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.