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Grade 11 - Claim 1 - Target A

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Mathematics

Target A

Extend the properties of exponents to rational exponents; Use properties of rational and irrational numbers; Reason quantitatively and use units to solve problems

Sample Item

Grade 11

Test

Claim 1

Concepts and Procedures

Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.

Grade

Grade 11

Content Domain

Number and Quantity

Standards

RN-1RN-2
Supporting

Standards

  • RN-1

    Explain how the definition of the meaning of rational exponents follows from extending the properties of...

  • RN-2

    Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Clarifications

Tasks for this target will require students to use the definition of radicals and rational exponents and identify equivalent numeric and algebraic expressions involving rational exponents and radicals. Tasks for this target will...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student rewrites expressions in radical form into an equivalent expression with rational exponents.

  • 2

    The student rewrites expressions with rational exponents into an equivalent expression in radical form.

  • 3

    The student uses the properties of exponents to write equivalent expressions involving radicals and rational exponents.

  • 4

    The student solves equations that require an understanding of the definitions of radicals and rational exponents.

  • 5

    The student finds exact or approximate values of numeric expressions involving rational exponents or radicals.

  • 6

    The student compares expressions involving rational exponents or radicals with other numbers.

Item Guidelines

Depth of Knowledge

  • M-DOK1

    Recall includes the recall of information such as fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one-step, well-defined, and straight algorithmic procedure should be...

  • M-DOK2

    Skill/Concept includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a...

Allowable Item Types

  • Multiple Choice, single correct response
  • Matching Tables
  • Equation/Numeric
  • Multi-Select, multiple correct response

Allowable Stimulus Materials

numerical expressions involving radicals, numerical expressions involving rational exponents, algebraic expressions involving radicals, algebraic expressions involving rational exponents

Key/Construct Relevant Vocabulary

exponent, radical, rational exponent

Allowable Tools

None

Target-Specific Attributes

properties of integer exponents, properties of rational exponents

Accessibility

Item writers should consider the following Language and Visual Element/Design guidelines [1] when developing items. Language Key Considerations: Use simple, clear, and easy-to-understand language needed to assess the construct or aid in the understanding of the...

Development Notes

None

Task Models

Task Model 1a

  • Item Types

    Multiple Choice, single correct response

  • Depth of Knowledge

    M-DOK1

  • Standards

    RN-2

Target Evidence Statement

  • The student rewrites expressions in radical form into an equivalent expression with rational exponents.

  • Allowable Tools

    None

Task Description

Prompt Features: Given an expression that includes radicals, identify an equivalent expression that includes rational exponents. Stimulus Guidelines: For radicals (e.g., $\sqrt[q]{p^{r}}$) p may be either a number (except 0 or 1), or a variable. Item difficulty...

Stimulus

The student will be presented with an expression of the form prq \sqrt[q]{p^{r}}.

Example 1

Example Stem: Select an expression that is equivalent to 369\sqrt[{9}]{3^{6}}.

A. 323 3^{\frac{2}{3}}

B. 3323^{\frac{3}{2}}

C. 333^{3}

D. 3153^{15}

Rubric: (1 point) The student correctly selects the equivalent rational form (e.g., A).