# Teacher Reflections

In these videos, we hear a teacher reflecting on her planning, teaching, assessing, and management every day during a week of teaching.

The focus is on how the teacher reflects on student understanding from the daily lesson then adapts her plans accordingly. The teacher discusses difficult concepts and skills for students and how she plans to address the needs.

The discussions also include ideas about how teacher differentiates and manages vocabulary, grading notebooks, and homework.

This has a collection of 5 video chapters from five different days during *Growing, Growing, Growing*. It includes parts of Investigation 3, 4, and 5.

As you view the video, consider the following:

- What does the teacher use as evidence of students’ understanding and reasoning? What prior understandings does she see students building upon?
- How does the teacher use her reflection of the lesson to plan for the next day?
- How is the teacher facilitating the development of students’ understanding and reasoning through the use of differentiation, vocabulary, homework, notebooks?

- Watch Day 1
- Watch Day 2
- Watch Day 3
- Watch Day 4
- Watch Day 5
- Goals for CMP2 Investigation 3
- Determine a non-whole number growth factor using information in a table or a graph
- Determine the growth rate, or percent change
- Use sample population data to write an equation to model population growth
- Investigate the growth of an investment with a given growth rate (percent increase)
- Relate growth rates and growth factors
- Review and extend understanding of percent
- Understand the role of initial value (y-intercept) in compound growth

- Goals for CMP2 Investigation 4
- 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 CMP2 Investigation 5
- Examine patterns in the exponential and standard forms of powers of whole numbers
- Use patterns in powers to estimate the ones digits for unknown powers
- Use patterns in powers to develop rules for operating with exponents
- Become skillful in operating with exponents in numeric and algebraic expressions
- Describe how varying the values of a and b in the equation y = a(bx) affects the graph of that equation

- Goals for CMP3 Investigation 4
- 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
- Goals for CMP3 Investigation 5
- Exponential Functions Explore problem situations in which two or more variables have
an exponential relationship to each other
- Identify situations that can be modeled by 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 recognizie 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
- Use an exponential equation to describe the graph and table of an exponential 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 represent
- 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 vairety of different subject areas, including sciences and business, using an equation, table or graph
- Observe that one exponential equation can model different contexts
- Compare exponential and linear functions

- Equivalence Develop understanding of equivalent exponential expressions
- Write and interpret exponential expressions that represent the depends variable in an exponential function
- Develop the rules for operating with rational exponents and explain why they work
- Write, interpret, and operate with numerical expressions in scientific notation
- Write equivalent expressions using the rules for exponents and operations
- Solve problems that involve exponents, including scientific notation

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