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

### Exponential functions describe a common ratio at which variables change.

1 week

Evidence of Understanding

• use rate of change to define exponential functions (focus on base 2, 10, and e)
• identify an asymptote and justify its existence
• explain why an exponential function does not have turning points (mins or maxs)
• distinguish exponential growth from decay from a graph, table, sequence, or situation
• identify quantities and words that indicate exponential growth or decay
• analyze situations, graphs, and tables to justify an exponential function model (versus other models)
• introduce the natural base (base e) to model situations that continuously change
• given 3+ data points, calculate the base (growth or decay rate) of the exponential function

• create representations of exponential functions(focus on base 2, 10, and e)
• identify the initial value and common ratio of change from a situation, sequence, table or graph
• generate an exponential graph, table, explicit function rule, or recursive function rule
• connect features of exponential functions across representations
• match an exponential function rule with a sequence, situation, table or graph
• Ex: recognize “an 8% annual increase” models exponential growth with a base of 1.08

• evaluate exponential functions(focus on base 2, 10, and e)
• calculate exact output values given an input
• evaluate an expression or equation written in function notation from a graph, table, or equation
• Ex: evaluate f(3) by looking at the points on graph or in the table
• analyze a situation to consider viable and nonviable domain and range values
• compare end behavior of the exponential function with the limits of the situation
• Ex: continuous exponential functions have no limits on the domain but in a situation there may be limits to how much the outputs can grow or decay

Develop conceptual understanding:

asymptote, exponential growth, exponential decay, natural base e, base

Supporting terms to communicate:

function, independent, dependent, input, output, domain, range, ratio, initial value, function rule, function notation, end behavior, intercept, rate of change
Core Resource
A core resource supports multiple days of instruction. COMING SOON!
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate. COMING SOON!
Instructional Routine: Connecting Representations

These tasks are embedded within the instructional routine called Connecting Representations.

• Exponential Function Rules from Tables
Chunk a table to find connections between tables of values and the function rules for exponential functions.
Resource:
Exponential Function Rules from Tables

Chunk a table to find connections between tables of values and the function rules for exponential functions.

All Resources From:
• Unit 2