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# Shifting Functions: How can we describe them?

Lesson 6 of 16

## Objective: SWBAT use horizontal and vertical shifts and stretching to sketch the graphs of functions and identify key features of the graphs and how transformations change these key features.

## Big Idea: Students apply their newly acquired knowledge of shifting functions while reviewing how to describe the key features of the graphs.

*50 minutes*

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Before starting today’s activity, I am going to take a few minutes to talk about the mathematical practice standard of the day. Today I want students to focus on **MP6 by attending to precision** as they complete this worksheet. I want student to understand that this is definitely a practice that we all should always be cognizant of in a mathematics classroom. To help students better understand this standard I will give them a few examples: This practice could mean making precise graphs by labeling the axis and scaling and accurately plotting the points. Or it could mean working precisely with numbers by rounding correctly and as appropriate (maybe an estimate is only required) and using the correct units. It could mean communicating (listening, reading, writing, and speaking) precisely by using correct vocabulary and symbols. And THIS is specifically what I would like them to workon today. Work on using correct notations to communicate to others the key features of the graphs.

Students should complete the five problems on the Shifting and Key Features of Basic Functions worksheet today in class. One goal of this lesson is for students to have time to work on this in class so that they can get help on any concepts they don’t understand. I am not going to limit the questions students ask today. Instead, I plan to just make myself available in the classroom and have students come sit down with me when they need some extra tutoring. This will allow me to do some small group tutoring to catch up struggling students. When I do a ‘tutoring station’ like this, I am sure to not sit at my desk. Typically, I pull up together a few student desks on the side or back of the room (somewhere I can still keep an eye on the class and that my students feel I am accessible). Then I like to have some whiteboards and markers available to assist with tutoring. Due to not working the classroom as much as I normally do and the fact that I am not sure how motivated my students are going to be, I am planning on ‘collecting’ (or really just walking around and checking it off on a roster) and grading this worksheet on completion.

**Tip for newbies: **New teachers: stop collecting so many papers! That was the best advice I ever received from a veteran teacher. Eventually we hope to get our students so intrinsically motivated to learn mathematics that we won’t need to score their work other than for the sake of providing feedback, however, my students aren’t there yet. So if I do feel the need to check in on their work, I like to just carry around a clipboard and check off whether or not a student has completed the work. They then get a stamp for completion and are asked to go file their paper in their folder (I have 5 crates labeled by period with a manila folder with students’ names). I tell students that I will go back and look at it in more detail later. Does that happen? Not typically. :)

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**Narrative: **In the last few minutes of class today, have students stop and summarize today’s learning by writing a Postcard to Absent Student. If you choose to do so, now would be a good time to check students work while they decompress the learning for today.

**Preparation:** You may want to have index cards available for students to complete today’s closure on. I think it helps to have this limited space to write so that students are required to summarize the learning instead of writing about everything.

#### 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: Getting to Know You, Getting to Know All About You...
- LESSON 2: Ahoy team! What can you see? Finding functions.
- LESSON 3: Function Zoo - Basic Function Families
- LESSON 4: Parent Functions
- LESSON 5: Shifting Functions: How do they move?
- LESSON 6: Shifting Functions: How can we describe them?
- LESSON 7: Dicey Functions Day 1: Piecewise functions are basic functions... just cut up!
- LESSON 8: Dicey Functions Day 2: Piecewise functions are basic functions... just cut up!
- LESSON 9: Fun with Functions: Basic Inverse and Function Operations
- LESSON 10: Compositions in Context
- LESSON 11: Inundated with Inverses: Restricting the Range of an Inverse (Day 1 of 2)
- LESSON 12: Inundated with Inverses: Algebraic Inverse and Composition to Verify (Day 2 of 2)
- LESSON 13: Jeopardy: Basic Functions
- LESSON 14: Review Day
- LESSON 15: Test Review
- LESSON 16: Basic Functions Test