Primary Type: Formative Assessment
Status: Published
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Resource ID#: 69872
Rational Exponents - 2
Students are asked to convert numerical expressions from exponential to radical form.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, radicals, roots, rational exponents
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_RationalExponents2_Worksheet.docx
MFAS_RationalExponents2_Worksheet.pdf
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 problems on the Rational Exponents - 2 worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the relationship between radicals and rational exponents.
Examples of Student Work at this Level
The student:
Interprets the exponent as a coefficient (e.g., rewrites
as
and
Interprets the numerator of the exponent as a coefficient (e.g., rewrites
as
).
as
.
page 1 of 4 Uses the denominator of the rational exponent as a coefficient of the radical (e.g., rewrites
as
).
Questions Eliciting Thinking
What does 52 mean? What does
mean?
What is meant by the index of a radical? What does the index mean?
Instructional Implications
If needed, review related terminology such as radical, radicand, index, exponent, base, and power. Also, review the properties of exponents. Review the meaning of the
index of a radical and how to represent a radical such as
or
in equivalent exponential form. Ask the student to revise the responses to the first two questions.
Explain the definition of rational exponents and provide examples of expressions written in both radical and exponential form. Ask the student to revise the response to the
third question. Model rewriting
as
or
. Review the meaning of a negative exponent and allow the student to revise the response to the fourth problem.
Provide additional examples of numerical and variable expressions written in exponential form and ask the student to rewrite each in an equivalent radical form.
Moving Forward
Misconception/Error
The student interchanges the index and the power in the rational exponent when the power is different from one.
Examples of Student Work at this Level
The student rewrites
as
and
as
. However, the student rewrites
as
and
as
.
Questions Eliciting Thinking
What does the numerator of the rational exponent mean? What does the denominator of the rational exponent mean?
Can you simplify
? What would you do first? Then what?
Instructional Implications
page 2 of 4 Review the definition of rational exponents and provide examples of expressions written in both radical and exponential form. Remind the student that
or
so
. If needed, review the meaning of a negative exponent and allow the student to revise the response to the fourth problem. Provide additional
examples of numerical and variable expressions written in exponential form and ask the student to rewrite each in an equivalent radical form.
Almost There
Misconception/Error
The student errs when working with negative exponents.
Examples of Student Work at this Level
The student correctly rewrites the first three expressions in radical form. However, the student rewrites
incorrectly.
Questions Eliciting Thinking
What does a negative exponent mean? Can you rewrite
in an equivalent form with a positive exponent?
Instructional Implications
Review the properties of exponents (in particular, the quotient rule). Show the student an expression such as:
Then use the quotient rule to simplify
as
. Explain that
must equal
which is equivalent to
.
in order for the properties of exponents to apply to integer exponents, and
extending the properties of exponents to integer exponents allows for a definition of negative exponents. Guide the student to rewrite
as
and then as
.
Provide additional examples of numerical and variable expressions written in exponential form and ask the student to rewrite each in an equivalent radical form.
Got It
page 3 of 4 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 rewrites each expression in radical form.
or
or
or
Questions Eliciting Thinking
How would you describe, in general, the relationship between rational exponents and the radical notation?
Why do you suppose taking a square root of a number is equivalent to raising the number to the one-half power?
Instructional Implications
Challenge the student with additional more complex exponential expressions to convert to radical form.
Consider implementing other MFAS tasks for standard N-RN.1.2: Rational Exponents - 1, Rational Exponents - 3, and Rational Exponents - 4.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Rational Exponents - 2 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.N-RN.1.2:
Description
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
page 4 of 4