MA.912.A.3.5Archived Standard

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Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.

Remarks

Example 1: You are selling tickets for a play that cost $3 each. You want to sell at least $50 worth. Write and solve an inequality for the minimum number of tickets you must sell.

Example 2: An alloy is a metal that contains combinations of different types of metal. A manufacturing company needs to make an alloy that has nickel content between 43% and 47% (based on mass). The company already has an alloy with 50% nickel and another alloy with 40% nickel. They plan to mix them to make the alloy they need. Find the least and greatest mass (in kg) of a 50% nickel alloy that should be mixed with a 40% nickel alloy to end up with 100 kilograms of an alloy containing the required percentage of nickel.

General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Standard: Linear Equations and Inequalities - Solve linear equations and inequalities.
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 , FR item(s)

  • Clarification :
    Students will interpret and/or solve real-world problems involving linear equations or linear inequalities.
  • Content Limits :

    Items may require students to express inequalities on a number line, or to use an inequality for a response.

    Items may include compound inequalities presented in written format, graphically, and/or algebraically.

    Items will not include the use of interval notation, e.g. (3,∞), or set notation, e.g. { x I x > 3}.

  • Stimulus Attributes :

    Items must be set in real-world contexts.

    Items should use methods that are graphical and/or algebraic.

    Graphics should be used in some of these items, as appropriate.

Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question:

    The out-of-pocket costs to an employee for health insurance and medical expenses for one year are shown in the table below. 

     

    According to the plan outlined in the table, total annual health care costs, C, depend on the employee’s medical expenses for that year. If x represents the total medical expenses of an employee on this plan and x 500, which of the following equations can be used to determine this employee’s total health care costs for that year?

  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question:

    Karen works as a salesperson for a local marketing company. Using the equations shown below, the company calculates her monthly earnings based upon her total sales for the month.

     

    Karen’s total sales were greater than $5,000 in October. If her total monthly earnings for October were $3,000, what was the value of her total monthly sales, s ?

  • Difficulty: N/A
  • Type: FR: Fill-in Response

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 Plan

Math in Mishaps:

Students will explore how percentages, proportions, and solving for unknowns are used in important jobs. This interactive activity will open their minds and address the question, "When is this ever used in real life?"

Type: Lesson Plan

Problem-Solving Task

MIT BLOSSOMS - The Broken Stick Experiment: Triangles, Random Numbers and Probability:

This learning video is designed to develop critical thinking in students by encouraging them to work from basic principals to solve a puzzling mathematics problem that contains uncertainty. One class session of approximately 55 minutes is necessary for lesson completion. First-year simple algebra is all that is required for the lesson, and any high school student in a college-preparatory math class should be able to participate in this exercise. Materials for in-class activities include: a yard stick, a meter stick or a straight branch of a tree; a saw or equivalent to cut the stick; and a blackboard or equivalent. In this video lesson, during in-class sessions between video segments, students will learn among other things: 1) how to generate random numbers; 2) how to deal with probability; and 3) how to construct and draw portions of the X-Y plane that satisfy linear inequalities.

Type: Problem-Solving Task

Professional Development

Mathematical Modeling: Insights into Algebra, Teaching for Learning:

This professional development resource provides a rich collection of information to help teachers engage students more effectively in mathematical modeling. It features videos of two complete lessons with commentary, background information on effective teaching, modeling, and lesson study, full lesson plans to teach both example lessons, examples of student work from the lessons, tips for effective teaching strategies, and list of helpful resources.

  • In Lesson 1 students use mathematical models (tables and equations) to represent the relationship between the number of revolutions made by a "driver" and a "follower" (two connected gears in a system), and they will explain the significance of the radii of the gears in regard to this relationship.
  • In Lesson 2 students mathematically model the growth of populations and use exponential functions to represent that growth.

Type: Professional Development

Video/Audio/Animation

Basic Linear Function:

This video demonstrates writing a function that represents a real-life scenario.

Type: Video/Audio/Animation

Student Resources

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

Video/Audio/Animation

Basic Linear Function:

This video demonstrates writing a function that represents a real-life scenario.

Type: Video/Audio/Animation

Parent Resources

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