Solving and Modeling Inequalities

In this lesson, students get to put together everything they've learned about inequalities.  They'll write, solve, and graph the solution sets in this lesson.

Students work independently on the Think About It problem.  The purpose of this problem is to have students access everything they know about inequality problems.  After 3 minutes of work time, I ask for a volunteer to share his/her work on the document camera.  As the student is sharing, I ask the rest of the class:

• Why is this an inequality problem?
• What does your classmate's variable stand for?
• Why did your classmate use an open circle on his/her graph?
• How can we check to see if your classmate's answer is right?

Because this lesson does not contain new material, I complete a few problems with students as Guided Practice before they move into partner and independent practice.  I want to be sure that students are comfortable with all of the steps.  Going through guided practice with the class allows me to identify which students might need extra support during work time.

For Problem 3 students need to determine which inequality symbol is needed for the solution set.  If students struggle with this problem type, I try a more scaffolded approach by having them start without a variable:

1. Write an addition equation, using 4 as an addend. (e.g., 4 + 3 = 7)
2. Replace 4 with a variable
3. Use the graph to determine the inequality symbol and change the equation to an inequality

This approach usually helps students to move ahead quickly.

I ask students work together on the Partner Practice problems.  As they work, I circulate around the classroom.  I am looking for:

• Are students correctly identifying the solution to the inequality?
• Are students explaining their work in complete sentences?
• Are students graphing the solution correctly, when needed?
• Are students checking their answers using substitution?

I am asking pairs:

• How did you determine the solution set to the inequality?
• How did you graph the inequality?
• Why did you use a closed/open circle?
• How did you check that your solution is correct?
• What was Marcus' mistake here (problem 1)?
• What steps did you take to create your own inequality?

Before students move to Independent Practice, we discuss Problem 6 as a class.  I want students to see that there are an infinite number of possible answers here.  I have one pair share the inequality that they wrote for the multiplication problem.  I then ask for another group to share their inequality (I identify the groups I am going to call on while I am circulating).  I ask the class which one is right.  Once we've determined that both are correct, I ask the class if any other group has a different inequality that works for the graph.

Students work on the Independent Practice problem set.  As they work, I circulate and look for and ask the same questions as I did during the partner practice.

After independent work time, the class comes back together.  I pull a popscicle stick to cold call a student to share his/her work to Problem #8.  The student displays his/her work on the document camera, and I ask the class for positive and constructive feedback about the work.

Students then work independently on the Exit Ticket to end class.