##
* *Reflection: Vertical Alignment
Reasoning About Inequality Solution Sets - Section 2: Intro to New Material

If we have a snowy school year, and I need to make up some instructional days, this lesson is one that I can cut from the unit. I include this lesson, though, to set students up for success for the rest of the unit.

There is a lot of practice we need to do, in terms of correctly reading inequalities. More so, we need practice in naming the inequality symbols. My students generally come to me prepared to read 6 < 19 as 'six is less than 19.' However, when asked to name the symbol that would allow us to compare 7 and 18, students generally don't come to me ready to say the less than symbols.

Frequent responses: "the mouth is open to the 18," or "the alligator is eating the 18!" Often, students are drawing teeth in their inequality symbols (and some have even made 'nom nom nom' sounds :) )

This lesson is really all about making sure students have the academic vocabulary to talk about inequalities.

*Academic Language - No Alligators!*

*Vertical Alignment: Academic Language - No Alligators!*

# Reasoning About Inequality Solution Sets

Lesson 1 of 7

## Objective: SWBAT determine whether a given number in a specified set makes an inequality true and justify their response using substitution.

#### Think About It

*8 min*

Students work in partners on the Think About It problem. The key idea I want to come out during our conversation is that the equation has one solution and the inequality has a solution set.

I plan to ask my students why they chose not to circle 10 as part of the solution to x < 10. My goal is to use this discussion as a lead in to the Introduction of New Material. I hope that my students will articulate that 10 is not less than 10, so it can't be a part of the solution.

#### Resources

*expand content*

#### Intro to New Material

*20 min*

An inequality might be a true statement for some values of the variable, and a false statement for others. Solving is a process of reasoning to find the numbers which make an inequality true, which can include checking if a given number is a solution. This is the message that I want to convey to my students today.

At 20 minutes in length, this is one of the longer INM sections that I teach. Many of my students have never seen the 'greater than or equal to' or 'less than or equal to' symbols (the 'equal to' is the new piece). While they will have compared decimals in 5th grade using the less than and greater than symbols (5.NBT.A.3b), they are extending their knowledge today.

One habit that I want students to acquire today is 'reading the inequality,' starting with the variable. During this lesson I'll spend time having my students re-write inequalities so that the variable comes first (rather than 43<y, writing y>43). I find that this helps my students to reason about the solution sets more accurately. It will also make graphing the solution sets easier when we get to that point.

#### Resources

*expand content*

- Are students using substitution to solve for the solution set and to justify their answer?
- Are students precisely describing the solution set?

I'm asking pairs of students:

- How did you know the solution was x = ?
- Why can’t x = ?
- How can you describe the solution of the set?

After 15 minutes of work time, I will ask my students to complete the Final_Check_for_Understanding problem on their own. I have students vote with thumbs up/down about whether or not 6 is part of the solution set of the inequality. I then ask for a volunteer to show his/her work to the class on the document camera.

*expand content*

#### Independent Practice

*15 min*

Students work on their own on the Independent Practice problem set. As I circulate, I am looking for and asking the same questions as in the partner practice section.

It's important during this lesson that students are practicing using substitution to decide whether a number is part of the solution set. Some of my more advanced students will use mental math and are able to reason about the solution sets in their heads. It's important that students are building the habits that will help them be successful in future math classes. I make sure I am looking to see that students are taking the time to carefully write out the steps needed to substitute and evaluate each expression in the inequalities.

#### Resources

*expand content*

#### Closing and Exit Ticket

*7 min*

After student work time, the class comes back together for a conversation about one of the independent work problems. I like to use problem 2, as it really gets at the key idea that inequalities have a solution *set*, rather than a solution.

Students work on the Exit Ticket independently. For the third problem, an exemplar response will show the substitution work, as seen in this Exit Ticket Sample.

*expand content*

This is everything I have been looking for to introduce inequalities and a plain and simple manner. THANK YOU!!

| one year ago | Reply

I like the ideas on the work sheets. Thanks for your great work.

| 2 years ago | Reply

I am really looking forward to teaching this lesson with to students. Your examples are clear and consise. Thanks

| 2 years ago | Reply*expand comments*

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- UNIT 1: Number Sense
- UNIT 2: Division with Fractions
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Coordinate Plane
- UNIT 5: Rates and Ratios
- UNIT 6: Unit Rate Applications and Percents
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- UNIT 11: Analyzing Data

- LESSON 1: Reasoning About Inequality Solution Sets
- LESSON 2: Writing Simple Inequalities
- LESSON 3: Modeling Inequalities on Number Lines
- LESSON 4: One-Step Inequalities and the Real World
- LESSON 5: Solving One-Step Inequalities Using Reasoning (Addition and Subtraction)
- LESSON 6: More Solving One-Step Inequalities Using Reasoning (all operations)
- LESSON 7: Solving and Modeling Inequalities