COMPARE: Which One Doesn’t Belong?
Study the tables below to identify patterns, similarities, and differences. Then, answer the question.
OBJECTIVES & STANDARDS
Math Objectives
Recognize that exponential patterns grow by a constant growth factor
Distinguish between exponential and linear functions
Common Core Math Standards
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
OBJECTIVES & STANDARDS
Math Objectives
Recognize that exponential patterns grow by a constant growth factor
Distinguish between exponential and linear functions
Common Core Math Standards
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
COMPARE: Which One Doesn’t Belong?
Study the tables below to identify patterns, similarities, and differences. Then, answer the question.
Which table doesn’t belong? Explain your reasoning.
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.
Do you think the results would have been different if you did this with a stadium full of people? Why or why not?
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.
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.
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)
Level 2:
The graph below represents the value of Lucas’ investments, which average 8% annual returns.
Level 3:
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.
