Graph related linear inequalities

Graph related linear inequalities

In this lesson, students will learn what linear (two-variable) inequalities are, how to pair them, how to graph the pairs using a computer, how to hand-sketch them, and how to locate a point in the solution space.

Objectives

  • Students will use technology tools to enhance mathematical learning.
  • Students will graph linear inequalities.
  • Students will hand-sketch the solution set of a system of linear inequalities.
  • Students will locate a point in the solution space.
  • Students will identify parallel, perpendicular and horizontal linear inequalities.

Learning Outcomes

  • Students formulate a hypothesis with dependent and independent variables about generational differences in attitude.
  • Students design, write, and administer a questionnaire that elicits responses to questions about generational differences.
  • Students analyze the survey results using Microsoft Office Excel.
  • Students present their findings to the class using Microsoft Office Excel or Microsoft Office PowerPoint.

Lesson procedure

Introduction

Find a partner.

Solving linear (two-variable) inequalities is an essential part of algebra. In this activity you will learn to pair linear inequalities, graph a pair of linear inequalities using the computer, hand-sketch the inequalities, and locate a point in the solution set.

Distribute the inequality cards that you cut out and scrambled to the class.

Each of you is holding a card with a related inequality on it. Read the inequality and the relationship (parallel or perpendicular) on the card you have been given. For example, y < 2x + 1, Perpendicular. Using the clue on the card, find your partner. Your partner will be the student who has the card with the related inequality. For example, the related inequality for

y < 2x + 1 Perpendicular

is

y > -.5 x +1 Perpendicular

The two students who have these two cards are partners.

Once you have found your partner, you will work with that person to graph both inequalities.

Teacher Tips

  • Starting line

    Ask the students to discuss what they have learned about linear equations. What do they know about the slopes of perpendicular lines? How about parallel lines?

  • Relationships matter

    A business is maximizing their profits when a product costs less than $2.50 USD to produce. Write an inequality that describes this relationship. What does the solution set tell you about the products they can produce?

Student activity

Follow the steps below to guide your students through this lesson plan.

Note teachers: Please download the student activity handouts located in the sidebar under Software and Materials Needed, for additional details about the main activities for this lesson plan.
 
  • Step 1: " Graph and sketch related inequalities"
  • Step 2: " Pair other inequalities" 
  • Step 3 " Graph all the pairs of related inequalities listed in Step 2"

Lesson extension activities

Ask more advanced students to design the survey form in Microsoft Office Excel. For help designing a form using a Microsoft Office Excel template, click the Microsoft Office button, select New, click Installed Templates, click More Categories, and then click Surveys.

Conclusion

  • Observe students as they complete each step of the activities.
  • Evaluate all graphs that students have created and their answers on Step 2 of the student handout.