5.2 Exploring Expontential Growth

Last updated about 1 year ago

19 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Recognize that exponential patterns grow by a constant growth factor
Distinguish between exponential and linear functions
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP4
CCSS.HSF.LE.A.1
CCSS.HSF.LE.A.1.A
CCSS.HSF.LE.A.3
Personal Finance Objectives
Recognize that investments grow exponentially
National Standards for Personal Financial Education
Investing
4a: Describe the impact of inflation on prices over time
4b: Explain the relationship between nominal and real returns.
8-5a: Explain the benefit of compound interest as compared with simple interest.
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems
Visual Pattern Cards

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Recognize that exponential patterns grow by a constant growth factor
Distinguish between exponential and linear functions
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP4
CCSS.HSF.LE.A.1
CCSS.HSF.LE.A.1.A
CCSS.HSF.LE.A.3
Personal Finance Objectives
Recognize that investments grow exponentially
National Standards for Personal Financial Education
Investing
4a: Describe the impact of inflation on prices over time
4b: Explain the relationship between nominal and real returns.
8-5a: Explain the benefit of compound interest as compared with simple interest.
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems
Visual Pattern Cards

Intro/Warm-Up

Explore It

Learn It

Practice It

Learn It & Practice It

Application Problems

5.2 Exploring Expontential Growth

Last updated about 1 year ago

19 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Recognize that exponential patterns grow by a constant growth factor
Distinguish between exponential and linear functions
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP4
CCSS.HSF.LE.A.1
CCSS.HSF.LE.A.1.A
CCSS.HSF.LE.A.3
Personal Finance Objectives
Recognize that investments grow exponentially
National Standards for Personal Financial Education
Investing
4a: Describe the impact of inflation on prices over time
4b: Explain the relationship between nominal and real returns.
8-5a: Explain the benefit of compound interest as compared with simple interest.
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems
Visual Pattern Cards

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Recognize that exponential patterns grow by a constant growth factor
Distinguish between exponential and linear functions
Common Core Math Standards
Link to all CCSS Math
CCSS.PRACTICE.MP4
CCSS.HSF.LE.A.1
CCSS.HSF.LE.A.1.A
CCSS.HSF.LE.A.3
Personal Finance Objectives
Recognize that investments grow exponentially
National Standards for Personal Financial Education
Investing
4a: Describe the impact of inflation on prices over time
4b: Explain the relationship between nominal and real returns.
8-5a: Explain the benefit of compound interest as compared with simple interest.
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems
Visual Pattern Cards

Intro/Warm-Up

COMPARE: Which One Doesn’t Belong?
Study the tables below to identify patterns, similarities, and differences. Then, answer the question.

What do you notice about the tables?_______  Identify 3 similarities or differences between them.
_______ 
_______
 _______ 

Explore It

MOVE: Exponential Growth
Follow your teacher’s instructions to complete this activity. Then, answer the questions.

In Round 1, how many people stood up with each tap?

In Round 2, how many people stood up with each tap?

Which round did you complete the fastest? Explain why you think that was the case.

Learn It

DESMOS#1: Exponential Growth in Circles
You’ve seen how exponential growth can happen quickly. Next, you’ll explore an exponential function in more detail, with both a visual pattern and numbers, to learn how to measure its growth. Follow your teacher’s instructions to complete this Desmos activity. 

Practice It

Now that you’re familiar with exponential patterns, you’ll explore their different representations with your group. It’s okay if some parts seem new or confusing; it might take some work to figure out. Follow your teacher’s instructions to complete this activity.
CREATE: Exponential Patterns Jigsaw
Let’s explore exponential change using visual patterns. Exponential change happens when you have a starting value that you repeatedly multiply by a certain value, called the growth factor. In this activity, you’ll work with your group to understand one visual exponential pattern and represent it in different ways.
Part I: Explore Your Pattern
Your teacher will assign you to a group to work on one of the Visual Pattern Cards. Work with your group to complete the table below based on your assigned pattern.

Draw a representation of the next step in the pattern. If the next step has too many pieces, you can draw a partial representation and explain what the complete step would look like.

Which pattern do you think would have the largest y value when x = 20? Explain your reasoning.

Learn It & Practice It

Desmos #2 Exponential vs Linear Patterns (Financial Algebra 5.2)
COMPARE: Exponential vs Linear Patterns
Now that you’ve explored exponential growth, consider how it compares to linear growth.

Application Problems

Level 1:  Desmos #3:  Growth Factor and Investments (Financial Algebra 5.2)

Level 2: 
The graph below represents the value of Lucas’ investments, which average 8% annual returns.

a. What was the initial balance in the account?_______ 
b. Approximately how much did the value of Lucas’ investments increase in the first 10 years?_______ 
c. Is the account growing by the same number of dollars each year? Explain how you know._______ 

The table below represents the growth of an investment account over 3 decades. 

