Solving One-Step Inequalities Using Reasoning (Addition and Subtraction)

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SWBAT solve a simple one-step inequality using reasoning to find the solution set that makes the inequality true.

Big Idea

Inequalities can be solved using reasoning and substitution. We know that a solution set is correct if you choose values that satisfy the solution set, substitute them into the original inequality, and see if the inequality is satisfied.

Think About It

7 minutes

Students work in partners to write an inequality that represents the Girl Scout cookie scenario in the Think About It problem.  They then come up with the solution set for the problem.

Students are able to come up with the inequality fairly easily on their own.  Many students struggle with the solution set.  Students come up with either 9 or 10 boxes of cookies.  When I hear 9 as an answer, I ask students to substitute 9 back into the inequality and then ask if Amell will meet her goal selling 9 boxes of cookies.   Once we've established that 9 cannot be a part of the solution, I ask for someone to share his/her thinking about 10 being a solution.  Substitution shows that 10 will work but by this point in the conversation students realize that there are an infinite number of possible answers.  What if Amell is a super cookie seller, and sells 4000 more boxes?  What if she sells 20 more boxes?  How can we represent this?  These questions guide students to create the solution set of b > 9.

Intro to New Material

20 minutes

In previous lessons, students have found solutions to inequalities by substituting and seeing if the value made the inequality true.  Today we are going to solve inequalities to find the entire solution set that would make the inequality true.

The skills that students use in this lesson (evaluating expressions, substitution, reasoning about solutions) are all ones that have been mastered in earlier units.  This lesson gives students the chance to put all of these skills together.  

Organization is especially important in this lesson, as there are a number of steps students need to follow in order to provide a complete response to the problems.  The steps are outlined in the Visual Anchor, which is displayed on the document camera as students work in partners and independently.  

In this lesson, students may start to reason with integers, although we do not learn to compute with negative numbers until 7th grade (7.NS.A.1).  A student, for example, might pick a number to test  for x - 15 < 7 that leaves her with 4-15 < 7.  She might not be able to simplify this to -11 < 7, but she can reason that 4 -15 results in a negative number.  Negative numbers are always less than positive numbers.  

Partner Practice

10 minutes

Students work together on the Partner Practice problems.  An example of what the completed work can look like is provided with this Student Sample.  As students work, I am circulating around the room.  

I am looking for:

  • Are students identifying the correct solution to each inequality?
  • Are students testing a number bigger and a number smaller than the maximum/minimum value?
  • Are students using substitution in the original inequality to check that their solution is correct?

I'm asking pairs:

  • How did you know the minimum value was x = ___?
  • How did you know the maximum value was x = ___?
  • How did you know to include the value of x = ____?
  • What numbers are you going to use to test your solution set?
  • Is x = __ a solution to the set?




Independent Practice

15 minutes

Students work on the Independent Practice problems.  As they are working, I am looking for and asking the same things as I did during partner practice.

On the first page of the independent practice, all of the problems are inequalities that contain subtraction.  For future years, I plan to change this problem set so that it has a mix of addition and subtraction.  I want my students to practice both!

Closing and Exit Ticket

8 minutes

After independent work time, we come back together as a class and discuss problem 12 from the independent practice problems.  

If students do not have a firm grasp on reasoning about solutions, they will often say that the maximum value in the solution set is 9.  I want the class to talk about why this isn't reasonable.  I also want them to discuss how they can use substitution to check whether or not 9 as a maximum value makes sense.

After we discuss the problem, students work on the Exit Ticket to end class.