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* *Reflection: Developing a Conceptual Understanding
Inequalities - Section 3: Instruction & Teacher Modeling

This reflection speaks to the importance of ensuring students understand the verbiage behind inequalities.

*Developing a Conceptual Understanding: Inequalities In Words*

# Inequalities

Lesson 8 of 15

## Objective: SWBAT recognize, write, and graph inequalities when given a mathematical phrase.

*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*

For today's opening exercise, I will write each the following numbers on a small whiteboard: 649, 725, 647. Then, I will ask for three volunteers to come to the front of the room, and give a the whiteboards to each student. Using the white boards, I will have the students compare the three numbers.

I will ask them the following questions:

- What words can you use to compare the first two numbers? The second number and the third number? What about the first and the third number?
- What symbol can you use to compare the first two numbers? The second number and the third number? What about the first and the third number?

This exercise is to show students the meaning of inequality.

Then, to determine the extent of student understanding when it comes to certain mathematical phrases, I will have students write, in their own words, what they think the following phrases mean:

- 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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In today's instructional piece, we will first attend to vocabulary. I will ensure that my students can recognize the symbols of and understand the meaning of the following mathematical terms:

- inequality
- greater than
- less than
- greater than or equal to
- less than or equal to

We will also discuss the difference between an inequality and an equation. I will explain to my students that an equation has to be balanced. That one side of the equation must have the same value as the other side of the equation. When it comes to inequalities, this is not true. An inequality allows for many solutions.

To illustrate the concept of inequalities, I will ask the following questions.

*What is a possible number less than 3?*Samples answers: 2, 1, 0*What is a possible number greater than or equal to 7?*Sample answers: 7, 8, 9, 10

The two questions above will show students how there can be many solutions to one question while the question below shows how an inequality can be used to compare two quantities.

*How can you compare 5 and 8?*5 is less than 8; 8 is greater than 5

After ensuring that students understand the vocabulary in context, my students and I will then go back to the word phrases presented in the engagement portion of this lesson. At this point, the students will share their responses to these phrases and we will discuss what these word phrases tell us as far as math is concerned.

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

Next, we will write the inequality represented by the phrases and then, I will then show my students these same phrases written as a scenario. It is my hope that if the students see these key phrases as they would be written in a wordy scenario that they will see that it is still quite easy to pull the key phrase out of the scenario so that they can easily write an inequality that represents what is happening in the scenario.

Also, during this lesson, I want to ensure that I address phrases that can be a little tricky. Student have a tendency to mix up phrases such as those written below:

- "No more than" - Students tend to think that this phrase means that they should be using a greater than symbol.
- "No Less than" - Students tend to think that this phrase means that they should be using a less than symbol.
- "At Least" - Students tend to think that this phrase means that they should be using a less than symbol.
- "At Most" - Students tend to think that this phrase means that they should be using a greater than symbol.

#### Resources

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#### Try It Out

*10 min*

During the guided practice of this lesson. I will present the attached document to my students. Together, we will break down the first two problems presented, showing how the scenario presented is a depiction of the inequality shown.

After going through these two scenarios and how they are a depiction of their corresponding inequalities, the students will then write their own scenarios for the two inequalities presented in the document.

I will give my students approximately 5 minutes to come up with their scenarios and then I will choose several students to present their scenarios and explain how their scenario is a depiction of the given inequality.

#### Resources

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#### Independent Exploration

*20 min*

For the independent practice portion of this lesson, I will have my students translate four mathematical scenarios into an inequality mathematical sentence. Then, they will write a scenario for a given inequality. They will be given four inequalities for which they will need to write scenarios.

#### Resources

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#### Closing Summary

*20 min*

To close out this lesson, I will select four students to tell us what inequality they used to represent the given scenarios. These students will have to articulate why the inequality that they wrote is the proper inequality to depict what is happening in the scenario.

Then, I will choose several students (as many as time will allow) to present to the class their written scenarios to the inequalities that I gave them.

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- 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