Systems of Inequalities**Day 7:**Optimization Using Systems of Inequalities**Day 8:**Quiz 2.5 to 2.6**Day 9:**Unit 2 Review**Day 10:**Unit 2 Test

###### Unit 3: Function Families and Transformations

**Day 1:**Interpreting Graphs**Day 2:**What is a function?**Day 3:**Translating Functions**Day 4:**Quiz 3.1 to 3.3**Day 5:**Quadratic Functions and Translations**Day 6:**Square Root Functions and Reflections**Day 7:**Absolute Value Functions and Dilations**Day 8:**Equations of Circles**Day 9:**Quiz 3.4 to 3.7**Day 10:**Unit 3 Review**Day 11:**Unit 3 Test

###### Unit 4: Working with Functions

**Day 1:**Using Multiple Strategies to Solve Equations**Day 2:**Solving Equations**Day 3:**Solving Nonlinear Systems**Day 4:**Quiz 4.1 to 4.3**Day 5:**Combining Functions**Day 6:**Composition of Functions**Day 7:**Inverse Relationships**Day 8:**Graphs of Inverses**Day 9:**Quiz 4.4 to 4.7**Day 10:**Unit 4 Review**Day 11:**Unit 4 Test

###### Unit 5: Exponential Functions and Logarithms

**Day 1:**Writing Exponential Functions**Day 2:**Graphs of Exponential Functions**Day 3:**Applications of Exponential Functions**Day 4:**Quiz 5.1 to 5.3**Day 5:**Building Exponential Models**Day 6:**Logarithms**Day 7:**Graphs of Logarithmic Functions**Day 8:**Quiz 5.4 to 5.6**Day 9:**Unit 5 Review**Day 10:**Unit 5 Test

###### Unit 6: Quadratics

**Day 1:**Forms of Quadratic Equations**Day 2:**Writing Equations for Quadratic Functions**Day 3:**Factoring Quadratics**Day 4:**Factoring Quadratics. Part 2.**Day 5:**Solving Using the Zero Product Property**Day 6:**Quiz 6.1 to 6.4**Day 7:**Completing the Square**Day 8:**Completing the Square for Circles**Day 9:**Quadratic Formula**Day 10:**Complex Numbers**Day 11:**The Discriminant and Types of Solutions**Day 12:**Quiz 6.5 to 6.9**Day 13:**Unit 6 Review**Day 14:**Unit 6 Test

###### Unit 7: Higher Degree Functions

**Day 1:**What is a Polynomial?**Day 2:**Forms of Polynomial Equations**Day 3:**Polynomial Function Behavior**Day 4:**Repeating Zeros**Day 5:**Quiz 7.1 to 7.4**Day 6:**Multiplying and Dividing Polynomials**Day 7:**Factoring Polynomials**Day 8:**Solving Polynomials**Day 9:**Quiz 7.5 to 7.7**Day 10:**Unit 7 Review**Day 11:**Unit 7 Test

###### Unit 8: Rational Functions

**Day 1:**Intro to Rational Functions**Day 2:**Graphs of Rational Functions**Day 3:**Key Features of Graphs of Rational Functions**Day 4:**Quiz 8.1 to 8.3**Day 5:**Adding and Subtracting Rational Functions**Day 6:**Multiplying and Dividing Rational Functions**Day 7:**Solving Rational Functions**Day 8:**Quiz 8.4 to 8.6**Day 9:**Unit 8 Review**Day 10:**Unit 8 Test

###### Unit 9: Trigonometry

**Day 1:**Right Triangle Trigonometry**Day 2:**Solving for Missing Sides Using Trig Ratios**Day 3:**Inverse Trig Functions for Missing Angles**Day 4:**Quiz 9.1 to 9.3**Day 5:**Special Right Triangles**Day 6:**Angles on the Coordinate Plane**Day 7:**The Unit Circle**Day 8:**Quiz 9.4 to 9.6**Day 9:**Radians**Day 10:**Radians and the Unit Circle**Day 11:**Arc Length and Area of a Sector**Day 12:**Quiz 9.7 to 9.9**Day 13:**Unit 9 Review**Day 14:**Unit 9 Test

#### Learning Targets

Explain how the input and output of a logarithm describe an exponential relationship.

Rewrite exponential equations as logarithmic equations and vice versa.

Evaluate logarithmic expressions.

Use exponents and logarithms to solve equations.

Tasks/Activity | Time |
---|---|

Activity | 15 minutes |

Debrief Activity with Margin Notes | 10 minutes |

QuickNotes | 10 minutes |

Check Your Understanding | 15 minutes |

#### Activity: What Does the Gallas Function Do?

#### Lesson Handouts

##### Media Locked

##### Media Locked

#### Answer Key

##### Media Locked

#### Homework

##### Media Locked

#### Experience First

Not sure about you, but if I'm being honest, I didn't really understand what a logarithm was until I had to teach it. Before that, I had simply just memorized how to use them and how to rewrite them as exponential expressions. So I made it mission to try to find a way to help my students understand logarithms better than I had.

To start, I wanted to take down the intimidation factor. Even the name, *logarithm*, is scary to a student! So let's call it something else. How about the Gallas Function? (Make sure you change the name to your name and the bitmoji to yours when you use this in your class.)

After introducing your new function to the class, students can work through the whole activity. The goal is that students notice the pattern in the function and that they recognize that the function is giving out an exponent. Once they have an understanding of what the Gallas Function does, they can investigate some special cases.

#### Formalize Later

When the groups have finished the activity, we'll debrief with the margin notes. At this point, we will explain that it turns out that the Gallas Function isn't new. Someone else already came up with it and it's called a logarithm. Ask the groups that wrote their work on the board to explain their patterns that they found. Generalize their patterns and rules with logarithms in the margins.

After debriefing the activity, we need to go through the QuickNotes and the Check Your Understanding problems. It's important to note here that we didn't cover all of the learning targets in the activity. We introduced the idea of a logarithm and hopefully developed some conceptual understanding of what it does. But we also need students to know that it is the inverse operation of an exponential function and how to use it to solve equations. You will need to explain this idea during the QuickNotes. Students will get a chance to practice this in the Check Your Understanding problems.