Exponential Functions

13 Components
Initial Task
Multiplying Cells
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Selecting a formative assessment lesson for Algebra II Unit 2 Comparing Investments Having Kittens
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 End of Unit Assessment Teacher Resources ALG II Unit 2 Find aligned Regents questions with Quiz Banker
A2 U2: Exponential Functions
Browse Components
Initial Task
Multiplying Cells
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Selecting a formative assessment lesson for Algebra II Unit 2 Comparing Investments Having Kittens
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 End of Unit Assessment Teacher Resources ALG II Unit 2 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 1

Sequences are discrete functions defined by their rates of change.

1 week
See Standards
Common Core: Major Standards:
F-BF.A.2

Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences recursively and with an explicit formula, use them to model situations, and translate between both forms.*

Common Core: Supporting Standards:
F-LE.A.2

Linear, Quadratic, & Exponential Models: Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Common Core: Additional Standards:
F-IF.A.3

Understand the concept of a function and use function notation. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1,  f(n+1) = f(n) + f(n–1) for n ≥ 1.

Evidence of Understanding

  • compare a variety of sequences and describe how to extend each sequence
    • describe the relationship between the term of a sequence and the number in the sequence
      • Example: In the sequence 3, 5, 7, 9,... the first term is the number 3, the third term is 7, etc.
    • determine when a sequence can be generated by a consistent pattern and describe the pattern
      • describe an arithmetic sequence using thecommon difference
      • describe a geometric sequence using thecommon ratio or multiplier
    • use the common difference or ratio to find missing values in the sequence
  • represent a sequence with a visual diagram or graph
    • explain why the graph of a sequence is always discrete
    • use rate of change to justify why geometric sequences are modeled by exponential functions
      • connect the common difference of an arithmetic sequence with the constant rate of change for a linear function
      • connect the common ratio of a geometric sequence with the constant factor of change for an exponential function
    • analyze a visual or graph to determine if a given value belongs in the sequence
  • create an explicit or recursive rule for an arithmetic or geometric sequence
    • use a function rule to determine if a value belongs in an arithmetic or geometric sequence
    • generate a rule from a situation, graph, table, or visual
      • given non consecutive values in an arithmetic or geometric sequence, create and justify an explicit rule
    • compare and convert between the explicit and recursive rules for a sequence

Develop conceptual understanding:

arithmetic, geometric, common difference, common ratio, multiplier, discrete, explicit, recursive

Supporting terms to communicate:

term, linear, exponential, rate of change, initial value, coefficient, constant, base, exponent, integer, consecutive 

Core Resource

A core resource supports multiple days of instruction.

Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate.