# More Solving One-Step Inequalities Using Reasoning (all operations)

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## Objective

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.

7 minutes

Students work in partners to create an inequality to represent the scenario in the Think About It problem.

After a few minutes of work time, I facilitate a conversation with the class about this scenario. Students are able to write 3r < 30, where r is the rate Marissa is paid.  Students had practice in the previous lesson with and solving inequalities with addition and subtraction.  The focus of this conversation is around why we need an inequality, and not an equation.

This problem also presents a great opportunity to talk about how we define the variable in this scenario.  In every class, there will be at least one student who decides to write 3h < 30, and will define h as the number of hours Marissa works.  The unknown here is her hourly rate, and not how long she works.

Yesterday we used a process of reasoning to find the maximum and minimum values that make an equation true in order to find the entire solution set to an inequality.  Today we will be doing the same exact thing, but work with multiplication and division as well.

## Intro to New Material

15 minutes

The first two problems presented to students in the Intro to New Material section requires them to determine which numbers in the provided sets are part of the solution sets of the given inequalities.  I have students complete these problems independently, and then I ask students for the strategies they used as they worked.  It isn't efficient to test every given number.  I want students to articulate that they were able to reason about the solutions set by thinking about the maximum or minimum value for each inequality.

In this lesson, students are using the same steps that they followed in the previous lesson.  Because they are familiar with the process to follow, our conversation in this section is focused around making wise choices around the numbers to test for each inequality.  For example, for inequalities that involve reasoning with multiplication, it makes sense to use 1 or 0 for the 'smaller' number to test.  Similarly, using 100 as the 'bigger' number is efficient.

Instructional Note: When working with inequalities that involve reasoning with division, I want students to think about multiples.  If students are working with x/4 > 7, I don't want students wrestling with dividing 27 by 4 (if they pick 27 as their test number smaller than 28). Rather, I want them to use 24, 20, 16, etc.

## Partner Practice and Discussion

20 minutes

Students work in partners on the Partner Practice problem set.  As they are working, I am looking for:

• Are students correctly writing a solution to the inequality?
• Is work organized?
• Are students using numbers that are efficient for their 'smaller' and 'bigger' test numbers?
• Are students using substitution to check that their solution is correct?

As I circulate, I am asking students:

• How did you know this value was the maximum/minimum value for x?
• How do you check this work with substitution?
• What are other possible values for x?
• Why did you use that value for your test number?
• Are possible values of x greater than or less than or equal to the solution to the inequality? How do you know?

Before students move on to the independent practice, we discuss the final check for understanding problem.  I have 3-4 students share their thoughts about Ilana's work and how they would correct her mistake.

## 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.

## Closing and Exit Ticket

8 minutes

At the end of the 15 minutes of work time, we discuss the first problem on the second page of the independent practice.  I want students to hear a variety of strategies they can use to solve a problem like this, where they need to evaluate the solutions to 4 different inequalities.  There are multiple pathways to the answer here, and I want students to share how they decided to work.

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