# MAFS.912.A-REI.4.12

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
General Information
Subject Area: Mathematics
Domain-Subdomain: Algebra: Reasoning with Equations & Inequalities
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Represent and solve equations and inequalities graphically. (Algebra 1 - Major Cluster) (Algebra 2 - 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 of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications
Assessed with:

MAFS.912.A-CED.1.2

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

A system of inequalities is shown.

A. Use the Add Arrow tool to graph the boundary lines of the system.

B. Drag a star to each region that is in the solution set of the system.

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

## Related Courses

This benchmark is part of these courses.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200370: Algebra 1-A (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912070: Access Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022 (current), 2022 and beyond)
7912080: Access Algebra 1A (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022 (current), 2022 and beyond)
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200375: Algebra 1-A for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912100: Fundamental Algebraic Skills (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))
1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.A-REI.4.AP.12a: Graph a linear inequality in two variables using at least two coordinate pairs that are solutions.
MAFS.912.A-REI.4.AP.12b: Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality.
MAFS.912.A-REI.4.In.12a: Graph a linear inequality in two variables using at least two coordinate pairs that are solutions.
MAFS.912.A-REI.4.In.12b: Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality.

## Related Resources

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

## Assessments

Sample 4 - High School Algebra 1 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 1 - High School Algebra 1 State Interim Assessment:

This is the State Interim Assessment for high school.

Type: Assessment

## Educational Game

Solving Inequalities: Inequalities and Graphs of Inequalities:

In this challenge game, you will be solving inequalities and working with graphs of inequalities. Use the "Teach Me" button to review content before the challenge. During the challenge you get one free solve and two hints! After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck!

Type: Educational Game

## 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

## Formative Assessments

Graph a System of Inequalities:

Students are asked to graph a system of two linear inequalities.

Type: Formative Assessment

Which Graph?:

Students are asked to select the correct graph of the solution region of a given system of two linear inequalities.

Type: Formative Assessment

Linear Inequalities in the Half-Plane:

Students are asked to graph all solutions for a non-strict <= or >= linear inequality in the coordinate plane.

Type: Formative Assessment

Graphing Linear Inequalities:

Students are asked to graph a strict < or > linear inequality in the coordinate plane.

Type: Formative Assessment

## Lesson Plans

This lesson allows students to graph systems of inequalities with two variables and view three types of solutions.

Type: Lesson Plan

Solving Systems of Inequalities:

This lesson aligns to the Mathematics Formative Assessment System (MFAS) Task Graph a System of Inequalities (). In this lesson, students with similar instructional needs are grouped according to MFAS rubric levels: Getting Started, Moving Forward, Almost There, and Got It. Students in each group complete an exercise designed to move them toward a better understanding of solutions of systems of inequalities and their graphs.

Type: Lesson Plan

Defining Regions Using Inequalities:

This lesson unit is intended to help you assess how well students are able to use linear inequalities to create a set of solutions. In particular, the lesson will help you identify and assist students who have difficulties in: representing a constraint by shading the correct side of the inequality line and understanding how combining inequalities affects a solution space.

Type: Lesson Plan

## Original Student Tutorial

Graphing Linear Inequalities:

Learn to graph linear inequalities in two variables to display their solutions as you complete this interactive tutorial.

Type: Original Student Tutorial

Solution Sets:

The typical system of equations or inequalities problem gives the system and asks for the graph of the solution. This task turns the problem around. It gives a solution set and asks for the system that corresponds to it. The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations. Students have to focus on what the graph is showing. When you are describing a region, why does the inequality have to go one way or another? When you pick a point that clearly lies in a region, what has to be true about its coordinates so that it satisfies the associated system of inequalities?

This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.

## Tutorial

Graph the solution to a system of inequalities.:

This video will demonstrate how to graph the solution to a system of inequalities.

Type: Tutorial

## Unit/Lesson Sequence

Sample Algebra 1 Curriculum Plan Using CMAP:

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

### Using this CMAP

To view an introduction on the CMAP tool, please .

To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.

To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app.

To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.

All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx

Type: Unit/Lesson Sequence

## MFAS Formative Assessments

Graph a System of Inequalities:

Students are asked to graph a system of two linear inequalities.

Graphing Linear Inequalities:

Students are asked to graph a strict < or > linear inequality in the coordinate plane.

Linear Inequalities in the Half-Plane:

Students are asked to graph all solutions for a non-strict <= or >= linear inequality in the coordinate plane.

Which Graph?:

Students are asked to select the correct graph of the solution region of a given system of two linear inequalities.

## Original Student Tutorials Mathematics - Grades 9-12

Graphing Linear Inequalities:

Learn to graph linear inequalities in two variables to display their solutions as you complete this interactive tutorial.

## Student Resources

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

## Original Student Tutorial

Graphing Linear Inequalities:

Learn to graph linear inequalities in two variables to display their solutions as you complete this interactive tutorial.

Type: Original Student Tutorial

## Educational Game

Solving Inequalities: Inequalities and Graphs of Inequalities:

In this challenge game, you will be solving inequalities and working with graphs of inequalities. Use the "Teach Me" button to review content before the challenge. During the challenge you get one free solve and two hints! After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck!

Type: Educational Game

Solution Sets:

The typical system of equations or inequalities problem gives the system and asks for the graph of the solution. This task turns the problem around. It gives a solution set and asks for the system that corresponds to it. The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations. Students have to focus on what the graph is showing. When you are describing a region, why does the inequality have to go one way or another? When you pick a point that clearly lies in a region, what has to be true about its coordinates so that it satisfies the associated system of inequalities?

This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.

## Tutorial

Graph the solution to a system of inequalities.:

This video will demonstrate how to graph the solution to a system of inequalities.

Type: Tutorial

## Parent Resources

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