##
* *Reflection: Developing a Conceptual Understanding
Exponential and Logarithmic Functions Test - Section 1: Test

The most interesting problem on this test was definitely problem 6 which asks students to create equations for three graphed exponential functions. I think that it really tested the students' understanding of the structure of exponentials. The correct solution has two equations with a base that is greater than 1 and one where the base is between 0 and 1. I expected a solution like f(x)= 1/2^{x}, f(x) = 2^{x}, and f(x)= 3^{x}. I was surprised by the range of solutions. The most common issue I saw was replacing the 1/2^{x} with something like (-2)^{x } as seen in this Student Work. This tells me that we did not spend enough time on both exponential decay functions and the problem with negative bases. Looking back, we did address negative bases but I will extend the discussion of this next year.

*Developing a Conceptual Understanding: Negative Exponential Functions*

# Exponential and Logarithmic Functions Test

Lesson 15 of 15

## Objective: Students will be able to test their knowledge of exponential and logarithmic functions.

*51 minutes*

#### Test

*50 min*

I always make two versions of a test and pass them out checkerboard style. I ask students to show work.

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#### Puzzles

*1 min*

I offer a variety of Extra Credit puzzles for students who finish early and have no make up work to complete. This includes, but is not limited to; sudoku, mathdoku, logic problems, picture mazes, and pixel puzzles. A couple of my favorites are: Griddlers and Concept is puzzles

Both sites offer a number of free puzzles as well as purchasable books. Pixel Puzzles are a particular favorite. The Mathdoku are also great. They can increase a student's numeracy abilities if done regularly.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Rational Exponents
- LESSON 2: Real Number Exponents
- LESSON 3: Exponential Models Day 1 of 2
- LESSON 4: Exponential Models Day 2 of 2
- LESSON 5: Exponential Functions
- LESSON 6: Exponential Decay Functions
- LESSON 7: Simplifying Logarithms
- LESSON 8: Exponential and Logarithmic Equations
- LESSON 9: Logarithmic Functions
- LESSON 10: Exponential Growth and Interest Day 1 of 2
- LESSON 11: Exponential Growth and Interest Day 2 of 2
- LESSON 12: Natural Logarithms
- LESSON 13: Exponential and Logarithmic Functions Review Day 1
- LESSON 14: Exponential and Logarithmic Functions Review Day 2
- LESSON 15: Exponential and Logarithmic Functions Test