# MAFS.912.N-RN.1.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents.
General Information
Subject Area: Mathematics
Domain-Subdomain: Number & Quantity: The Real Number System
Cluster: Level 1: Recall
Cluster: Extend the properties of exponents to rational exponents. (Algebra 1 - Major Cluster) (Algebra 2 - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications
Also assesses:
MAFS.912.N-RN.1.1

MAFS.912.N-RN.2.3

• Assessment Limits :
Expressions should contain no more than three variables.

For N-RN.1.2, items should not require the student to do more than
two operations.

• Calculator :

Neutral

• Clarification :
Students will use the properties of exponents to rewrite a radical
expression as an expression with a rational exponent.

Students will use the properties of exponents to rewrite an
expression with a rational exponent as a radical expression.

Students will apply the properties of operations of integer exponents
to expressions with rational exponents.

Students will apply the properties of operations of integer exponents

Students will write algebraic proofs that show that a sum or product
of two rational numbers is rational; that the sum of a rational number
and an irrational number is irrational; and that the product of a
nonzero rational number and an irrational number is irrational.

• Stimulus Attributes :
Items should be set in a mathematical context.
• Response Attributes :
Items may require the student to complete an algebraic proof.

Items may require the student to determine equivalent expressions
or equations.

Responses with square roots should require the student to rewrite
the square root so that the radicand has no square factors

Sample Test Items (1)
• Test Item #: Sample Item 1
• Question:

Jeremy determines that . Part of his work is shown. Which expression or equation should be placed in the blank to correctly complete Jeremy's work?

• Difficulty: N/A
• Type: MC: Multiple Choice

## Related Courses

This benchmark is part of these courses.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200330: Algebra 2 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200370: Algebra 1-A (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1207310: Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1206330: Analytic Geometry (Specifically in versions: 2014 - 2015 (course terminated))
1200410: Mathematics for College Success (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1200700: Mathematics for College Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
7912070: Access Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
7912080: Access Algebra 1A (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
7912090: Access Algebra 1B (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200335: Algebra 2 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
1200375: Algebra 1-A for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 and beyond (current))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
7912095: Access Algebra 2 (Specifically in versions: 2016 - 2018, 2018 - 2019, 2019 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.N-RN.1.AP.2a: Convert from radical representation to using rational exponents and vice versa.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Assessment

Sample 4 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

## Formative Assessments

Rational Exponents - 4:

Students are asked to rewrite expressions involving radicals and rational exponents in equivalent forms.

Type: Formative Assessment

Rational Exponents - 2:

Students are asked to convert numerical expressions from exponential to radical form.

Type: Formative Assessment

Rational Exponents - 3:

Students are asked to convert a product of a radical and exponential expression to a single power of two.

Type: Formative Assessment

Rational Exponents - 1:

Students are asked to convert numerical expressions from radical to exponential form.

Type: Formative Assessment

## Lesson Plans

Students will rewrite radical expressions that can be simplified to one term and perform operations on radical expressions. They will solve problems in a Row-by-Row activity. Pairs of students work on different problems at different complexity levels that lead to the same solution. The students will challenge each other to prove their solutions are correct. This activity does not address rational exponents.

Type: Lesson Plan

This lesson unit is intended to help you assess how well students are able to:

• Use the properties of exponents, including rational exponents, and manipulate algebraic statements involving radicals.
• Discriminate between equations and identities.

There is also an opportunity to consider the role of the imaginary number , but this is optional.

Type: Lesson Plan

## Original Student Tutorials

Solving Rational Equations: Cross Multiplying:

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Type: Original Student Tutorial

Learn to rewrite products involving radicals and rational exponents using properties of exponents in this interactive tutorial.

Type: Original Student Tutorial

Checking a Calculation of a Decimal Exponent:

In this example, students use properties of rational exponents and other algebraic concepts to compare and verify the relative size of two real numbers that involve decimal exponents.

Rational or Irrational?:

This makes for a good follow-up task on rational irrational numbers after the students have been acquainted with some of the more basic properties, asking students to reason about rational and irrational numbers (N-RN.3) in a variety of ways. In addition to eliciting several different types of reasoning, the task requires students to rewrite radical expressions in which the radicand is divisible by a a perfect square.

## Tutorial

Power of a Power Property:

This tutorial demonstrates how to use the power of a power property with both numerals and variables.

Type: Tutorial

## Unit/Lesson Sequence

Sample Algebra 1 Curriculum Plan Using CMAP:

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

### Using this CMAP

To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.

To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app.

To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.

All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx

Type: Unit/Lesson Sequence

## Video/Audio/Animations

Rational Exponents:

Exponents are not only integers and unit fractions. An exponent can be any rational number expressed as the quotient of two integers.

Type: Video/Audio/Animation

Radical expressions can often be simplified by moving factors which are perfect roots out from under the radical sign.

Type: Video/Audio/Animation

## MFAS Formative Assessments

Rational Exponents - 1:

Students are asked to convert numerical expressions from radical to exponential form.

Rational Exponents - 2:

Students are asked to convert numerical expressions from exponential to radical form.

Rational Exponents - 3:

Students are asked to convert a product of a radical and exponential expression to a single power of two.

Rational Exponents - 4:

Students are asked to rewrite expressions involving radicals and rational exponents in equivalent forms.

## Original Student Tutorials Mathematics - Grades 9-12

Solving Rational Equations: Cross Multiplying:

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Learn to rewrite products involving radicals and rational exponents using properties of exponents in this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Solving Rational Equations: Cross Multiplying:

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Type: Original Student Tutorial

Learn to rewrite products involving radicals and rational exponents using properties of exponents in this interactive tutorial.

Type: Original Student Tutorial

Checking a Calculation of a Decimal Exponent:

In this example, students use properties of rational exponents and other algebraic concepts to compare and verify the relative size of two real numbers that involve decimal exponents.

## Tutorial

Power of a Power Property:

This tutorial demonstrates how to use the power of a power property with both numerals and variables.

Type: Tutorial

## Video/Audio/Animations

Rational Exponents:

Exponents are not only integers and unit fractions. An exponent can be any rational number expressed as the quotient of two integers.

Type: Video/Audio/Animation

Radical expressions can often be simplified by moving factors which are perfect roots out from under the radical sign.

Type: Video/Audio/Animation

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Checking a Calculation of a Decimal Exponent:

In this example, students use properties of rational exponents and other algebraic concepts to compare and verify the relative size of two real numbers that involve decimal exponents.