## Real Life- Absolute Value Functions Day - Section 4: Modeling with Absolute Value Functions

# Absolute Value Functions: Transformations Day 2

Lesson 21 of 24

## Objective: Students will be able to use transformations of absolute value functions to graph, model and solve absolute value inequalities.

#### Warm Up and Homework Check

*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. The video narrative explains this lesson’s warm up where students demonstrate understanding of yesterday's content as they use transformations to solve an absolute value equation graphically.

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

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This is the second day of a two-day lesson. The PowerPoint includes the material from both days as each class will have finished the first portion in different places. Please go to **Absolute Value Functions Day 1** for for more information on the first portion of the PowerPoint.

The goal of this section is to give the students an opportunity to Practice Graphing the transformations that they just learned. There are several problems for them to graph and then each student writes the equation of an absolute value function that includes transformations. The students switch with their partner to graph. Once they have graphed their partner’s equation, they switch back and check each other’s work (**Math Practice 3**).

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My students have already looked at inequalities but this will be their first experience with Inequalities that aren’t linear (at least since Algebra 1). This extension should make sense to them. There are two inequalities to graph and shade. I have them check their partner’s work before we discuss it as a class. I always encourage them to use a test point to check their shading.

Depending on the class, we may discuss points the solution sets to these absolute value inequalities. We looked at this during the lessons on equalities but I find that sometimes it doesn’t hurt to talk about it again. One method of reviewing would be to have students take turns giving each other points on the coordinate plane and stating whether they are solutions.

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The final portion of the lesson gives students the opportunity to write the equation of an absolute value graph using a real life scenario. The students get to take information they just learned and use it in a new way (**Math Practice 1**). There are two scenarios, one using the reflection of the sun and the other a miniature golf shot, that provide students with two points on an absolute value graph. I will provide the students with a short introduction and then let them grapple with it with their partner. If there is time, I will use the **Note Card Activity**. If not, we will discuss it as a class.

Some scaffolding may need to be provided to individual pairs as they work. I always recommend that they graph the points and sketch the absolute value if they haven’t done so. If they need more help, I ask if there are any vertical or horizontal translations. The stretch/shrink may be problematic. Since each side is linear, the concept of slope can be used here, however I am careful of this as students want to extend that to non-linear functions later on. I like to refer the students back to the fact that this is a stretch/shrink.

These problems were adapted from problems found here and here.

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#### Exit Ticket

*2 min*

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

This Exit Ticket asks students to graph an absolute value inequality.

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The goal of this Homework is to reinforce the skills learned in the last two lessons. The first eight problems ask students to graph absolute value equations and inequalities. The goal of these is to help students master each type of transformation. The next two problems give students an absolute value graph and ask them to write the equation. The final pair of problems are similar to the miniature golf problem in the lesson. The second of these is an extension problem that will push students (**Math Practice 1**) because the center of the absolute value is not as obvious. I will use this one as extension depending on my students.

This assignment was created with **Kuta Software**, one of my favorite educational tools.

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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: Mathematical Modeling: Properties of Functions Day 1 of 2
- LESSON 2: Mathematical Modeling: Properties of Functions Day 2 of 2
- LESSON 3: Mathematical Modeling: Linear Functions
- LESSON 4: Mathematical Modeling: Linear Functions Design Project
- LESSON 5: Finding Equations of Parallel and Perpendicular Lines
- LESSON 6: Inverse Functions
- LESSON 7: System of Equations Day 1 of 2
- LESSON 8: Systems of Equations Day 2 of 2
- LESSON 9: Modeling Systems of Equations
- LESSON 10: Function Review
- LESSON 11: Function Mid Test
- LESSON 12: The Tortoise and The Hare Project Day 1
- LESSON 13: The Tortoise and The Hare Project Day 2
- LESSON 14: The Tortoise and The Hare Project Day 3
- LESSON 15: The Tortoise and the Hare Project Day 4
- LESSON 16: The Tortoise and the Hare Piece-wise Functions
- LESSON 17: Step Functions
- LESSON 18: Absolute Value Equations
- LESSON 19: Absolute Value Inequalities
- LESSON 20: Absolute Value Functions: Transformations Day 1
- LESSON 21: Absolute Value Functions: Transformations Day 2
- LESSON 22: Functions Test Review Day 1
- LESSON 23: Functions Test Review Day 2
- LESSON 24: Functions Test