Absolute Value Functions: Transformations Day 2

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Objective

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

Big Idea

Students model sun reflection and miniature golf in this extension on the transformation of absolute value functions.

Warm Up and Homework Check

10 minutes

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.  

Graphing Transformations Guided Practice

13 minutes

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).  

Graphing Absolute Value Inequalities

10 minutes

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.  

Modeling with Absolute Value Functions

15 minutes

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.

Exit Ticket

2 minutes

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.

Homework

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.