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Grade 11 - Claim 1 - Target G

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Mathematics

Target G

Create equations that describe numbers or relationships

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

CED-1CED-2
Supporting

Standards

  • CED-1

    Create equations and inequalities in one variable and use them to solve problems. Include equations arising from...

  • CED-2

    Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate...

Clarifications

Tasks for this target will require students to create equations and inequalities in one variable to solve problems. Other tasks will require students to create and graph equations in two variables to represent relationships...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student creates one variable equations arising from linear, quadratic, simple rational, and exponential functions in one variable.

  • 2

    The student creates one variable inequalities arising from linear, quadratic, simple rational, and exponential functions in one variable.

  • 3

    The student graphs equations on the coordinate axes with labels and scales to represent the solution to a contextual problem.

  • 4

    The student creates equations in two or more variables to represent relationships between quantities.

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
  • Graphing

Allowable Stimulus Materials

two-way table of values, graphs of linear equations or inequalities, graphs of quadratic equations or inequalities graphs of exponential equations or inequalities

Key/Construct Relevant Vocabulary

Inequality, exponential, quadratic, linear, equation

Allowable Tools

Calculator

Target-Specific Attributes

Equations can be linear, quadratic, simple rational, or exponential.

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

Equations are higher priority content than inequalities within this target, so item development plans should include more development for task models focused on equations.

Task Models

Task Model 1

  • Item Types

    Equation/Numeric

  • Depth of Knowledge

    M-DOK2

  • Standards

    CED-1

Target Evidence Statement

  • The student creates one variable equations arising from linear, quadratic, simple rational, and exponential functions in one variable.

  • Allowable Tools

    Calculator

Task Description

Prompt Features: The student is prompted to create an equation in one variable that can be used to solve a given problem. Stimulus Guidelines: The student is presented with a contextual situation familiar to 16- to...

Stimulus

The student is presented with a contextual problem.

Example 1

Example Stem 1: Consider the given equation that models a train’s distance from its departing station, where:

  • y represents the distance in miles,
  • x represents the speed of the train in miles per hour, and
  • t represents the time traveled from the departing station in hours.

y=xty = xt

Enter an equation for which the solution is the speed of the train, in miles per hour, where the train’s distance from the departing station is 162 miles and it has traveled for 3 hours.

Rubric: (1 point) The student correctly enters an equation (e.g., 162=3x or any equation equivalent to x=54x = 54).

Example 2

Example Stem 2: Consider the equation that gives the minimum stopping distance, d, in feet, for an automobile, where:

  • v represents the automobile speed, in feet per second,
  • s represents the driver’s response time, in seconds, to apply the brakes,
    and
  • m represents the coefficient of friction between the tires and the road.

d=vs+v264md = vs + \frac{v^{2}}{64m}

Enter an equation for which the solution is the speed, in feet per second, of an automobile with a stopping distance of 200 feet, a driver’s response time of 0.5 second, and a coefficient of friction equal to 0.8.

Rubric: (1 point) The student correctly enters an equation (e.g., equation equivalent to 200=0.5v+v251.2200 = 0.5v + \frac{v^{2}}{51.2}).

Example 3

Example Stem 3: A sales clerk’s daily earnings include $125 per day plus commission equal to xx percent of his daily sales.

Enter an equation that can be used to find the commission percentage (xx), if the clerk’s daily sales are $1375 and his total earnings for that day are $180.

Rubric: (1 point) The student correctly enters an equation [e.g., $125+x100⋅$1375=$180 \$125 + \frac{x}{100} \cdot \$1375 = \$180 or equivalent].

Example 4

Example Stem 4: Jim can paint a house in 12 hours. Alex can paint the same house in 8 hours.

Enter an equation that can be used to find the time in hours, tt, it would take Alex and Jim to paint the house together assuming they both work at the rates they work when working alone.

Rubric: (1 point) The student correctly enters an equation (e.g., 112+18=1t\frac{1}{12} + \frac{1}{8} = \frac{1}{t} or equivalent).