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# Sorting out the Change

Lesson 7 of 14

## Objective: SWBAT analyze the rate of change to determine whether a relationship is linear or exponential and write the corresponding equation.

## Big Idea: Students identify the type of function (linear or exponential) which represents a situation & writes equations to model these situations.

*50 minutes*

#### Warm-up

*10 min*

Depending on where class left off and how students responded to the Thumbs Assessment yesterday, I will have students complete the *Isotope Problem *and/or review the various solution methods. I may have students present their approaches. Hopefully I can find an example of the three approaches that I am seeing (and maybe even ones that I’m not thinking about) and have those students just slip their work under the document camera with a quick explanation.

The three main approaches I will be looking for to be demonstrate (or I will demonstrate) are:

1) Finding from two points (like page 19 of flipchart)

2) Writing the exponential function in terms of number of half-lives and then substituting in the half lives as a function of time.

3) Identifying the rate of change in the table and using the initial value to write the equation.

#### Resources

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#### Sorting Out the Change

*35 min*

The next task I want students to work through is the Student Handout Sorting out the Change.docx. Check out this video, Sorting the Change, video narrative, middle.MP4, for more details on how I like to run this activity.

This activity was adapted from a task written by The mathematics Vision Project. The original lesson can be found at www.mathematicsvisionproject.org.

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Technically, students have been exposed to everything of extreme importance in this unit at this point. Over the next week students will be practicing a bit more with finding equations of exponential functions and real world applications and will also take a more in-depth look at stretching exponentials. So at this point I would like to know how students feel that they are progressing. I want students to complete a **3-2-1 Assessment** for this unit. I will ask students for 3 things they’ve learned, 2 questions they still have, and 1 thing they want to tell me.

#### Resources

*expand content*

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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