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# Rational Equations

Lesson 12 of 15

## Objective: Students will be able to solve rational equations.

*50 minutes*

#### 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 which asks students to explain to solve an equation with fractions.

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

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#### Rational Equations

*38 min*

I begin with a work problem (**Math Practice 4**).

*Gina and Lionel can paint a room together in 6 hours. If Gina could paint it by herself in 9 hours, how many hours would it take just Lionel?*

In the last lesson, students learned how to set up work problems. Today, they will extent that into equations with variables in the denominator. This is an excellent place to use **note card** method because it will deepen the discussion.** **

The remainder of the lesson revolves around solving rational equations in different formats. After each problem, I give students an opportunity to share out any different methods they used. We also look at finding solutions graphically.

The third problem they solve has no solution. I allow them to do the problem and once they believe they have a solution, I ask if they are confident in that solution. I then have them graph it on their calculator which gives them a visual representation. Once they see the situation graphically, they do a think-pair-share to determine how we know if there is an extraneous solution algebraically (**Math Practice 5**).

The remainder of the problems builds upon these concepts so that students can solve a wide range of rational equations.

Please see the PowerPoint- Solving Rational Equations resource which includes detailed presentation notes.

#### 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.

Today's Exit Ticket asks students to solve a rational equation.

#### Resources

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This assignment ensures that students can solve rational equations as well as identify extraneous solutions (**Math Practice 2**). Students are also given a work problem. This will lead into the lesson which covers modeling with rational equations.

This 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: Quotients of Monomials
- LESSON 2: Modeling Rational Functions
- LESSON 3: Transformations of Rational Functions
- LESSON 4: Properties of Rational Functions Investigation Day 1 of 2
- LESSON 5: Properties of Rational Functions Investigation Day 2 of 2
- LESSON 6: Rational Functions Quiz
- LESSON 7: Modeling and Simplifying Rational Expressions
- LESSON 8: Multiplying and Dividing Rational Expressions
- LESSON 9: Adding and Subtraction Rational Expressions
- LESSON 10: Complex Rational Expressions
- LESSON 11: Equations with Rational Coefficients
- LESSON 12: Rational Equations
- LESSON 13: Rational Functions Review Day 1
- LESSON 14: Rational Function Review Day 2
- LESSON 15: Rational Functions Test