Recognize and represent proportional relationships between quantities.
  1. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
  2. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  3. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
  4. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Subject Area: Mathematics
Grade: 7
Domain-Subdomain: Ratios & Proportional Relationships
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes


Examples of Opportunities for In-Depth Focus

Students in grade 7 grow in their ability to recognize, represent, and analyze proportional relationships in various ways, including by using tables, graphs, and equations.


  • Item Type(s): This benchmark may be assessed using: MC , MS , ETC , OR , EE , GRID item(s)

  • Assessment Limits :
    Ratios should be expressed as fractions, with “:” or with words. Units may be the same or different across the two quantities.
  • Calculator :


  • Context :



  • Test Item #: Sample Item 2
  • Question: Kara is mixing paint. Each batch has twice as much blue paint as yellow paint.

    Plot points to represent the amount of blue and yellow paint used in three different-sized batches.


  • Difficulty: N/A
  • Type: GRID: Graphic Response Item Display

  • Test Item #: Sample Item 3
  • Question: The points on the coordinate plane show the amount of red and yellow paint in each batch.


    Write an equation to represent the relationship between red paint, r, and yellow paint, y, in each batch.

  • Difficulty: N/A
  • Type: EE: Equation Editor

  • Test Item #: Sample Item 4
  • Question:

    The graph below represents the rate for the cost of b books.


    Write an equation to represent the cost, c.

  • Difficulty: N/A
  • Type: EE: Equation Editor

  • Test Item #: Sample Item 5
  • Question: The ordered pair (1, 5) indicates the unit rate of books to cost on the graph shown.


    What does the point on the graph represent?

  • Difficulty: N/A
  • Type: OR: Open Response