## Teaching Notes about Factoring.docx - Section 1: Warm-up

*Teaching Notes about Factoring.docx*

# Rational Approaches to Solving Rational Equations

Lesson 1 of 12

## Objective: SWBAT solve a rational equation for a specified variable.

#### Warm-up

*10 min*

To start off this unit, I want to first see what level of proficiency my students have with basic fraction operations. To do this, I am going to ask students to complete the three warm-up problems on slide 2 of the PowerPoint. I selected these problems to assess students’ knowledge of the rules of adding/subtracting fractions, multiplying/dividing fractions, and factoring. Question 3 is already simplified. I am expecting some students to still try to divide the terms. Once students have completed their warm-up problems. I plan to model how to simplify these for any students who got stuck.

Before we proceed with rational equations I want to talk with students about factoring, simplifying, and "canceling." There are often many misconceptions that surround factoring of rational expressions for students. They don’t know what ‘cancels’, when it ‘cancels,’ and what is left over. See Teaching Notes about Factoring for more detail about how I will lead students through this conversation.

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#### Closure: Here’s how…

*15 min*

As we finish today's lesson I will present Rational Approaches Closure Slide (slide 24 from the PowerPoint). I ask students to complete a Here’s How to close out today’s learning.

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I plan to assign Homework 1 - Rational Functions for homework this evening.

I also plan to start talking with my students about the presentations I would like them to do at the end of the week (4 lessons from now). I will begin this discussion as I present slide 14 in the PowerPoint. I want students to start researching an explanation that makes sense to them: **Why does dividing by zero causes a function to be undefined?**

#### Resources

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Rational Approaches to Solving Rational Equations
- LESSON 2: Speed Dating Rationally
- LESSON 3: Another Rational Approach to Solving: Graphing
- LESSON 4: Ahoy again! What can you see now? Building Rational Functions
- LESSON 5: Evolving Rational Functions
- LESSON 6: Rationalized Transformations: Shifting Rational Functions
- LESSON 7: Light it Up - Day 1: Modeling with Rational Functions
- LESSON 8: Light it Up – Day 2: Modeling with Rational Functions
- LESSON 9: You can’t Get There from Here: Finding the Asymptotes
- LESSON 10: Rational Functions Review Day
- LESSON 11: Rational Functions Test Review
- LESSON 12: Rational Functions and Equations Test