# Making Smaller Ballots

## Exponential Decay

Use for CMP2 and CMP3 Problem 4.1 Making Smaller Ballets.

Highlighted in this video is the learning trajectory from when students first see an example of exponential decay to where they feel confident enough to attempt a definition of decay factor.

The focus is on where students are in their development of the concept of exponential decay, and in their ability to reason algebraically.

The video concludes with the teacher reflecting her planning and what she knows from her formative assessments made during the lesson.

Real time is about 1.5 hour.

As you view the video, consider the following:

- What is the evidence of students’ understanding and reasoning? What prior understandings do you see students using or building upon?
- What is the evidence of students’ understanding and reasoning? What prior understandings do you see students using or building upon?
- What is the evidence of students’ use of the mathematical practices from the Common Core State Standards? To what extent are students growing in their sophistication of their use of the practices?
- Were there any “aha moments” in the video?
- How is the teacher facilitating the development of students’ understanding and reasoning?
- As a teacher, how would you use the information from this lesson to plan the next lesson?

- Full Length (31:53)

- Problem 4.1
- Goals for Problem 4.1 Making Smaller Ballots
- Use knowledge of exponential relationships to make tables and graphs and to write equations for exponential decay patterns
- Analyze and solve problems involving exponents and exponential decay
- Recognize patterns of exponential decay in tables, graphs, and equations
- Use information in a table or graph of an exponential relationship to write and equation
- Analyze an exponential decay relationship that is represented by an equation and use the equation to make a table and graph
- Video Transcript
- Suggestions for organizing Professional Development