Summary
In this lesson, students build on prior knowledge of solving equations to learn how to solve absolute value equations. Students then compare and contrast four types of equations including two-step, multi-step, literal, and absolute value equations. This is the fourth lesson in the four-part "Journey of the Isolated Variable" lesson series.
Essential Question(s)
How do you solve one-variable absolute value equations?
Snapshot
Engage
Students participate in a Collective Brain Dump activity on the terms “equations” and “absolute value” and draw connections between different types of equations.
Explore
Students solve absolute value equations using number lines in a Desmos Classroom activity.
Explain
Students solve absolute value equations and analyze their understanding of absolute value using a flowchart.
Extend
Students identify errors made in solving absolute value equations then correct the error, explain why the error was made, and justify the correct answer.
Evaluate
Students complete an Exit Ticket in which they solve examples of four types of equations and explain how each equation is unique.
Materials
Lesson Slides (attached)
Engage handout (attached; one per student)
Explore Activity handout (attached; one per student)
Flowchart handout (attached; one per student)
Flowchart Answer Key document (attached; for teacher use)
Extend handout (attached; one per student)
Extend Sample Responses document (attached; for teacher use)
Exit Ticket handout (attached; one per student)
Chromebooks or student devices with internet access
Pencils
Paper
Engage
10 Minute(s)
Introduce the lesson using the attached Lesson Slides. Display slide 3 and read aloud the lesson’s essential question, “How do you solve one-variable absolute value equations?” Display slide 4 and introduce the lesson objective.
Transition to slide 5 and introduce the Collective Brain Dump activity to students. Distribute one copy of the attached Engage handout to each student. Instruct students to write down everything they know about the terms “equations” and “absolute value” in the designated columns. Tell students to use words, pictures, symbols, and more to describe the terms. Allow students two minutes to complete the activity.
Organize students into small groups of two or three either by assigning groups or allowing students to choose groups. Tell students to compare their individual lists to those of their group members and add any new information to their lists as group members share.
Once all groups members have had the opportunity to share their responses, display slide 6. Lead a whole class discussion in which you invite students to share out what they know about equations and absolute value. As students share, add their responses to the slide under the appropriate columns.
Explore
30 Minute(s)
Display slide 7. Instruct students to navigate to student.desmos.com and enter the session code present on the slide.
Give each student one copy of the attached Explore Activity handout. Introduce the activity by reviewing students’ responses about absolute value from the Engage phase of the lesson. Guide students’ attention to the handout and tell them that they will complete a series of problems during the course of the Desmos Classroom activity. Notify students that once they arrive at screens 12–16 they will record the reasoning for their answers on the handout.
Have students begin the activity and complete screens 1–2. As students complete the problems, review their responses to see if some students need a review of concepts before proceeding.
Return to the dashboard of the activity and select the plus sign three times to allow students to progress through screens 3–5. Once students have completed screen 5, initiate a whole class discussion and invite students to share out their answers and explain how they found the distance between two values.
On the dashboard, select the plus sign three times to allow students to progress through screens 6–8. Once students have completed screen 8, initiate another whole class discussion and have students share out their expression for finding the distance between any two numbers.
Return to the dashboard and select the plus sign three times to allow students to progress through screens 9–11. After students complete screen 11, ask volunteers to share out the x value they found for the equation |x – 6| = 5.
Ask students how many solutions they think there are for that equation. Then, ask volunteers to share the sentence they created to describe the absolute value equation.
Click the orange “Stop” button on the dashboard, which will allow students to complete the activity at their own pace. Direct students to complete screens 12–16, which require students to illustrate absolute value equations on a number line. Remind students to record their reasoning for each problem on their Explore Activity handouts.
As students complete the activity, invite volunteers to share out their processes for solving absolute value equations that they described on screen 17.
Explain
30 Minute(s)
Display slide 8. Invite students to share how they determined the answers to the questions in the Desmos Classroom activity. Use the following questions to guide the discussion:
What key details helped you determine where the sliders should be moved?
Why do you think those details are important?
How might one solve the problems in a different way?
Display slide 9. Pass out a copy of the attached Flowchart handout to each student. Using the example equation on the slide, guide students through the process to solve for x. Prompt students to respond with “yes” or “no” to each question as you follow the steps. This equation will be easier for students to solve, as they can answer “yes” to the first step.
Transition to slide 10 and introduce students to the next absolute value equation. Similar to the equation on slide 9, students can answer “yes” to the first step on the flowchart for this equation as well. Have students work with a partner to complete this example using the flowchart. As they work, walk around the room to ensure that students are properly using the flowchart, guiding those that need help if necessary.
Once the majority of students have complete the equation on slide 10, transition through slides 11–13 to introduce increasingly difficult problems. These problems require students to answer “no” to the first step on the flowchart. Challenge students to try the example on slide 12 individually then compare their results with their partner.
Extend
30 Minute(s)
Display slide 14 and pass out one copy of the attached Extend handout to each pair of students. Tell students that each problem contains an error that another “student” made when solving the absolute value equation. Have to students complete the steps below for each problem and explain to them how you want them to document 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. Instruct pairs to join up with two other pairs of students to create groups of six. Have groups of six organize their papers into three stacks—one stack for each problem.
Tell groups to then organize back into three pairs and have each pair choose a problem. One pair will work on Problem 1, another on Problem 2, and another on Problem 3. Explain that pairs should review the papers for their chosen problem and verify the four steps identified earlier.
Evaluate
20 Minute(s)
Display slide 16 and give each student one copy of the attached Exit Ticket handout. Instruct students to complete each type of equation independently. Tell students to additionally justify how they solved each equation and explain what is unique about that type of equation in boxes below each problem. Help students to understand that the numbers and operations used in each equation are not unique to only that equation type.
Resources
K20 Center. (n.d.). Bell ringers and exit tickets. Strategies. https://learn.k20center.ou.edu/strategy/125
K20 Center. (n.d.). Collective brain dump. Strategies. https://learn.k20center.ou.edu/strategy/111
K20 Center. (n.d.). Desmos classroom. Tech tools. https://learn.k20center.ou.edu/tech-tool/1081
Stokes, A. (n.d.). Journey of the isolated variable, part 4 [Interactive activity]. Desmos. https://teacher.desmos.com/activitybuilder/custom/5ec2d10f4748f47be91b6681