Predicting the Ones Digit

Reasoning About Exponent Patterns

The video focus is about the importance of reasoning and proof in middle school mathematics. It concludes with the teacher reflecting on how she will use the information that she gathered from her formative assess to plan her next steps.

Real time is about 1.5 hours.

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 (25:11)
• CMP2 Predicting the Ones Digit Problem 5.1
• CMP3 Looking for Patterns Among Exponents Problem 5.1
• Goals for CMP2 Problem 5.1 Predicting the Ones Digit Correlates
  • 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 Problem 5.1 Looking for Patterns Among Exponents
  • 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 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 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
• Video Transcript