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# Comparing Absolute Value Functions

Lesson 6 of 9

## Objective: SWBAT describe the effects of transformations on the graphs of absolute value functions with and without graphing the functions.

#### Warm-Up

*30 min*

I plan for students to get started right away on this Warm-Up. Even though it may seem unnecessary, many of my students are still using number lines to complete data tables. This warm-up is a good chance to continue to encourage students to use different representations. I also want to encourage them to think more carefully about which information they need to find about a function. My students do not always begin by identifying the missing, needed information.

Using shortcuts, my should be able to complete all of the representations of one of these functions. The higher levels within this lesson will push students to make more generalizations or think in different ways. I plan to give students a good chunk of time to work on this warmup. I will also circulate to ask them lots of questions.

New tasks are included on this warm-up. I want to give students the chance to think more deeply about absolute value, now that they are familiar with the functions. I am trying the approach of starting by examining functions and then applying this to equations and inequalities.

My students will spend most of their time on section 1 today. I plan to give them more time in the following days to understand the equations and inequalities.

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#### Closing

*5 min*

After today, students should possess a general understanding about how changes to the function (or the verbal description) cause transformations in the graph. As we close out the lesson, I ask my students to consider this big idea: **Can you simply look at the function rule, or the verbal description, and immediately know how the graph will look? **

My goal is to encourage students to recognize that this is a good way to be thinking -- this is a time for them to learn to make productive generalizations (**MP7**, **8**). It is also a time to talk about the advantages of using models. As generalizations of a pattern or a pattern of behavior, models can save you time in the long run, as long as you know when to apply them. Explicitly discussing this with students helps make these words and ideas part of the classroom culture, supporting the development of mathematical practices.

As an Exit Ticket, I ask students to write something down that describes the generalizations they are making about these functions, as well as any lingering questions they have. I will be happy if a student produces a really thorough or well-organized generalization. I will look through what they write for examples to share with the class. I want my students to naturally look for these generalizations, and to think consistently about the best ways to organize them and present them (**MP6**).

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Exploring Distance Functions
- LESSON 2: Further Exploration of Distance Functions
- LESSON 3: From Descriptions to Graphs without Data Tables
- LESSON 4: More Distance Functions
- LESSON 5: Comparing Piecewise and Absolute Value Functions
- LESSON 6: Comparing Absolute Value Functions
- LESSON 7: Sometimes, Always, Never with Absolute Value
- LESSON 8: Absolute Value Equations and Inequalities
- LESSON 9: Absolute Value Summative Assessment