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# Modeling Compound Inequalities

Lesson 12 of 15

## Objective: Students will be able model and solve compound inequalities.

#### Warm up and Homework Review

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Compound Inequalities which asks students to analyze the accuracy of a solved inequality.

I also use this time to correct and record the previous day's Homework.

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#### Conjunctions

*20 min*

We are going to start today's lesson with a statement to model: *I can work no more than 15 hours per week making cake pops.* This problem seems simple at the onset but has a trick. My students work on this problem and then check with their partner. If this were just a regular inequality, its interval would extend to negative infinity but since we don't have negative hours, this is actually the conjunction [0, 15]. I don't warn them of this in advance If no one brings up the issue, I ask a question like “ Do all the numbers from (-∞, 15] fit our statement?” (**Math Practice 2**) I then have them re-discuss this with their partner and modify their solution

We classify this and define the term conjunction and talk about all of its representation including three “sided” conjunctions like *-7 *<* 4x + 5 *<* 3.* I have included a quadratic inequality. Many will not remember how to solve these so we will solve this one graphically. I have them graph both sides and then do a think-pair-share on the interval solution. Here is a good place to teach CALC, intersect if using a TI-84 calculator as the intersections aren’t at easy integers.

Finally they will solve a conjunction modeling problem.

My lesson PowerPoint includes detailed presentation notes.

#### Resources

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#### Disjunctions

*17 min*

We begin disjunctions with a real life problem. *Water is a liquid between 32 ^{o}f and 212^{o}f. Write an inequality that represents when water is NOT liquid*. With a problem like this, I often let my students know that there is a sneaky part to this problem. Then I l go around checking on their solutions and calling out recognition (sometimes with names and sometime just generally) when students get the right solution which we then discuss as a class.

At this point, we define and look at the representations of disjunctions.

The remainder of the lesson involves some practice problems located in second section of the lesson PowerPoint- Compound Inequalities. This includes another modeling problem (**Math Practice 4**) and an ordinary two inequality disjunction to solve and graph. The final two problems are polynomial inequalities that need to be solved graphically.

#### Resources

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#### Exit Ticket

*2 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

This exit ticket asks students to solve the conjunction -4 < 3x – 2 < 10.

#### Resources

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This Homework provides a range of standard compound inequalities and modeling problems as well as a polynomial inequality to be solved graphically. Problem #9 is an extension problem that gives the students a three way conjunction that must be solved by splitting it into two separate inequalities or solved graphically (**Math Practice 1**).

One homework modeling problem was adapted from here.

The assignment was created with Kuta Software, an amazing resource for secondary mathematics teachers.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Turn Your Words Into Money
- LESSON 2: Crossing the Snake River
- LESSON 3: Interpreting Algebraic Expressions Day 1
- LESSON 4: Interpreting Algebraic Expressions Day 2
- LESSON 5: Mind Reading with Algebra
- LESSON 6: Selling Cake Pops Day 1 of 5
- LESSON 7: Selling Cake Pops Day 2 of 5
- LESSON 8: Selling Cake Pops Day 3 of 5
- LESSON 9: Selling Cake Pops Day 4 of 5
- LESSON 10: Selling Cake Pops Day 5 of 5
- LESSON 11: Representing Inequalities
- LESSON 12: Modeling Compound Inequalities
- LESSON 13: Modeling Expressions and Equations Review Day 1
- LESSON 14: Modeling Expressions and Equations Review Day 2
- LESSON 15: Modeling Expressions and Equations Test