MA.8.A.1.6Archived Standard

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Compare the graphs of linear and non-linear functions for real-world situations.

Remarks

Students should understand that some situations can be modeled by a linear function and others cannot.

 

Example: Mark had $100 and added $10 to it each year. Mandy put $100 in the bank, earned 10% interest each year on her total amount of money in the bank, and left the interest in the bank account. Make a table of their money for 5 years. Graph the values. Explain why one function is linear and the other one is not.

General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 8
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 1 - Analyze and represent linear functions, and solve linear equations and systems of linear equations.
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)

  • Clarification :
    Students will compare and translate between linear or nonlinear functions in real-world scenarios or graphical representations.
  • Content Limits :
    Items may include stimuli of a scenario with four different graphs for options or a graph with four different scenarios.

    Items will ask students to interpret graphical representations but not to solve them.
  • Stimulus Attributes :
    Items should be set in a real-world context.

    Graphics should be used in all of these items.

    Items may present a linear or non-linear graph and ask the student to identify the representative real-world scenario.
Sample Test Items (1)
  • Test Item #: Sample Item 1
  • Question: In a certain city, the number of new houses built each month during the first half of the year decreased at a constant rate. During the second half of the year, the number of new houses built each month remained the same. Which graph best illustrates the number of houses built each month in this city?
  • Difficulty: N/A
  • Type: MC: Multiple Choice

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.

Lesson Plans

Interpreting Distance-Time Graphs:

This lesson takes a formative assessment approach to assessing whether students can interpret distance-time graphs. Whole-class discussion, group work, and individual activities help students interpret distance-time graphs related to real-world scenarios.

Type: Lesson Plan

Discovering Kepler's Law for the Periods of Planets:

Students listen to a video that describes Kepler's determination that planetary orbits are elliptical and then will use data for the solar distance and periods of several of the planets in the solar system, then investigate several hypotheses to determine which is supported by the data.

Type: Lesson Plan

Asteroids:

In this lesson, students show and discuss that the planets' orbits follows a pattern, compare sizes of asteroids relative to the size of Earth and Earth's moon, make asteroid models, research impact craters, and discuss the likelihood and effects of an asteroid impact on Earth.

Type: Lesson Plan

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

Student Resources

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Parent Resources

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