MA.6.A.3.2Archived Standard

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Write, solve, and graph one- and two- step linear equations and inequalities.

Remarks

The context should include patterns, models and relationships. Students should explore how "greater than or equal to" and strictly "greater than" are similar and different.

A number line is a useful tool for modeling situations and inequalities such as "You have to be at least 40 inches tall to a ride roller coaster." and "x = 40".

 

Graphing on coordinate plane is still limited to the first quadrant, but they can explore negative and positive integers on number line.

 

Example: The height of a tree was 7 inches in the year 2000. Each year the same tree grew an additional 10 inches. Write an equation to show the height h of the tree in y years. Let y be the number of years after the year 2000. Graph the height of the tree for the first 20 years.
The most literal equation might be 7 + 10y = h.

General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 6
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 3 - Write, interpret, and use mathematical expressions and 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 , GR item(s)
    • Also assesses MA.6.A.3.4 Solve problems given a formula.
  • Clarification :
    Students will solve a one- or two-step linear equation, inequality (e.g. <, ≤ , >, or ≥), or formula.

    Students will translate a real-world situation to a mathematical equation or inequality

    Students will choose a representative graph for a given equation or inequality.
  • Content Limits :
    Items may include patterns, graphic models, situations, number lines, graphs, and relationships. 

    Items may include up to three variables, if the third variable is isolated on one side, as when using a formula (e.g., d rt). 

    Items may have up to two operations, with no more than three procedural steps needed to evaluate the equation, expression, and/or inequality. 

    Items involving the graphing of inequalities will be limited to one procedural step. 

    Graphs must be limited to the first quadrant. 

    In items involving inequalities, the inequality must include only one variable and may be on a number line. 

    Items that involve solving inequalities may only use positive coefficients.

  • Stimulus Attributes :
    Items should be set in a real-world or mathematical context.

    Formulas used in items need not be limited to those found on the reference sheet or to commonly used mathematical formulas.
Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question: Five students practiced the long jump for an upcoming track meet. Their coach plotted the shortest distance and the longest distance jumped during practice.
    Number Line

    Let d represent any distance jumped during practice. Based on the graph above, which inequality best describes the range of possible values of d?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question: Mr. Schmidt is purchasing film for his camera. With the roll of film that is in his camera now, he can take 18 pictures. Mr. Schmidt wants to purchase several rolls of film that can each produce up to 36 pictures. The equation below can be used to determine p, the total number of pictures Mr. Schmidt can take based on r, the number of rolls of film he purchases.

    p = 36r + 18

    If Mr. Schmidt purchases 3 rolls of film, what is the total number of pictures he can take?

  • Difficulty: N/A
  • Type: GR: Gridded-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.

Educational Software / Tool

Free Graph Paper:

A variety of graph paper types for printing, including Cartesian, polar, engineering, isometric, logarithmic, hexagonal, probability, and Smith chart.

Type: Educational Software / Tool

Tutorials

Solving Equations With the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.

Type: Tutorial

Solving Equations with One Variable :

This Khan Academy presentation models solving two-step equations with one variable.

Type: Tutorial

Simple Equations:

Introduction to solving one variable multiplication equations of the form px = q.

Type: Tutorial

Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation

Virtual Manipulative

Graphing Equations Using Intercepts:

This resource provides linear functions in standard form and asks the user to graph it using intercepts on an interactive graph below the problem. Immediate feedback is provided, and for incorrect responses, each step of the solution is thoroughly modeled.

Type: Virtual Manipulative

Student Resources

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

Tutorials

Solving Equations With the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.

Type: Tutorial

Solving Equations with One Variable :

This Khan Academy presentation models solving two-step equations with one variable.

Type: Tutorial

Simple Equations:

Introduction to solving one variable multiplication equations of the form px = q.

Type: Tutorial

Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation

Virtual Manipulative

Graphing Equations Using Intercepts:

This resource provides linear functions in standard form and asks the user to graph it using intercepts on an interactive graph below the problem. Immediate feedback is provided, and for incorrect responses, each step of the solution is thoroughly modeled.

Type: Virtual Manipulative

Parent Resources

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

Tutorials

Solving Equations With the Variable on Both Sides.:

This video models solving equations in one variable with variables on both sides of the equal sign.

Type: Tutorial

Simple Equations:

Introduction to solving one variable multiplication equations of the form px = q.

Type: Tutorial

Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation