SWBAT solve Absolute Value Equations and Inequalities

Students will use a graphing calculator and writing compound inequalities to develop a conceptual understanding compared to memorizing.

10 minutes

This is Day Two of this lesson, so I use the Warm Up to access my students' prior knowledge. I expect for this Warm Up to take about 15 minutes for the students to complete and for me to review with the class. I ask my students to solve one Absolute Value Equation and two Absolute Value Inequalities. I designed the Warm Up to give us the opportunity to review the different types of solutions that result from solving these problems.

I make sure that each student has a copy of the Exit Slip from yesterday's lesson. Some students completed it in class or as homework and still have it. If students forget their Exit Slip, I have them review with the use of their table partner's Exit Slip.

I demonstrate reviewing the Warm Up in the video below.

15 minutes

After reviewing the Warm Up with the students, I hand each student a copy of today's Graphing Activity. The Activity asks students to solve Absolute Value Equation and Inequalities using graphs on the coordinate plane. In the last part of the Graphing Activity, I have students solve the Absolute Value Equation and Inequalities by dropping the Absolute Value and writing it as two Compound Inequalities. I review parts of the Graphing Activity in the video below.

15 minutes

The Independent Practice is a formative assessment to check for student understanding at the end of this two-day lesson. The goal of this two-day lesson was for students to build a deep understanding from a variety of different methods, and to be able to apply them to solve Absolute Value Equations and Inequalities. Students are usually more successful at solving Absolute Value Equations, but I did not want students to just memorize the procedure of solving Absolute Value Inequalities with no understanding.

If students recognize a pattern based from the conceptual understanding and continue to apply it correctly, it is still different than memorizing. If students forget the set up of the problem or the steps, the hands on activities should help them recall why a problem is set up a certain way. By moving from the concrete hands on activities to the more abstract inequalities themselves, it should be easier for students to make connections and solve.

10 minutes

The goal for this two-day lesson was for my students to be able to solve absolute value equations and inequalities using deep conceptual understanding instead of just memorizing the procedures. To see how much progress we made, with 10 minutes left in the period, I have students compare their Independent Practice with their assigned table partner. I have the partners work in homogeneous groups. If necessary, students may complete the Independent Practice as homework.

**With their partner, students are to compare their answers, and if there is a discrepancy, review and discuss until a solution is agreed upon.** Once a solution is agreed upon, I want students to report on a piece of paper, the number of the problem, and the mistake that was made. I also want students to summarize the discussion that happened as they determined the correct solution. I want to know what method that the two students applied to solve the problem (**MP3**). I ask students to complete a report on at least one problem before they leave. This report of corrections is to be handed in as an Exit Slip. If time permits, students can complete another problem. If the table partners do not find any mistakes, I will ask them to find another pair that is having trouble agreeing on an answer. With the new pair, they should complete a report on one problem.

I have provided an example of common mistakes made on Number 10 of the Independent Practice. The first example shows a student that automatically assumes that the answer is no solution when it has the -12. The second example shows a student going through the process of solving the inequality despite the negative. The third example is the actual solution. When taking the absolute value of any expression or number the answer will always be positive. Therefore, for the absolute value of three x plus six to be greater than or equal to -12 is always true. The or allows the solution to be true if either greater than or equal to are true. When taking the absolute value, the answer is always greater than a negative number.

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