# Teacher Questions

Use for CMP2, *Growing, Growing, Growing* Problems 4.1 and 4.2

Use for CMP3, *Growing, Growing, Growing* Problems 4.1 and 4.2

This segment highlights various questions that the teacher uses during class to encourage and guide students' understanding and reasoning.

The video shows the teacher questioning students in different situations, one on one, small group, and large group. The questions have different purposes and consequences.

The focus is on the kinds of questions and for what purposes the teacher asks and then how does the teacher listen to and interpret the responses.

The 12 minute video has a collection of 6 clips from different days during *Growing, Growing, Growing*, Investigation 4.

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’ 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?
- What does the teacher do when students have a misperception?
- What are the various purposes for the questions a teacher asks?

- Full Length (12:23)
- Problem 4.1
- Problem 4.2
- Goals for CMP2 Growing, Growing, Growing Problems 4.1 and 4.2
- 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

- Goals for CMP3 Growing, Growing, Growing Problems 4.1 and 4.2
- Exponential Functions Explore problem situations in which two or more variables have
an exponential relationship to each other
- Identify situations that can be modeled with an exponential function
- Identify the pattern of change (growth/decay factor) between two variables that represent an exponential function in a situation, table, graph or equation
- Represent an exponential function with a table, graph or equation
- Make connections among the patterns of change in a table, graph and equation of an exponential function
- Compare the growth/decay rate and growth/decay factor for an exponential function and recognize the role each plays in an exponential situation
- Identify the growth/decay factor and initial value in problem situations, tables, graphs and equations that represent exponential functions
- Determine whether an exponential function represents a growth (increasing) or decay (decreasing) pattern, from an equation, table or graph that represents an exponential function
- Determine the values of the independent and dependent variables from a table, graph, or equations of an exponential function
- Use an expponential equation to describe the graph and table of an exponental function
- Predict the y-intercept from an equation, graph, or table that represents an exponential function
- Interpret the information that the y-intercept of an exponential function represents
- Determine the effects of the growth factor and initial value for an exponential function on a graph of the function
- Solve problems about exponential growth and decay from a variety of different subejct areas, including science and business, using an equation, table, or graph
- Observe that one exponential equation can model different contexts
- Compare exponential and linear functions

- Exponential Functions Explore problem situations in which two or more variables have
an exponential relationship to each other
- Video Transcript
- Suggestions for organizing Professional Development