Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 59832
Writing an Exponential Function From a Table
Students are asked to write an exponential function represented by a table of values.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, exponential function, table, constructing a function
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_WritingAnExponentialFunctionFromATable_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problem on the Writing an Exponential Function From a Table worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the basic form of an exponential function.
Examples of Student Work at this Level
The student attempts to write a linear function or an exponential expression.
Questions Eliciting Thinking
What is an exponential function? What does the equation of an exponential equation look like?
How would you describe this graph? Is it linear?
Instructional Implications
Provide opportunities for the student to explore and investigate exponential functions, both growth and decay, in context. Have the student make a table of values for
page 1 of 3 each example. Then guide the student to identify the two parameters of an exponential function, the initial amount and the growth/decay factor, as well as the basic form
of an exponential function, y =
. Be sure the student understands the difference between the growth/decay factor and the rate of growth or decay. Explain that the
growth factor is (1 + r) where r is the rate of growth and the decay factor is (1 – r) where r is the rate of decay.
Provide additional opportunities for the student to write exponential functions from verbal descriptions, tables of values, and graphs.
Moving Forward
Misconception/Error
The student is unable to correctly calculate one or both parameters.
Examples of Student Work at this Level
The student understands the basic form of an exponential function but:
Is unable to find either parameter.
Is able to find the initial amount but not the growth factor.
Questions Eliciting Thinking
What are the two important parameters of an exponential function? Can you describe them in words?
I see you were able to find the initial amount. Can knowing this value help you find the growth factor?
Instructional Implications
Demonstrate how the two given points can be used to find both the initial amount and the growth factor. Provide additional examples of tables of values for exponential
functions beginning with pairs of values of the form (0,
) and (1,
) and progressing to pairs of values such as (x,
) and (x + 2,
). In each example, ask the student
to calculate the initial amount and the growth/decay factor and then write an equation of the form f(x) =
. Provide feedback as needed.
Almost There
Misconception/Error
The student makes an error in writing the function.
Examples of Student Work at this Level
The student:
Correctly calculates the initial amount and the growth factor, but neglects to write the exponential function.
Reverses the initial amount and the growth factor in the equation.
Questions Eliciting Thinking
What is the basic form of an exponential function? Did you write the function?
Which value, 3 or 5, is the initial amount?
How can you check if the ordered pairs given in the table satisfy your function?
Instructional Implications
Provide specific feedback to the student and allow the student to correct the error. Provide additional opportunities to write exponential functions given their graphs.
Consider implementing other MFAS exponential tasks Writing an Exponential Function From a Graph (F-LE.1.2), Writing an Exponential Function From a Description (FLE.1.2), and What Is the Function Rule? (F-LE.1.2).
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
page 2 of 3 The student correctly finds both the initial amount and the growth factor and writes the function as y =
. All work is correctly and completely shown.
Questions Eliciting Thinking
Could the growth factor also have been -3 since
= 9?
How would you have found the equation if (0, 5) had been replaced by (1, 15)?
Instructional Implications
Provide the student with tables containing at least three ordered pairs, some of which can be modeled by linear functions and some of which can be modeled by
exponential functions. Challenge the student to write an appropriate function for each table.
Consider implementing other MFAS exponential tasks Writing an Exponential Function From a Graph (F-LE.1.2), Writing an Exponential Function From a Description (FLE.1.2), and What Is the Function Rule? (F-LE.1.2).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Writing an Exponential Function From a Table worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.F-LE.1.2:
Description
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). ★
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