Illustrative Math Alignment: Grade 7 Unit 7

Understanding linear inequalities is essential for mastering SAT Math, especially within the Heart of Algebra domain, which makes up approximately 35% of the SAT Math section. This 45-minute lesson focuses on solving and graphing linear inequalities in one and two variables. Students will learn how to manipulate inequalities algebraically, including what happens when multiplying or dividing by negative numbers, and how to graph solution sets on the number line and coordinate plane.

This 45-minute lesson is part of Media4Math’s 35-lesson SAT Math prep series. It focuses on solving and graphing systems of linear inequalities—a topic within the Heart of Algebra domain, which makes up about 33% of the SAT Math section. Students will learn how to graph inequalities on the coordinate plane, determine boundary line types, apply test points, and find the region where multiple inequalities intersect.

This 45-minute lesson is part of Media4Math’s 35-lesson SAT Math prep series. It focuses on absolute value equations and inequalities, which are occasionally featured on the SAT Math section—typically one question or fewer per test. Mastery of this topic reinforces algebraic reasoning and function analysis, which are critical for overall SAT success.

This is the transcript for the video of same title. Video contents: In this episode of Algebra Applications, two real-world explorations of inequalities are developed: Hybrid Cars. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. Floods in Venice. Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril. Through a series of inequalities, students analyze the impact of flooding.

This is the transcript for the video of same title. Video contents: With the increasing demand worldwide for cars, the cost of gasoline continues to rise. The need for fuel-efficient cars makes hybrids a current favorite. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. Students use the Graphs and Geometry features of the TI-Nspire.

This is the transcript for the video of same title. Video contents: The city of Venice is slowly sinking into the Adriatic Sea. So what does a city whose streets are full of water do about flooding? Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril. Through a series of inequalities, students analyze the impact of flooding, rising sea levels, and sinking have on this grand, ancient city. Students use the Lists and Spreadsheets and the Program Editor features of the TI-Nspire.

This is the transcript for the video of same title. Video contents: Used in just about any industry, inequalities, like equations, are fundamental building blocks of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video explores inequalities -- concepts, properties, solutions, and notations -- connects them to real-world contexts, and uses the TI-Nspire to make the algebra meaningful. The focus of this program is on linear inequalities in one and two variables. Concepts explored: Equations, inequalities

This is the transcript for the video of same title. Video contents: In this Investigation we explore linear inequalities in one variable.

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This is the transcript for the video of same title. Video contents: In this Investigation we look at linear inequalities in two variables.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Graphing a Linear Inequality.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Graphing a Linear Inequality Using Sliders.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Graphing a Quadratic Inequality.

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Topic

Topic: Inequalities

Topic

Topic: Inequalities

Description

This video models an inequality to explain how floodgates in Venice prevent flooding during storms. The key concept is the activation threshold, where the water level exceeds a critical value. Vocabulary includes inequality, threshold, variable, and model. Using a TI-Nspire, the video demonstrates creating a random variable for water levels and a function to evaluate if floodgates should activate. It illustrates real-world applications in engineering and environmental management.

Topic

Inequalities

Description

This video introduces inequalities, contrasting them with equations, and discusses their properties and solution methods. Key concepts include graphing solutions, interval notation, and inequality symbols. Applications are contextualized through scenarios like semester grades and fitness ranges. Key terms include inequality, interval notation, and solution set.

Topic

Inequalities

Description

In this Math Lab explore compound inequalities on a number line.

This video highlights key concepts in inequalities, offering practical examples that make abstract math principles more accessible. Through a comprehensive approach, students can connect theoretical knowledge to real-world applications.

Relevance: This video directly supports the topic by illustrating inequalities in a clear and engaging way, making it easier for students to understand complex ideas.

Topic

Inequalities

Description

Building on Part 1, this video explores systems of inequalities and their geometric representations. Applications include business profit modeling using linear inequalities. Key vocabulary includes half-planes, slope-intercept form, and solution regions. Real-world examples, like yoga studio budgeting, highlight practical uses of inequalities.

Topic

Inequalities

Description

In this Math Lab explore graphical solutions to linear inequalities.

This video highlights key concepts in inequalities, offering practical examples that make abstract math principles more accessible. Through a comprehensive approach, students can connect theoretical knowledge to real-world applications.

Relevance: This video directly supports the topic by illustrating inequalities in a clear and engaging way, making it easier for students to understand complex ideas.

In this TI-Nspire CX tutorial, the Graph Window is used to graph inequalities.

In this TI-Nspire CX tutorial, the Graph Window is used to graph inequalities using sliders.

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library