What is the growth factor of this function?_______

Level 3:

Part 1:  Growth Factor
The table below represents the growth of an investment account over 5 years. Complete the table and answer the questions.

a.  What is the growth factor of this function?_______ 

b.  What is the annual rate of return in this account? Hint: By what percentage does this function increase each year?_______ %

c.  What was the initial value in the investment account?$_______ 

5.2 Exploring Expontential Growth

5.2 Exploring Expontential Growth

In Round 1, how many people stood up with each tap?

In Round 2, how many people stood up with each tap?

Which round did you complete the fastest? Explain why you think that was the case.

Part I: Explore Your Pattern

Draw a representation of the next step in the pattern. If the next step has too many pieces, you can draw a partial representation and explain what the complete step would look like.

Which table doesn’t belong? Explain your reasoning.

In Round 1, how many people stood up with each tap?

In Round 2, how many people stood up with each tap?

Which round did you complete the fastest? Explain why you think that was the case.

Do you think the results would have been different if you did this with a stadium full of people? Why or why not?

Part I: Explore Your Pattern

Draw a representation of the next step in the pattern. If the next step has too many pieces, you can draw a partial representation and explain what the complete step would look like.

Describe the way you see the pattern increasing or decreasing. Be sure to identify the growth factor and explain what that means in your pattern.
Note: for Pattern D, it will be called the decay factor.

Create a table representing the pattern with numbers. (draw it in show your work if that is easier)

Plot the points from the table on the graph to illustrate the pattern. ( you may also screen shot a desmos with the points in the show your work)

The table below represents the value of an investment account, y, after x years.

Which of the equations options do you think represents the account’s growth? Justify your response using math terms from this lesson.

Which table doesn’t belong? Explain your reasoning.

Do you think the results would have been different if you did this with a stadium full of people? Why or why not?

Describe the way you see the pattern increasing or decreasing. Be sure to identify the growth factor and explain what that means in your pattern.
Note: for Pattern D, it will be called the decay factor.

Create a table representing the pattern with numbers. (draw it in show your work if that is easier)

Plot the points from the table on the graph to illustrate the pattern. ( you may also screen shot a desmos with the points in the show your work)

The table below represents the value of an investment account, y, after x years.

Which of the equations options do you think represents the account’s growth? Justify your response using math terms from this lesson.

5.2 Exploring Expontential Growth

5.2 Exploring Expontential Growth

In Round 1, how many people stood up with each tap?

In Round 2, how many people stood up with each tap?

Which round did you complete the fastest? Explain why you think that was the case.

Part I: Explore Your Pattern

Draw a representation of the next step in the pattern. If the next step has too many pieces, you can draw a partial representation and explain what the complete step would look like.

Which table doesn’t belong? Explain your reasoning.

In Round 1, how many people stood up with each tap?

In Round 2, how many people stood up with each tap?

Which round did you complete the fastest? Explain why you think that was the case.

Do you think the results would have been different if you did this with a stadium full of people? Why or why not?

Part I: Explore Your Pattern

Draw a representation of the next step in the pattern. If the next step has too many pieces, you can draw a partial representation and explain what the complete step would look like.

Describe the way you see the pattern increasing or decreasing. Be sure to identify the growth factor and explain what that means in your pattern.Note: for Pattern D, it will be called the decay factor.

Create a table representing the pattern with numbers. (draw it in show your work if that is easier)

Plot the points from the table on the graph to illustrate the pattern. ( you may also screen shot a desmos with the points in the show your work)

The table below represents the value of an investment account, y, after x years. Which of the equations options do you think represents the account’s growth? Justify your response using math terms from this lesson.

Which table doesn’t belong? Explain your reasoning.

Do you think the results would have been different if you did this with a stadium full of people? Why or why not?

Describe the way you see the pattern increasing or decreasing. Be sure to identify the growth factor and explain what that means in your pattern.Note: for Pattern D, it will be called the decay factor.

Create a table representing the pattern with numbers. (draw it in show your work if that is easier)

Plot the points from the table on the graph to illustrate the pattern. ( you may also screen shot a desmos with the points in the show your work)

The table below represents the value of an investment account, y, after x years. Which of the equations options do you think represents the account’s growth? Justify your response using math terms from this lesson.

Describe the way you see the pattern increasing or decreasing. Be sure to identify the growth factor and explain what that means in your pattern.
Note: for Pattern D, it will be called the decay factor.

The table below represents the value of an investment account, y, after x years.

Which of the equations options do you think represents the account’s growth? Justify your response using math terms from this lesson.

Describe the way you see the pattern increasing or decreasing. Be sure to identify the growth factor and explain what that means in your pattern.
Note: for Pattern D, it will be called the decay factor.

The table below represents the value of an investment account, y, after x years.

Which of the equations options do you think represents the account’s growth? Justify your response using math terms from this lesson.