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Grade 11 - Claim 1 - Target C

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Mathematics

Target C

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

Q-1
Supporting

Standards

  • Q-1

    Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in...

Clarifications

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student chooses units consistently in formulas.

  • 2

    The student chooses the scales for graphs and data displays.

  • 3

    The student chooses appropriate quantities for answering a question in a real-world context.

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
  • Drag and Drop
  • Matching Tables
  • Multi-Select, multiple correct response

Allowable Stimulus Materials

unit conversions, blank coordinate planes, graphs in the coordinate plane, bar graphs, histograms, table of values

Key/Construct Relevant Vocabulary

square units, cubic units, unit conversion, axis scale

Allowable Tools

Calculator

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

Tasks for this target will require students to choose and interpret units in formulas and the scale in a graph. In Claims 2-4, this reasoning will be extended to include defining appropriate quantities when modeling...

Task Models

Task Model 1a

  • Item Types

    Multiple Choice, single correct response

  • Depth of Knowledge

    M-DOK1

  • Standards

    Q-1

Target Evidence Statement

  • The student chooses units consistently in formulas.

  • Allowable Tools

    Calculator

Task Description

Prompt Features: The student is prompted to choose the units of measurement that are appropriate for quantities represented in formulas. Stimulus Guidelines: Item difficulty can be adjusted via these example methods, but is not limited...

Stimulus

The student is presented with a formula that uses measurements given in different units.

Example 1

Example Stem: Given the formula, K=12mv2K = \frac{1}{2}mv^{2} where

  • K represents kinetic energy,
  • m represents mass and has units of kilograms (kg), and
  • v represents velocity and has units of meters per second (m/s).

Select an appropriate measurement unit for kinetic energy.

A. kg m2s\frac{\text{kg }m^{2}}{s}

B. kg2m2s2\frac{\text{kg}^{2} m^{2}}{s^{2}}

C. kg m s2\frac{\text{kg m }}{s^{2}}

D. kg m2s2\frac{\text{kg }m^{2} }{s^{2}}

Rubric: (1 point) Student selects the correct response (e.g., D).