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Grade 8 - Claim 1 - Target C

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Mathematics

Target C

Understand the connections between proportional relationships, lines, and 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-5EE-6
Major

Standards

  • EE-5

    Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different...

  • EE-6

    Use similar triangles to explain why the slope m is the same between any two distinct...

Clarifications

Tasks for this target will ask students to graph one or more proportional relationships and connect the unit rate(s) to the context of the problem. Other tasks will ask students to apply understanding of the...

Range Achievement Level Descriptors

Evidence Required

  • 1

    The student graphs proportional relationships.

  • 2

    The student interprets the unit rate as the slope of the graph of a proportional relationship.

  • 3

    The student will compare two different proportional relationships presented in different formats.

  • 4

    [Retired this Evidence Required statement]

  • 5

    The student finds the equation Y = mx or y = mx + b for a line.

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

  • Graphing
  • Multiple Choice, single correct response
  • Equation/Numeric

Allowable Stimulus Materials

graphs, tables, equations, verbal descriptions

Key/Construct Relevant Vocabulary

proportional relationship, unit rate, slope, y-intercept, similar triangles, origin, coordinate plane, ordered pairs

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

Tasks for this target will ask students to compare two different proportional relationships presented in different formats. Many of these tasks will contribute evidence to Claims 2 and 4.

Task Models

Task Model 1

  • Item Types

    Graphing

  • Depth of Knowledge

    M-DOK1

  • Standards

    EE-5

Target Evidence Statement

  • The student graphs proportional relationships.

  • The student interprets the unit rate as the slope of the graph of a proportional relationship.

  • Allowable Tools

    None

  • Accessibility Note

    Graphing items are not currently able to be Brailled. Minimize the number of items developed to...

Task Description

Prompt Features: The student is prompted to create a graph of a proportional relationship. Stimulus Guidelines: Unit rates can be positive rational numbers in whole numbers, fraction, or decimal form. Tables should have four to six rows...

Stimulus

The student is presented with a proportional relationship that may be represented as a verbal statement, table, or equation.

Example 1

Example Stem 1: The cost c, in dollars, for p pounds of meat is shown in the table.

p c
3 15
5 25
7 35
9 45
10 50

Use the Add Arrow tool to graph the proportional relationship between the number of pounds of meat and the total cost.

Interaction: Student is given a coordinate plane with axes labeled. The Add Point, Add Arrow, and Delete tools are provided.

Rubric: (1 point) Student creates a line with the correct slope passing through the origin.

Example 2

Example Stem 2: Meat costs $5.00 per pound at a store.

Use the Add Arrow tool to graph the proportional relationship between the number of pounds of meat and the total cost.

Interaction: Student is given a coordinate plane with axes labeled. The Add Point, Add Arrow, and Delete tools are provided.

Rubric: (1 point) Student creates a line with the correct slope passing through the origin.

Example 3

Example Stem 3: The cost c, in dollars, for p pounds of meat can be represented by the equation c = 5p.

Use the Add Arrow tool to graph the proportional relationship between the number of pounds of meat and the total cost.

Interaction: Student is given a coordinate plane with axes labeled. The Add Point, Add Arrow, and Delete tools are provided.

Rubric: (1 point) Student creates a line with the correct slope passing through the origin.