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Grade 8 - Claim 1 - Target B

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Mathematics

Target B

Work with radicals and integer exponents

Sample Item

Grade 8

Test

Claim 1

Concepts and Procedures

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

Grade

Grade 8

Content Domain

Expressions & Equations

Standards

EE-1EE-2EE-3EE-4
Major

Standards

  • EE-1

    Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32{3}^{2} × 3−53^{-5} = 3−33^{-3} = frac133frac{1}{3^{3}} = frac127frac{1}{27}.

  • EE-2

    Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of...

  • EE-3

    Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much...

  • EE-4

    Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large...

Clarifications

Tasks for this target will require students to select or produce equivalent numerical expressions based on properties of integer exponents. Other tasks will ask students to solve simple equations whose solutions can be expressed as...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student generates equivalent numerical expressions by applying the properties of integer exponents.

  • 2

    The student generates solutions to equations of the form x² = p using square root symbols.

  • 3

    The student generates solutions to equations of the form x³ = p using cube root symbols.

  • 4

    The student states how many times as large or as small one number, written as a single digit times a power of 10, is than another, to estimate very large or very...

  • 5

    The student performs operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

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...

Allowable Item Types

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

Allowable Stimulus Materials

numbers written as a single digit multiplied by an integer power of 10, numbers in scientific notation

Key/Construct Relevant Vocabulary

rational number, irrational number, scientific notation, decimal notation, exponent, power, base, radical, square root, cube root, perfect square, perfect cube, exponent

Allowable Tools

None

Target-Specific Attributes

Exponents should be integers. Roots should be square roots or cube roots of positive rational numbers. Perfect squares should be positive rational numbers that are less than or equal to 400. Perfect cubes should be positive rational...

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

    Multi-Select, multiple correct response

  • Depth of Knowledge

    M-DOK1

  • Standards

    EE-1

Target Evidence Statement

  • The student generates equivalent numerical expressions by applying the properties of integer exponents.

  • Allowable Tools

    None

Task Description

Prompt Features: The student determines equivalent numerical expressions by applying the properties of integer exponents. Stimulus Guidelines: The bases are integers between –5 and 5. Item difficulty can be adjusted via these example methods: One-step multiplication or division...

Stimulus

The student is presented with a numerical expression involving integer exponents.

Example 1

Example Stem: Select all expressions equivalent to (45•4−3)−2(4^{5} • 4^{- 3})^{- 2}.

A. 1256\frac{1}{256}

B. 256256

C. 4−104^{- 10} • 464^{6}

D. 434^{3} • 4−54^{- 5}

Answer Choices: There should be four answer choices with at least two correct choices that will be expressions or numbers. Incorrect answer choices will reflect errors in understanding negative exponents or error applying exponent rules.

Rubric: (1 point) Student selects all equivalent expressions (e.g., A and C)