# Journey of the Isolated Variable, Part 4

## Absolute Value Equations

Amber Stokes, Matthew McDonald, Amber Stokes | Published: July 13th, 2022 by K20 Center

• Subject Mathematics
• Course Algebra 1
• Time Frame 2-3 class periods
• Duration 120 minutes

### Summary

In this lesson, students will build on their prior knowledge of solving equations to learn how to solve absolute value equations. Students will then compare and contrast the four types of equations: two-step, multi-step, literal, and absolute value equations. This is the fourth lesson of four in the “Journey of the Isolated Variable” lesson series.

### Essential Question(s)

How do I solve one-variable absolute value equations?

### Snapshot

Engage

Students draw connections among different types of equations by participating in a Collective Brain Dump activity about the terms "equations" and "absolute value."

Explore

Students explore absolute value equations by using number lines in a Desmos Classroom activity.

Explain

Students analyze their understanding of absolute value equations through a flowchart.

Extend

Students complete three "find the error" problems in which they identify the error another "student" made while solving an absolute value equation. Students then correct the error, explain how one might have made that error, and justify the correct answer.

Evaluate

Students compare and contrast the four types of equations on an Exit Ticket by solving an example of each, justifying their steps, and explaining what is unique about each type of equation.

### Materials

• Lesson Slides (attached)

• Engage handout (attached; one per student; printed front only)

• Explore Activity handout (attached; one per student; printed front only)

• Flowchart Absolute Value Equations (attached; one per student; printed front only)

• Flowchart Answer Key (attached; for teacher use)

• Extend handout (attached; one per student; printed front only)

• Extend Sample Responses (attached; for teacher use)

• Exit Ticket (attached; one per student; printed front only)

• Chromebooks or student devices with internet access

• Pencils

• Paper

### Engage

10 Minute(s)

Introduce the lesson using the attached Lesson Slides. Display slide 3 to share the lesson’s essential question: How do I solve one-variable absolute value equations? Display slide 4 to go over the lesson’s learning objective. Review these slides with students to the extent you feel necessary.

Go to slide 5. Introduce students to the Collective Brain Dump strategy. Pass out the attached Engage handout to each student. Instruct students to individually write down everything they know about the terms "equations" and "absolute value" in the designated columns on their handout. Give students about 2 minutes to write what they know.

Next, invite students to get in small groups of two or three students. You may assign groups or let students choose their groups. Within each group, have students compare their lists of information. Guide students to add new items to their lists as their group members share out.

Display slide 6. Once all students have had the chance to share in their groups, have a whole-class discussion. On the slide, create a collective list of knowledge the class has about "equations" and "absolute value."

### Explore

30 Minute(s)

Display slide 7. Then, have students go to student.desmos.com and enter the session code.

Pass out the attached Explore Activity handout to each student. Introduce the activity by referring to the "absolute value" list created during the Engage section of the lesson, highlighting some of the key items that students shared. Let students know they will use the handout to write down their thought process for solving the problems on screens 12–16 in the Desmos Classroom activity. Screen numbers are in the top-right corner of the Desmos activity.

As students are finishing screens 1–2, use student responses to see if students need a review before moving forward.

On the Dashboard, press the plus sign three times to allow students to progress to screens 3–5. As students finish screen 5, bring the class together to share and explain their thinking for how they found the distance between two values.

Press the plus sign three times on the Dashboard to allow students to progress to screens 6–8. As students finish screen 8, again bring the class together to share their expression for finding the distance between any two numbers.

On the Dashboard, press the plus sign three times to allow students to progress to screens 9–11. As students complete screen 11, ask for volunteers to share the x-value they found that was a solution to |x – 6| = 5. Ask students how many solutions they think there should be. Then ask for volunteers to share their sentence that represents that absolute value equation.

On the Dashboard, click the orange "Stop" button; now students can complete the Desmos activity at their own pace. Remind students to use their handout for screens 12–16, where they will be illustrating absolute value equations on a number line. Desmos is designed to give students feedback on screens 12–14. Use the Teacher Dashboard to provide students feedback for screens 15–16.

As students complete the Desmos Classroom activity, ask for volunteers to share their description of the process of solving absolute value equations that they typed on screen 17.

### Explain

30 Minute(s)

Display slide 8. As a whole class, discuss how students determined their answers in the Desmos Classroom activity. Ask the following questions:

• What key parts helped you determine where the sliders should be moved?

• Why do you think those parts are important?

• How might one solve the problems in a different way?

Display slide 9. Pass out a copy of the attached Flowchart Absolute Value Equations handout to each student. Using the example equation provided on the slide and the flowchart steps, show students how to follow the steps to solve an absolute value equation. The first two examples will be easier problems for them because they can answer "Yes" to the first step.

Go to slide 10 for another simple absolute value equation. Have students work with a partner to complete example 2 using the flowchart. As students begin to comprehend the steps of solving absolute value equations while using the flowchart as a guide, introduce harder problems that require a "No" on one or both of the flowchart steps, such as the examples provided on slides 11–13. Challenge students to try the fourth example (on slide 12) on their own then compare their results and work with their partner. Feel free to add, delete, or modify the equations to best fit students' needs.

### Extend

30 Minute(s)

Display slide 14. Pass out a copy of the attached Extend handout to each pair of students. Each of the three problems contains an error that another "student" made in their steps while solving an absolute value equation. Direct pairs of students to complete all four of the following steps for each problem. Inform students how you would like them to communicate their thinking for each step.

• Step 1: Identify the error in solving the absolute value equation.

• Step 2: Correct the error by showing the correct steps.

• Step 3: Explain how and why a student might have made that error.

• Step 4: Justify the correct answer and steps taken.

After students have completed the handout, display slide 15 . Have pairs find two other pairs of students (creating groups of 6). Within the new group of 6, have students organize the questions into stacks of Problem 1, Problem 2, and Problem 3. Then have two students pick one of the absolute value equations to verify the four steps as identified above, such that all of the questions are reviewed.

### Evaluate

20 Minute(s)

Display slide 16. Students will complete an Exit Ticket to close this lesson.

Pass out a copy of the attached Exit Ticket handout to each student. Direct students to work independently to solve each type of equation. Instruct students to also complete the table by justifying how they solved each equation and explaining what is unique about that equation type. Encourage students to go beyond the idea that numbers or operations are unique to each equation type.