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Grade 8 - Claim 1 - Target D

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Mathematics

Target D

Analyze and solve linear equations and pairs of simultaneous linear equations

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-7EE-7aEE-7bEE-8EE-8aEE-8bEE-8c
Major

Standards

  • EE-7

    Solve linear equations in one variable.

  • EE-7a

    Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into...

  • EE-7b

    Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

  • EE-8

    Analyze and solve pairs of simultaneous linear equations.

  • EE-8a

    Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

  • EE-8b

    Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y...

  • EE-8c

    Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects...

Clarifications

Tasks for this target will ask students to solve linear equations in one variable and recognize when one, infinite, or no solutions exist. Some problems will require students to apply the distributive property...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student identifies and writes examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

  • 2

    The student solves linear equations in one variable with rational coefficients, including equations with solutions that require expanding expressions using the distributive property and collecting like terms.

  • 3

    The student estimates solutions by graphing systems of two linear equations in two variables.

  • 4

    The student recognizes when a system of two linear equations in two variables has one solution, no solution, or infinitely many solutions.

  • 5

    The student solves a system of two linear equations in two variables algebraically, or solves real-world and mathematical problems leading to two linear equations in two variables.

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

  • Drag and Drop
  • Multi-Select, multiple correct response
  • Multiple Choice, single correct response
  • Equation/Numeric
  • Graphing

Allowable Stimulus Materials

Linear equations, solutions of linear equations, systems of linear equations (a single brace may be used to indicate a system), solutions of systems of linear equations, graphs of systems of linear equations, real-world scenarios...

Key/Construct Relevant Vocabulary

Linear equation, y–intercept, slope, standard form, intersection, system, solution, coefficient, constant, ordered pair, x-coordinate, y–coordinate

Allowable Tools

Calculator

Target-Specific Attributes

Equations must be linear with rational coefficients.

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

8.EE.C.8a will be assessed in connection with targets from Claims 2 and 3.

Task Models

Task Model 1a

  • Item Types

    Drag and Drop

  • Depth of Knowledge

    M-DOK2

  • Standards

    EE-7a

Target Evidence Statement

  • The student identifies and writes examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

  • Allowable Tools

    Calculator

  • Accessibility Note

    Drag and Drop items are not currently able to be Brailled. Minimize the number of items...

Task Description

Prompt Features: The student is prompted to create a linear equation in one variable that has exactly one solution, infinitely many solutions, or no solutions. Stimulus Guidelines: Item difficulty can be adjusted via these example...

Stimulus

The student is presented with a linear equation in one variable with missing numbers.

Example 1

Example Stem 1: Drag a number into each box to create an equation that has exactly one real solution.

3(2x+5)–x=□x+□3(2x + 5) – x=\square x + \square

Rubric: (1 point) Correct answer is any number other than 5 for the coefficient of x and any number as the constant.

Example 2

Example Stem 2: Drag a number into each box to create an equation that has no real solution.

3(2x+5)–x=□x+□3(2x + 5) – x=\square x + \square

Rubric: (1 point) Correct answer is 5 for the coefficient of x and any number other than 15 for the constant.

Example 3

Example Stem 3: Drag a number into each box to create an equation that has an infinite number of solutions.

3(2x+5)–x=□x+□3(2x + 5) – x=\square x + \square

Rubric: (1 point) Correct answer has 5 for the coefficient of x and 15 for the constant.