MA.7.A.1.5Archived Standard

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Distinguish direct variation from other relationships, including inverse variation.

Remarks

Direct variation between y and x is when y/x=k where k is a constant, or equivalently y=kx. Indirect variation is when xy=k where k is a constant, or equivalently y=k/x.
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 7
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 1 - Develop an understanding of and apply proportionality, including similarity.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC item(s)
    • At Grade 7, this benchmark will be assessed using MC items.
  • Clarification :
    Students will identify a representation of a direct or inverse variation given in a graph, table of values, or real-world situation.

    Students will determine whether or not a situation, graph, or table of values represents a direct or inverse variation.

    Items will not require students to use formulas to solve problems. The intent of this benchmark is for students to distinguish between direct and inverse variations and determine how they differ.
  • Content Limits :
    Items may include graphs, using four quadrants, function tables, and situations.

    Representations (graphs, tables, situations) used in the item may be non-linear; however, items will not assess the vocabulary related to non-linear relationships (i.e., parabolas, quadratic).

    Graphs in items with real-world context are limited to the first quadrant only.

    Graphs in items with mathematical context may use all four quadrants.
  • Stimulus Attributes :
    Items should be set in a real-world or mathematical context.

    Graphics should be used in some of these items, as appropriate.
Sample Test Items (1)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Unit/Lesson Sequence

Direct and Inverse Variation:

"Lesson 1 of two lessons teaches students about direct variation by allowing them to explore a simulated oil spill using toilet paper tissues (to represent land) and drops of vegetable oil (to simulate a volume of oil). Lesson 2 teaches students about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers of different sizes as compared to the area of the containers' bases." from Insights into Algebra 1 - Annenberg Foundation.

Type: Unit/Lesson Sequence

Virtual Manipulative

Line of Best Fit:

This manipulative allows the user to enter multiple coordinates on a grid, estimate a line of best fit, and then determine the equation for a line of best fit.

Type: Virtual Manipulative

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Virtual Manipulative

Line of Best Fit:

This manipulative allows the user to enter multiple coordinates on a grid, estimate a line of best fit, and then determine the equation for a line of best fit.

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.