### General Information

**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Number & Quantity: The Real Number System

**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 Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

### Test Item Specifications

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

to radical expressions.

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 # |
Question |
Difficulty |
Type |

Sample Item 1 | 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? |
N/A | MC: Multiple Choice |