One-Step Inequalities and the Real World

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SWBAT write a one-step inequality to model a real-world problem and determine whether a particular value satisfies the inequality.

Big Idea

Inequalities can be written to express verbal descriptions.

Think About It

5 minutes

Students work in partners to reason and match the scenarios with the inequalities in the Think About It problem.

I ask the class why these scenarios require inequalities, and not equations.  I then ask for students to share out how they annotated the problems, to help them make sense of the scenarios.  I want to pull out the words or phrases that helped them point to the addition or the multiplication inequality.  I end the conversation by asking for values for each scenario that could be true - how many hours could Joseph have driven?  How many more cones might Joseph sell?

Intro to New Material

15 minutes

In the Intro to New Material section of this lesson, I guide students through the steps that they will take to create inequalities to represent real-world scenarios.  We read and annotate the problem, to make sense of the scenario.  We define the variable to represent the unknown.

In this section, I'll ask questions to have students articulate what's happening.  Why do we need to use an inequality?  What are we trying to find? Is there multiplication or division?  Is there addition or subtraction?  What's our comparison value in this problem?  Do we need the 'equal to' part of our symbol?  Why or why not? How can we check our inequality?

When it is time to check the inequality, students are using substitution.  They'll pick a value that could be part of the solution set and try it in the inequality.  It is part of my expectation for complete responses that students are taking this step. 

For students who need more support in determining if the inequality is greater than/less than, I coach them to draw a number line showing the comparison value.  They then 'test' out a number lower and a number higher than the comparison value.  

Partner Practice

15 minutes

Students work in pairs on the Partner Practice problems.  As they are working, I circulate around the room.

I am looking for: 

  • Are students annotating the problems?
  • Are students defining the variables?
  • Are students writing inequalities that correctly represent real-world scenarios?
  • Are students listing possible solutions to the inequalities they create and using substitution to check their solutions?

 I'm asking pairs:

  • How did you know what operation was being indicated?
  • How did you know which inequality symbol to use?
  • Why is the variable you chose an appropriate variable for this scenario?
  • If a scholar said this problem was _______ operation, what would you tell this scholar?
  • What are possible values for the variable?
  • What's one number that cannot be a value for the variable? Why?
  • How can you check your answer? 


Problem number 3 is one that is difficult for students.  They tend to incorrectly apply 'triple' to the variable in the inequality (Student Error).  We talk about this problem as a class.  First, I ask students to share with the class what we know.  I want it to come out that there are more people this week at the museum than last week.  I write on the board "3p > 186, where p = people" and tell the class that I saw a number of groups write this as the inequality for this problem.

I tell students that I know more about this museum.  I tell them that four weeks ago, 10 people came to visit.  And then the week after than, attendance tripled.  I ask students to call out how many people came to the museum.  I then tell them that next week, 250 people will come to the museum.  If attendance triples the week after that, how many people will come to visit?  I then have students turn and talk with their partners about how to revise the inequality for this problem. 

Students come up with either p > 3*186 (or p > 558) or p/3 > 186.

Independent Practice

15 minutes

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.

Closing and Exit Ticket

10 minutes

At the end of work time, the class comes back together to discuss the work they've done.  I like to use problem 6 from the independent practice problems for conversation, because the problem asks students to create an inequality, change and reason about change to the inequality, and provide examples of possible values for the variable.  There's much to think about and discuss!  

Students work independently on the Exit Ticket to end the lesson.