Math = Love: Guest Post: Solving Absolute Value Equations with a Little Creativity

## Friday, November 18, 2016

### Guest Post: Solving Absolute Value Equations with a Little Creativity

Good morning!  Today, I'm happy to share a guest post with you from Beaura Cavalier. She is a high school math teacher in Arkansas, and I am so excited to share with you what she has to say about teaching students to solve absolute value equations with a little creativity.  I'll let her take it away!

I was trying to find a way to help my Algebra 1 students remember how to do Absolute Value Equations. During a class, I came up with the following analogy.

Okay, so here is the problem.

The prisoners (3x – 1) are in jail (absolute value bars). They want to get out of jail, but first they have to wait until their visitors (any number outside of the absolute value bars) leave. So, add, subtract, multiply, or divide (on both sides of the equation) to get their visitors to leave.

Now that you have the prisoners all by themselves (in their jail cell) on one side of the equal sign, they prisoners can get parole! Once they are released from jail, they have two options. They can choose to be good (equal to the positive of whatever is on the other side of the equal sign) or they can choose to be bad (equal to the negative of what is on the other side of the equal sign).

Then solve both equations to get two values for x.

The students laughed at my ideas, but now they are quick to point out that the prisoners have the choice of being bad or good, so x has two values!

Thank you so much Beaura for sharing a bit of your classroom with us!

1. LOVE this! Big props to you, Beaura! I am going to use it next month when we get to abs value functions. Thank you!
-snapdragon

1. Glad you found it useful!

1. Thank you for some food for thought!

2. Exactly my thought Aaron.

3. Aaron, For many of my students, mathematical thinking is a struggle. Just as math teachers use "Please Excuse My Dear Aunt Sally" to help students remember the Order of Operations, my prisoner description is just a memory tool to help them remember the order of the steps to solve absolute value equations.

4. @Beaura I would write a similar reply regarding teacher use of PEMDAS. I would point readers to the article "Questioning the Order of Operations" in Mathematics Teaching In The Middle School, October 2016. MTMS has additional articles on this topic from March of 2011, December of 2002. Teaching Children Mathematics has articles from February 2012 and August 2015 specifically on PEMDAS and more generally on forgoing rule, memory driven mathematics instruction. I'd be happy to provide PDF's of these articles (just don't tell NCTM).

We need to get away from the idea that math is about rules and remembering stuff. It isn't. It's about structures and strategies and flexible thinking. In what ways can our instruction engender flexible strategic thinking rather than an adherence to rules, mnemonics, and organizational tools?

3. I have a comparable one I've used for middle-schoolers since a class first sniggered: when things cuddle up, they multiply.

1. I use that too! And then I tell them that the product is their 'maths baby'. So many groans, so much remembering.

2. Oh my goodness. I haven't heard this one!