Big Idea:

Big Idea 1

Sequences are discrete functions defined by their rates of change.

1 week

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.

  • Studying Sequences
    This Core Resource makes connections between linear & exponential functions and arithmetic & geometric series respectively.
    Resource:
    Studying Sequences

    This Core Resource makes connections between linear & exponential functions and arithmetic & geometric series respectively. It also makes connections between visual sequences, graphs, and formulae for sequences.

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