In this lesson, students will explore exponential growth by cutting two different pieces of paper differently. Students will then explore exponential decay by throwing away pieces of paper that were cut. Students will create graphs and compare the different functions based on the exploration. Students will compare linear functions to exponential functions and make note of the key differences. Students will then be provided with different scenarios with multiple representations of exponential functions. Students will be introduced to percents as a rate of change in exponential functions. Students will be able to label the different parts of a function and create their own equations at the end of this lesson.

TEKS: 

Readiness Standard: A.9(C)- write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

Readiness Standard: A.9(D)- graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems

Supporting Standard: A.9(A)- determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities

Supporting Standard: A.9(B)- interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab^x in real-world problems

Supporting Standard: A.9(E)- write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems

Supporting Standard: A.12(A)- decide whether relations represented verbally, tabularly, graphically, and symbolically define a function

ELPS: 

4F- Use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

5B- write using newly acquired basic vocabulary and content-based grade-level vocabulary

Technology: 

5b- Students collect data or identify relevant data sets, use digital tools to analyze them, and represent data in various ways to facilitate problem-solving and decision-making 

CASEL: 

Practicing teamwork and collaborative problem-solving

Demonstrating curiosity and open-mindedness

1. What is the difference between linear and exponential equations?

2. How is growth different from decay?

3. How do you write an exponential equation?

4. Percentage of growth or decay?

5. What is asymptote?

6. What does the y-intercept represent?

7. What do you do if you have a percentage of growth or decay?

Content Objectives: 

Students will be able to identify the parts of an exponential function from multiple representations.

Language Objectives: 

Students will be able to write an exponential function from multiple representations.

Students will be able to describe the differences between a linear and exponential function.

• • Growth

  • Decay

  • Exponential

  • Multiplicative Rate of Change (MROC)

  • Initial Value 

  • Horizontal Asymptote

  • Domain

  • Range

1. Students will explain the difference between exponential growth and decay

2. Students will set up exponential equations

3. Students will compare linear and exponential functions

1. SWBAT identify the different parts of an exponential function

2. SWBAT set up exponential equations based on multiple representations

3. SWBAT identify exponential growth and decay based on percentages

Formative: 

• Warm-up

• Guided Inquiry (Probing)

• Open-ended/ Reflective questions (Handout)

• Exit ticket

Summative: 

• Test  

  • Multiple choice and work shown.

• Worksheet 

• Exit Ticket (Reflection part of worksheet)

Day 1 is in the Excel file under the tab titled decay.

Day 2 is the PDF file, which is the last file.

Day 3 is in the Excel file under the tab labled Zombie.

Unit Assessment: https://drive.google.com/file/d/1ROX2DpuSaw1mV877M3gU4LXKJPzQi1es/view?usp=drivesdk 

Warm-ups: https://docs.google.com/presentation/d/1WKrbzCTOFDfOftabBPl7oz3qccIa0Es_Qq_oCG60pCk/edit?usp=sharing

Translated Vocabulary Sheet: https://docs.google.com/file/d/1DpEBn0lY-b_z5gJFOMXzlpr2NfxpsPJu/edit?usp=docslist_api&filetype=msword