Solving Absolute Value Equations Scaffolded

Absolute value is a challenging for many students. Absolute value equations add an extra layer of challenge. This post presents a scaffolded handout. It starts with an initiation addressing absolute value and then is followed by scaffolded steps for solving that address written and mental steps.

The Scaffolding

The scaffolding walks students through mental steps to unpack the underlying concepts. The first is a general concept of absolute value. The next two are specific to the problem. At the end, students are prompted to check the solutions to reinforce the concept of two possible values, one being negative and one positive. Note: this is not addressing the case of =0.

Initiation

The scaffolded handouts are preceded by an initiation. The focus is to unpack the concepts underlying the equation steps. The key is for the students to understand that there are two possible solutions (aside from =0). The handout addresses the reason for two solutions and provides work with the absolute value symbol in this context. Here is a link to a Jamboard that helps unpack the concept of absolute value.

Blank Templates

There are 3 practice problems with the template. I use 2 and 6 to help compare the different situations. There is another page with blank templates.

Accessing the Handout

Here is a link to the handout.

Introduction to Absolute Value – Distance from Home

Here is a Jamboard to introduce the concept of absolute value (make a copy and you can edit – see photo at bottom of this post).

Start with prior knowledge of how many houses a child is from home. Emphasize that the number of houses is positive.

Change the setting from a row of houses to the number line and refer to the distance from home.

Change from distance to absolute value and emphasize that the symbol indicate distance from home and is called absolute value.

The house is removed and introduce the concept of the distance from 0.

Finally, convert from boys to the numbers and the distance from 0 for a number. Emphasize that the distance is positive, even for negative numbers.

To make a copy of the Jamboard.

Absolute Value is Absolutely not the Opposite

I have frequently encountered the presentation of absolute value as a positive value or opposite. This is part of the repertoire of memory devices we (certainly I have in the past) use as a short cut to learning how to do the steps for a problem. The meaning of the absolute value of a number is it’s distance from 0 (below).

Below is an image of a Do Now or Initiation handout I use to introduce absolute value. From the start I focus like a laser on the meaning of distance for absolute value. I start with a situation that may be prior knowledge for them. Then take a step towards the mathy part with the numbers and slowly make my way to the symbol.