I Absolute(ly) Don't Care About Direction: Solving and Proving Absolute Value Equations and Inequalities
Lesson 7 of 10
Objective: SWBAT...1. Solve one variable equations and inequalities with absolute values. 2. Graph absolute value equations as functions.
I like to use Entry Tickets that are grounded in a real-world scenario to help make the concepts relevant to students. Absolute values are a bit difficult to apply in a meaningful way to model scenarios, but this example gets at the difference in being interested in how much money someone makes/loses (direction matters) verses the total amount of money that changes hands (direction doesn't matter).
For the Compliance Officer example, the idea is that students have to take the absolute value for each day that Sam trades, and not the absolute value of the sum of the money he won/lost. This lends itself to a nice discussion around the rules and patterns of absolute values.
Instructional Note: The emphasis of this lesson is aligned with a Massachusetts Common Core Standard - A.REI.MA.3.a. The MA Standard specifically addresses solving absolute value equations and inequalities. This lesson also aligns with the Common Core Standard A-REI.3 on solving equations and inequalities.
The next section of class is a mini, 15 minute Active Note-Taking section. Students watch a Khan Academy video on Solving Absolute Value Equations. During the time, students are taking Two-Column Notes.
I also pause the video throughout and ask students to engage in Turn and Talks to complete a problem with a partner and then compare their own steps with those demonstrated in the video.
The next section of class is a mini, 15 minute Active Note-Taking sections. Students interact with a Khan Academy video on Solving Absolute Value Inequalities. During the time, students are actively taking Two-Column Notes.
I also pause the video throughout and ask students to complete Turn and Talks to complete the problem with a partner and then have them compare their steps with that of the video.
I typically only present one topic per class using the Explicit Instruction and Active Note-taking strategies. However, the topics of absolute value equations and inequalities are closely related and due to time and pacing, I decided to provide Explicit Instruction on both topics back to back. I then provide students an opportunity to practice both skills (solving absolute value equations and inequalities) later in the lesson.
For this section I have students work in groups to practice solving absolute value equations and inequalities. There are a number of sources I like to use for implementing this activity.
- The Oswego City School District Regents Exam Prep Center has a good set of practice problems for both Absolute Value Equations and Absolute Value Inequalities in their Algebra 2/Trig. prep center.
- Kuta Software has free worksheets on the topic in their Algebra I section. The links to the free worksheets are here:
- Absolute Value Equations Worksheet
- Absolute Value Inequalities Worksheet
I sometimes implement this section of the lesson using a Jigsaw or a Gallery Walk strategy. Both of these instructional strategies allow students to solve problems at a level of diffculty that is "just right" not too hot and not too cold.
Although this section of class does not involve a lot of application and/or modeling, the skills themselves involve higher order thinking which is why I focus on providing students time to process and practice solving absolute value equations and inequalities.
For today's Exit Ticket the class revisits some problems about the stock trader and the compliance officer. This exit ticket can be used in a number of different ways in the classroom. The assignment can be used as a formative assessment to assess student understanding of solving absolute value equations and inequalities. The assignment can also be split and rolled into a homework assignment where students are given the last few minutes of class to begin with the remainder due for homework next class.
The Exit Ticket also lends itself to a writing assessment for which students translate their mathematical reasoning into a well-structured written response. I have included a blank copy of the Idea Organizer as one possible support for students to organize their thoughts for a written response.
For homework I assign a problem set on Delta Math. I typically have students complete ten problems in a row, with a penalty of one for an incorrect response. In other words, if students complete the first 8 problems correctly, but then get the 9th incorrect, then they have credit for 7 in a row and need to complete 3 more problems in a row to get full credit for the assignment.
For a great overview video on Delta Math and how to set up an account (it is free!), click here: Delta Math Overview Video
As an alternative, the Exit Ticket for this lesson can be utilized as a homework assignment (see Exit Ticket section of this lesson for more info.!)