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# The Different Ways to Represent An Inequality

Lesson 9 of 15

## Objective: SWBAT represent inequalities using word phrases, graphs on a number line, and mathematical sentences.

## Big Idea: Inequalities Represented: Demonstrating the ability to understand inequalities and represent them in words, as a graph, and as a mathematical sentence.

*70 minutes*

#### Curriculum Reinforcer

*5 min*

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.

#### Resources

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#### Engagement

*5 min*

During today’s opening exercise, we will present the same inequality phrases that were presented in a previous lesson in this unit. Once again, I want to determine the extent of student understanding when it comes to certain mathematical phrases. To do this, I will have students review with me the meanings of the following mathematical phrases:

- No more than 30
- Less than 75
- More than 2
- No less than 45
- Up to 30
- As little as 3

#### Resources

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Using knowledge gained during the opening exercise, I will have my students then show me where a number that is…

- No more than 30
- Less than 75
- More than 2
- No less than 45
- Up to 30
- As little as 3

Could lie on a number line. To do this, each student will be given a worksheet that will have six small number lines on it. They will also be given six counter chips. They will take the counter chips and place them where they believe the values lie on the number line.

To deepen my students' understanding of this concept, I will ask probing questions such as:

- So does everyone have their counter chip in the same place? What does that mean?
- Did anyone actually put their counter chip directly on the quantity presented in the mathematical phrase? If so, why? If not, could you put your chip on the number for any of these mathematical phrases? If so, why?

I will use this activity to segue into teaching my students about inequalities as well as how to graph inequalities.

Students should learn in this lesson that inequalities provide a limit in one direction on the number line while allowing for infinite solutions on the other side of the number line. They will also learn when to graph an inequality with an open circle and when to graph an inequality with a closed circle.

To see more clearly how this section of this lesson should be presented, please watch the video attached to this section of this lesson.

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#### Try It Out

*10 min*

During the guided practice of this lesson. I will give students 4 phrases that represent inequalities. The students will have to write the inequality for the phrase and graph the inequality on a number line.

During this time, I will travel the room and check the students understanding of the concept. Ensuring that they understand when the graph should contain an open circle versus a closed circle, and also making sure that they are properly interpreting the meaning of the mathematical phrases.

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#### Independent Exploration

*20 min*

For the independent practice portion of this lesson, I will have my students translate 10 mathematical phrases into an inequality mathematical sentence. They will also have to graph the inequality and explain why they believe their answer to be correct.

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#### Closing Summary

*20 min*

During the closing, I will select students to complete specific problems. They will present the inequality that they wrote for their assigned scenario, as well as the graph for that inequality. The presenting student will also need to be able to explain why they know the inequality and graph that they are presenting for their assigned scenario is correct.

The rest of the students in my class need to be ready to critique, ask questions, and make comments regarding what is being presented by their peers. They should be able to catch any mistakes that may arise during presentations and add to the commentary of the presenting student in some way.

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###### Writing Algebraic Inequalities

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*Resources(13)*

Environment: Urban

- LESSON 1: Unit 4 Pre-Assessment
- LESSON 2: Keeping it in Balance: One Step Equations
- LESSON 3: A Rational Balancing Act: One Step Equations Continued
- LESSON 4: One-Step Algebraic Problem Solving
- LESSON 5: One-Step Equations... How Do They Function?
- LESSON 6: The One-Step Equation & Its Many Faces
- LESSON 7: Unit 4 Quiz 1: One-Step Equations
- LESSON 8: Inequalities
- LESSON 9: The Different Ways to Represent An Inequality
- LESSON 10: So Many Options: Solving One-Step Inequalities
- LESSON 11: Inequalities in the Real-World
- LESSON 12: Unit 4 Quiz 2: One-Step Equations
- LESSON 13: Unit 4: Addressing What They Still Don't Get
- LESSON 14: Unit 4 Assessment:One-Step Equations & Inequalities
- LESSON 15: Student Self-Assessment: One-Step Equations & Inequalities