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# Complex Rational Expressions

Lesson 10 of 15

## Objective: Students will be to simplify complex rational expressions.

*51 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. This lesson’s Warm Up- Complex Rational Expressions asks students to explain how to split 3/4 of a pizza between 3 people.

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

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#### Initial Activity

*15 min*

My goal for this Initial Activity of this PowerPoint is to give the students an opportunity to practice perseverance ( **Math Practice 1**). At this point, the students have the skills they need to simplify complex fractions; however, they have not put them together in this particular way. I present them with a challenging complex fraction, and let them know they have all the skills they need to simplify this expression. There will probably be a wide range of attempts from completion to very little effort depending on their skills and comfort level. As they work, I walk around providing some support for those who need it. It is fine if all groups don’t complete this as we will be building/refining this process during the remainder of the lesson.

Once all of the groups have made some decent process and several groups have finished, we will simplify the expression together.

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#### Guided Practice

*23 min*

The remainder of this lesson consists of a Guided Practice of Complex Rational Expressions. I may skip some of these problems depending on the performance of the class during the initial activity.

Please see the PowerPoint for detailed presentation notes.

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#### Exit Ticket

*3 min*

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

Today's Exit Ticket, I ask the students to simplify a rational expression.

#### Resources

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This Assignment provides students with an opportunity to simplify complex rational expressions. The last expression is an extension problem. One scaffolding measure would be to ask the students to simplify either the first four or the final three expressions. The final problem asks students to write a list of steps that one could use to simplify a rational expression (**Math Practice 3**).

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