13 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
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Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### 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:
• Unit 2

#### Exponential Functions

Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate.
• Difference of Two Sequences
Students will look at graph of an Arithmetic Sequence and a Geometric Sequence and calculate the difference of their next terms.
Resource:
Difference of Two Sequences

Students will look at graph of an Arithmetic Sequence and a Geometric Sequence and calculate the difference of their next terms.

All Resources From:
• Unit 2