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Grade 11 - Claim 1 - Target H

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Mathematics

Target H

Understand solving equations as a process of reasoning and explain the reasoning

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

Algebra

Standards

REI-2
Major

Standards

  • REI-2

    Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Clarifications

Tasks for this target will require students to solve radical and rational equations in one variable. Tasks that ask students to critique or justify a particular solution method will contribute evidence to Claim 3....

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student solves radical and/or simple rational equations in one variable, including identifying the number and type of real solutions that might exist for the equation (e.g., one, two, infinite, or no...

  • 2

    The student evaluates proposed solutions to radical or simple rational equations, and recognizes where extraneous solution(s) might arise during the solving of the equation.

  • 3

    The student solves radical or rational equations in multiple variables.

  • 4

    The student identifies equivalent equations to an equation with rational or radical expressions.

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

  • Equation/Numeric
  • Matching Tables
  • Multiple Choice, single correct response

Allowable Stimulus Materials

simple radical and rational equations

Key/Construct Relevant Vocabulary

radical, rational, real, solution

Allowable Tools

None

Target-Specific Attributes

None

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

Items that assess A.REI.A and A.REI.A.1 will be measured in Claim 3.

Task Models

Task Model 1a

  • Item Types

    Equation/Numeric

  • Depth of Knowledge

    M-DOK1, M-DOK2

  • Standards

    REI-2

Target Evidence Statement

  • The student solves radical and/or simple rational equations in one variable, including identifying the number and type of real solutions that might exist for the equation (e.g., one, two, infinite, or no real).

  • Allowable Tools

    None

Task Description

Prompt Features: Enter the solution for a rational or radical equation. Stimulus Guidelines: The student is presented with an equation that contains a rational or radical expression. The equation must have at least one solution. Solutions must be...

Stimulus

The stem will present a rational equation in one variable with exactly one rational solution.

Example 1

Example Stem 1 (DOK 1): Enter the value of x that makes the equation true.

1x=5\frac{1}{x} = 5

Rubric: (1 point) The student enters the correct value of x (e.g., 15\frac{1}{5}).

Example 2

Example Stem 2 (DOK 2): Enter the value of t that makes the equation true.

1t–4=3t\frac{1}{t – 4} = \frac{3}{t}

Rubric: (1 point) The student enters the correct value of t (e.g., 6).