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# Counting the Change: Linear, quadratic, or exponential? (Day 1 of 2)

Lesson 5 of 14

## Objective: SWBAT analyze the rate of change to determine whether a relationship is linear, quadratic, or exponential and write functions describing relationships.

## Big Idea: Students explore rates of change to identify function types and find patterns that help them to identify and define exponential functions.

*50 minutes*

#### Warm-up

*5 min*

As a warm-up to today’s lesson, have students reflect on the prompt on page 2 of the Flipchart - identifying change and writing exponentials (p.1-18) in their teams. This is an essential big idea in this unit. It is important that students are able to recognize that exponential growth functions will always exceed other functions as x gets larger and larger.

Once students have had a chance to discuss this in their teams, I will ask for a volunteer to share out. If there are no volunteers I will use a random method to call on a student. I always like to randomly call on kids so it keeps all students paying attention. One method I use to randomly call on students is to assign students a number (which works great for me becuase they are already assigned a number for their calculator use in class) and then use a random number generator to get a number. I have also used Popsicle sticks with student names in the past, but I just found that too time consuming initially and hard to keep up on.

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In this section of the lesson, students will work to identify the rates of change in order to determine the type of function modeled by the situation.

Here is a quick overview of this section of the lesson as well as the connections to the Mathematical Practices: Counting the change, video narrative, rates of change.

Here is a step-by-step narrative of Flipchart and how I will present the notes to my students: counting the change, video narrative, counting change notes.

Finally, my campus is focusing on a Cornell notes initiative this year. I decided last minute to make a guided notes template to help speed up students' note taking: Student Handout - Note Taking Template.

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#### Arcade Problem

*18 min*

Present page 19 of the Flipchart - identifying change and writing exponetials (p.1-19) and have students start working through the arcade problem in teams. One goal here is for students to see a real life example of how a percent rate of change can grow so much quicker than a constant rate of change. Also, this problem should be used to help students to write an exponential function from two points. Students may need to see this modeled. But I wanted to just give my students the steps and see if they can figure it out! It really is just a system of equations and they have all the Algebra skills needed. I will probably end up providing help to struggling teams to set up the problem and review how to solve a system of equations. I do expect students to be able to write the linear function for sure and complete the graphing on their own.

This problem will be continued tomorrow....

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#### Closure: Team Pair Check

*2 min*

To close out today's learning, have students take 2 minutes to compare their work so far with a table nearby. Remind students that we will continue working on this tomorrow. We want to be sure to give students plenty of time to struggle over finding the exponential equation given two points.

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Assign Homework 3 - Exponential Functions. Students will be taking a homework quiz over #1-3 on Monday.

#### Resources

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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: Cat Island (Day 1 of 2): Cats can’t add but they do multiply!
- LESSON 2: Cat Island (Day 2 of 2): Cats can’t add but they do multiply!
- LESSON 3: Graphing Exponential Functions
- LESSON 4: Shifting Exponential Functions
- LESSON 5: Counting the Change: Linear, quadratic, or exponential? (Day 1 of 2)
- LESSON 6: Counting the Change: Linear, quadratic, or exponential? (Day 2 of 2)
- LESSON 7: Sorting out the Change
- LESSON 8: Stretching Exponential Functions (and your mind)
- LESSON 9: Credit Card Investigation: What is interest? (Day 1 of 4)
- LESSON 10: Credit Card Investigation: What is interest? (Day 2 of 4)
- LESSON 11: Credit Cards Investigation: How is interest really calculated? (Day 3 of 4)
- LESSON 12: Credit Card Investigation: A Dastardly Scheme (Day 4 of 4)
- LESSON 13: Exponential Functions Test Review
- LESSON 14: Exponentials Functions Unit Test