##
* *Reflection: Perseverance
Flip It! - Section 1: Set the Stage

I made the assumption that my students were old enough and comfortable enough with functions that two examples would suffice to move them to independent work. I was wrong! Even my best students needed a greater variety of examples to be able to successfully work through the independent assignment. When I finished the two examples I'd prepared and asked if there were any questions, almost every hand went up. I called on one student and as he spoke about not really being clear about what to do first, I saw several others nodding in agreement. At that point I changed my plans and decided to work through more examples until my students felt confident to proceed on their own. Rather than using all the functions in the handout I asked my students to volunteer functions for me to "invert", with the condition that they needed to copy all the steps for each example. As I worked through a few more examples, I began to ask my students what should be done instead of just writing it out for them. It took an additional ten minutes or so, but I believe it was well worth it, not only because it gave my students a much stronger foundation to work from, but also because it helped foster a feeling of collaboration between me and my students as they learned that I was willing to listen to their concerns and address them immediately.

*Very gradual release!*

*Perseverance: Very gradual release!*

# Flip It!

Lesson 7 of 12

## Objective: SWBAT write the inverse given a simple rational equation.

## Big Idea: Take inverse functions to the next level with this lesson on inverse for rational equations.

*50 minutes*

#### Set the Stage

*10 min*

I have found that inverse functions can be both frustrating and confusing for many students so I use direct instruction and guided practice, I Do - We Do - You Do gradual release for this lesson. I want students to get comfortable with process of writing inverses in general first so I don't focus on restricted domains as we "set the stage", unless a student notices and questions whether or not an example inverse is a function.

I begin with two problems posted on the board as shown in my Educreations video below. I made the video for students to reference later if they need review.

After working the first problem for them while they copy my work, I ask my students to work through the second problem with me. There are a few who will resist copying the work, saying they understand it already or that they can remember how to do it. I've found however that by insisting they copy problems I avoid the need to re-teach and I reduce student frustration by giving them a handy reference and support tool since I'll ask students who have questions to share their copied problems and show me where they got lost. Before moving on to individual practice I give a brief definition of inverse functions and show my students the inverse function notation. I explain that like determining odd and even functions, you can verify inverse fucntions by confirming that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x

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#### Put It Into Action

*35 min*

For this section students work individually to hone their skills and understanding of inverse functions. I distribute the worksheet and explain that they have twenty minutes to finish these problems and then they should prepare to share with the class. **(MP1)** While they're working I walk around offering encouragement and assistance as needed. For example if a student is struggling with where to begin I might prompt them with "How can you rewrite this function using y instead of f(x)?" followed by "Okay, now how do you switch the variables - what would that look like?" This is usually sufficient, although I occasionally have a student who needs additional direct instruction, which I provide if time permits otherwise this gets schedule for out-of-class. This link offers an additional challenge/extension for bright students. When twenty minutes have passed or when everyone is done I randomly select students to post their solutions and work on the front board. I have room for 3-4 students at once, so no individual is put on the spot as they work. After the first set of problems is posted I ask the class to review and critique the work. **(MP3)** As they make corrections they know they are also expected to explain what they're doing and why, but sometimes I have to prompt with a question like "How did you know to do it that way instead of the way it was posted?" or "What let you know that it wasn't done correctly?" This is also when I introduce the idea of restricting the domain to make an inverse "work" as a function, by asking students to imagine running a horizontal line up the original function like they use the vertical line test for functions. Most students remember the vertical line test from Algebra, so this is a relatively easy connection to make. We continue until we've reviewed all twelve problems and everyone has had an opportunity to make corrections to their own papers. I've found that immediate feedback on practice problems helps students cement their understanding.

#### Resources

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#### Wrap It Up

*5 min*

To wrap up this lesson I ask each student to write a "how-to" in their own words. I explain that they can use functions as part of the "how to" but should focus on clear directions written for a classmate who is absent today. **(MP6)** These are today's "ticket out the door." I explain why I value this activity in my video.

#### Resources

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- UNIT 1: First Week!
- UNIT 2: Algebraic Arithmetic
- UNIT 3: Algebraic Structure
- UNIT 4: Complex Numbers
- UNIT 5: Creating Algebraically
- UNIT 6: Algebraic Reasoning
- UNIT 7: Building Functions
- UNIT 8: Interpreting Functions
- UNIT 9: Intro to Trig
- UNIT 10: Trigonometric Functions
- UNIT 11: Statistics
- UNIT 12: Probability
- UNIT 13: Semester 2 Review
- UNIT 14: Games
- UNIT 15: Semester 1 Review

- LESSON 1: Functions and Finance
- LESSON 2: Road Trip
- LESSON 3: A-OK
- LESSON 4: What's OK?
- LESSON 5: Tech Time
- LESSON 6: Odd or Even?
- LESSON 7: Flip It!
- LESSON 8: Pull the Old Switcheroo
- LESSON 9: Backwards, Upside Down or Inside Out?
- LESSON 10: Or Downside Up?
- LESSON 11: Show Your Stuff Day 1 of 2
- LESSON 12: Show Your Stuff - Day 2 of 2