## Investigation Narrative.docx - Section 2: Investigation and New Learning

*Investigation Narrative.docx*

# Exponential Data Tables

Lesson 6 of 26

## Objective: Students will be able to find the function rules for exponential functions given a few data points organized in a data table.

#### Warm-Up

*30 min*

This warm-up is basically asking the same question in several ways, but students can come to that realization themselves. If students are struggling to figure out any one problem, ask them to try to turn that problem into one of the other problems. When circulating, if a student seems unable to get started on any section, I ask the students to figure out how the data tables relate to the bunny problems. Usually this remainder is enough to help them understand what they are looking for. Once they realize that they are basically looking for the multiplier in all the situations, they start to look for shortcuts and this search for shortcuts will frame the entire lesson.

This lesson is another one that differentiates itself in the sense that students will develop their own methods to find these rules. The fractions will be challenging for some students, so there is a method described in the middle of the lesson that you can show these students if they have trouble getting started. If students are using the guess and check method, they can be encouraged to develop a more efficient method, two of which are described in the middle section of the lesson.

Today’s lesson is very much about MPS1 and MPS2. In terms of MPS1, the goal is for students to figure out their own way to understand or make sense of the problems and for them to be able to explain why their methods make sense to them. In terms of MPS2, student should be using both numerical and algebraic methods to solve these problems and to verify their solutions, and they should be encouraged to reflect on which methods they prefer and why.

#### Resources

*expand content*

- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Bunnies and Exponential Growth
- LESSON 2: More Bunnies and Exponential Growth
- LESSON 3: Candy Bars and Exponential Decay
- LESSON 4: Bunnies and Exponential Equations
- LESSON 5: Graphing Bunnies
- LESSON 6: Exponential Data Tables
- LESSON 7: Fitting Exponential Functions Given Two Points
- LESSON 8: Matching Exponential Graphs to Equations
- LESSON 9: Exponential Functions Review
- LESSON 10: Exponential Functions Portfolio and Summative Assessment
- LESSON 11: Exponential Functions and Approach Statements
- LESSON 12: Graphing Exponential Functions
- LESSON 13: Matching Graphs of Exponential Functions to their Equations
- LESSON 14: Exponential Function Designs
- LESSON 15: Graph Exponential Functions Review
- LESSON 16: Graph Exponential Functions Summative Assessment and Portfolio
- LESSON 17: Bouncy Ball Investigation
- LESSON 18: Percent Change: Growth and Decay
- LESSON 19: More Percent Changes and Exponential Functions
- LESSON 20: Writing Exponential Functions to Solve Problems
- LESSON 21: Different Time Intervals and Exponential Functions
- LESSON 22: Compound Interest
- LESSON 23: Compound Interest Formula
- LESSON 24: Continuously Compounded Interest
- LESSON 25: Applications of Exponential Functions Review
- LESSON 26: Applications of Exponential Functions Summative Assessment