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THIS RESOURCE IS ONLY AVAILABLE TO LOGGED IN USERS. PLEASE LOGIN AND TRY AGAIN. WE APOLOGIZE BUT THIS RESOURCE IS NOT AVAILABLE TO YOU. PLEASE READ BELOW FOR MORE INFORMATION. Resource ID#: 55272Primary Type: Formative Assessment

This task can be implemented individually, with a small group, or with the whole class.

The teacher asks the student to complete the problems on the Identifying Functions worksheet.

The teacher asks follow-up questions, as needed.

TASK RUBRIC

Getting Started

Misconception/Error

The student has little or no understanding of the concept of a function.

Examples of Student Work at this Level

The studentâ€™s response does not address the relationship between the variables. For example, the student makes a decision based on whether:

There are the same number of inputs as outputs.

Inputs (or outputs) repeat or are the same.

There is a pattern or not.

The student understands that a function is a relation, but does not understand its distinguishing characteristics. For example, the student writes a statement such as:

It is not a function because the x value cannot repeat.

The x-values (or the y-values) should all be the same in a function.

The x- and y-value cannot be the same number in a function.

It is not a function because the points do not make a straight line.

It is not a function because the relationship between the x- and y-values is not the same. For example, the y-value must always be twice the x-value.

Every input has an output, so it is a function.

Every y-value can only be paired with one x-value.

Questions Eliciting Thinking

Do you know what a relation is?

Do you know what makes a relation a function?

How many outputs can be associated with one input?

Can you explain why you thought this relation was/wasÂ notÂ a function?

Instructional Implications

Review the definition of a function with the student emphasizing that every input is paired with exactly one output. Discuss the definitions of the domain and range of a function, using a variety of terms like input and output or independent and dependent variables. For each example, have the student write the paired inputs and outputs as ordered pairs, emphasizing the defining feature of a function (i.e., every x-value is paired with exactly one y-value).

Provide the student with several empty or partially completed tables of values and have the student complete the tables so that some represent functions and others do not. Provide the student with several mapping diagrams that include the same set of inputs and outputs but do not include the lines or arrows that show how inputs and outputs are paired. Have the student complete each diagram so that some are examples and some are nonexamples of functions. Have the student justify his or her reasoning.

Moving Forward

Misconception/Error

The student is able to determine which examples represent y as a function of x and which do not but provides an incomplete (or nonmathematical) explanation and is unable to elaborate further.

Examples of Student Work at this Level

The student writes a statement such as:

If you put a number in, you should always get the same number out.

All of the different numbers have different outcomes.

Each x is being used.

Each domain has only one range.

Questions Eliciting Thinking

What is a function?

Can you explain further why you thought this relation was/was not a function?

Instructional Implications

Review the definition of a function with the student emphasizing that every input is paired with exactly one output. Model the use of mathematical reasoning and mathematical terminology in explaining why a relation is or is not a function.

Provide additional examples of relations represented by either a table of values or a mapping diagram. Be sure to include both examples and nonexamples of functions. Have the student determine whether each relation is a function and justify his or her answer.

Almost There

Misconception/Error

The student demonstrates an understanding of the concept of a function but makes an error in identifying one of the relations as a function.

Examples of Student Work at this Level

The student explains that a function is a relation in which each input or x-value is paired with one output or y-value. The student correctly determines whether or not three of the four examples represent functions. However, the student:

Decides that the second example is not a function because one x-value, three, is paired with more than one y-value.

Misinterprets the mapping diagram in the fourth example and states that it is not a function since some of the x-values are paired with more than one y-value.

Questions Eliciting Thinking

What is a function? Can you explain further why you thought this relation was/wasÂ not a function?

Did an x-value in the second example get paired with two differenty-values?

Can you write out each pairing shown by the fourth example as ordered pairs?

Instructional Implications

Encourage the student to write the paired inputs and outputs as ordered pairs. Then assist the student in examining the ordered pairs to identify and explain his or her error.

Provide additional examples of relations represented by either a table of values or a mapping diagram. Be sure to include both examples and nonexamples of functions. Have the student determine whether each relation is a function and justify his or her answer.

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 explains that the first example is not a function since the given x-value is paired with more than one y-value. The student correctly identifies the second, third, and fourth examples as functions. The student explains that each is a function because each x-value is paired with exactly one y-value.

Questions Eliciting Thinking

How could the domain of the first problem be changed so that it represents a function?

Instructional Implications

Introduce the student to the concept of one-to-one functions. Ask the student if there are any examples on the worksheet of one-to-one functions. Have the student rewrite the nonexamples, so they represent one-to-one functions.

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