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# Solving Compound Inequalities

Lesson 6 of 8

## Objective: SWBAT solve and graph Compound Inequalities

## Big Idea: Students recognize the meaning of "and" as an intersection of solutions, and "or" meaning that only one of the inequalities have to be true.

*50 minutes*

#### Warm Up

*10 min*

I intend for this Warm Up to take about 10 minutes for the students to complete and for me to review with the class. The purpose of this Warm Up is for students to be able to recognize the difference and importance between the words "and", and "or". Having a deeper understanding for these two words is going to help students be more successful when solving compound inequalities. In this Warm Up, I provide the students with two real world examples. The first example is about how much a restaurant charges based on age, and the second example is about the two different readings of blood pressure.

#### Resources

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#### Guided Practice

*15 min*

I set up the Guided Practice for students to work with me as a whole class. It takes about 15 minutes to work through the Guided Practice with the students. Part one (problems 1-6) of the Guided Practice is much easier for students to complete than Part Two (problems 7-11). Part one, gives the student a sentence, and the student is to write the inequality, as well as sketch its solution on a number line. Students have little difficulty with this part of the Guided Practice.

Students have more difficulty with Part Two of the Guided Practice which requires them to solve the given inequality and sketch its solutions. Students still have some difficulty remembering to change the direction of the inequality symbol when multiplying or dividing by a negative number. I also introduce the students to two special problems in number 10 and 11. The solution for number 10 is all real numbers and the solution for number 11 is no solution. I model these two problems in the video below.

#### Resources

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#### Independent Practice

*15 min*

The Independent Practice is made up of both types of compound inequalities. It provides the students with more practice to distinguish between "and", and "or". After the Guided Practice, I assign students to work on the Independent Practice.

When there is 10 minutes remaining in the period, I plan to hand my students an Exit Slip to complete. If they are not yet done with the Independent Practice, it is to be completed as homework. Students who are finished should hand in the Independent Practice worksheet before they leave.

I try to have an Answer Key to enable students to check their work on the Independent Practice. I think that immediate feedback is helpful at this point of the course.

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#### Exit Slip

*10 min*

I use this Exit Slip as a formative assessment to check for student understanding. It allows the student to practice setting up both an inequality that uses "and", and an inequality that uses "or". The real world example using Velocity, allows the students to see a case in which inequalities are set up differently based from their definitions.

One common mistake that students made on the Exit Slip was not to change the direction of the inequality when dividing by a negative number. If the student did not change the direction of the sign, the inequalities did not make sense, and students had difficulty with the questions. I show a Sample of the two problems demonstrating not changing the direction of the sign to the correct answers.

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Language of Algebra with Real World Contexts
- LESSON 2: Review of Solving Linear Equations
- LESSON 3: Solving Linear Equations Stations Activity
- LESSON 4: Solving Linear Inequalities with a Comparison to Linear Equations
- LESSON 5: Algebraic Properties and Literal Equations
- LESSON 6: Solving Compound Inequalities
- LESSON 7: Solving Absolute Value Equations and Inequalities (Day 1 of 2)
- LESSON 8: Solving Absolute Value Equations and Inequalities (Day 2 of 2)