Solving Absolute Value Equations and Inequalities from a Graphical and Algebraic Point of View.
I have struggled with helping my students understand how to solve absolute value equations and inequalities with only one variable like |2x – 8| = 4, |2x – 8| > 4, or |2x – 8| < 4. Some of my students in the past have understood it while others have not. Most of the time they forget or do not understand to solve half the problem. The will solve the 2x – 8 = 4 or 2x – 8 > 4 but not the other halves of those two problems or they do not understand when to use a compound inequalities versus two separate inequalities separated by an “or” statement.
I started my lesson from scratch and approached the material from a graphical and algebraic point of view. You can access my video lesson at https://youtu.be/oSmeu3cwsfY
Below is an overview of the approach I took with more details in the video. https://youtu.be/oSmeu3cwsfY
Solve |2x – 8| = 4 by graphing
Use the above picture and solutions to help students see the solutions for |2x – 8| > 4, and |2x – 8| < 4.
I follow this with the details of how the algebraic method ties into the graphical and how to get the solutions algebraically.
Tying in more than one perspective in our lessons will help students better understand and make more connections with the mathematical concepts we are trying to help them learn. It is not easy to make many of these connections. It takes lot of time to think and reflection plus time to design an effective lesson but it is well worth it since it helps our students learn.