Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 59834
Writing a Function From Ordered Pairs
Students are given a table of values and are asked to write a linear function.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, linear, function, table, constructing a function
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_WritingAFunctionFromOrderedPairs_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 a Function From Ordered Pairs 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 a linear function.
Examples of Student Work at this Level
The student:
Attempts to write the function recursively.
page 1 of 4 Calculates the slope or the y-intercept but is unable to write the function.
Attempts to provide a verbal description or a graph.
Attempts to look for a pattern but cannot find one.
Questions Eliciting Thinking
What is the basic form of a linear function?
Why is it important to calculate the slope when writing a linear function?
How did you find the y-intercept? What is always true of the y-intercept?
How can you use the slope and y-intercept to write the equation?
Instructional Implications
Review the concept of a linear function in two-variables emphasizing slope-intercept form. Be sure the student understands the specific role of the slope and the y-intercept
in determining functional values. Assist the student in using the slope and y-intercept to write the equation of the line in slope-intercept form. Ask the student to write the
equation using function notation. Then ask the student to calculate f(x) for several values of x given in the table to demonstrate that the function is correctly written.
Provide additional opportunities to write equations of lines given two points on the line.
If needed, review function notation and guide the student to use function notation when writing equations of lines. Provide frequent opportunities to use function
notation, so the student can become familiar and comfortable with its use.
Moving Forward
Misconception/Error
The student has some understanding of the form of a linear function but is unable to complete writing the function.
Examples of Student Work at this Level
The student correctly writes the basic form of a linear function (e.g., y = mx + b) on his or her paper but is unable to correctly calculate either the slope or the y-intercept
or does not substitute either into the equation correctly.
Questions Eliciting Thinking
What is the basic form of a linear function? What does m represent? What does b represent?
Can you explain why you wrote your function this way?
page 2 of 4 Did you check if the ordered pairs in the table satisfy your equation?
Instructional Implications
Be sure the student understands the role of the slope and y-intercept in writing the equation of a line in slope-intercept form. Assist the student in using the slope and yintercept to write the equation of the line in slope-intercept form. Ask the student to write the equation using function notation. Then ask the student to calculate f(x) for
several values of x given in the table to demonstrate that the function is correctly written.
If needed, review how to calculate the slope of a line given two points on a line. Assist the student in correctly setting up the slope calculation to avoid sign errors or the
calculation of the reciprocal value. Review the concept of the y-intercept. Be sure the student understands its basic form, i.e., (0, b), and how to recognize it in a table of
values.
If needed, ask the student to graph the values from the table and to use the graph to identify the y-intercept. Guide the student to then locate the y-intercept in the
table. Next, assist the student in using the graph to determine the slope. Relate this strategy to finding the slope using two ordered pairs from the table. Provide the
student with additional opportunities to identify the y-intercept and slope without graphing.
If needed, review function notation and guide the student to use function notation when writing equations of lines. Provide frequent opportunities to use function
notation, so the student can become familiar and comfortable with its use.
Almost There
Misconception/Error
The student makes a calculation or other minor error.
Examples of Student Work at this Level
The student:
Makes a calculation error when calculating the slope.
Neglects to use function notation or uses it incorrectly.
Questions Eliciting Thinking
Can you check your slope calculation again? Did you compute the slope correctly?
What is function notation? What does it look like? How can it be used to write this function?
Instructional Implications
Assist the student in identifying and correcting any calculation errors. Correct any errors with the use of function notation. Explain to the student that even though y = 6x
+ 2 correctly describes the relationship between the independent and dependent variable, function notation should be used when writing the equation since it was used in
the description of the problem and in the table. Provide frequent opportunities to use function notation, so the student can become familiar and comfortable with its use.
Consider using the MFAS tasks What Is the Function Rule? (F-LE.1.2) and Functions From Graphs (F-LE.1.2) if not used previously.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly finds the slope and y-intercept and writes the function as f(x) = 6x + 2.
Questions Eliciting Thinking
How did you know that (0, 2) was the y-intercept (if the student identifies the y-intercept in the table)?
Is there an easier way to find the y-intercept (if the student calculates the y-intercept)?
Suppose the directions did not state that this function was linear, how could you determine that it is linear?
Instructional Implications
page 3 of 4 Ask the student to write linear functions given a verbal description or a graph of the function. Consider using the MFAS tasks The Cost of Water (F-LE.1.2), What Is the
Function Rule? (F-LE.1.2), and Functions From Graphs (F-LE.1.2) if not used previously.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Writing a Function From Ordered Pairs 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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