Summary
This lesson is Part 4 of the Journey of the Isolated Variable lesson series. Students will build on their prior knowledge of solving equations in order to learn how to solve absolute value equations. Students will compare and contrast the four types of equations: two-step, multi-step, literal, and absolute value equations.
Essential Question(s)
How do I solve absolute value equations with one variable?
Snapshot
Engage
Students draw connections to solving other types of equations by completing a Brain Dump about equations and absolute value.
Explore
Students explore absolute value equations using number line in a Desmos Activity.
Explain
Students analyze their understanding through a flowchart.
Extend
Students identify the error another "student" made while solving an absolute value equation, correct the error, and justify the mistake and their correction.
Evaluate
Students compare and contrast the four types of equations through an Exit Ticket by solving, justifying their steps, and stating the uniqueness of the type of equation.
Materials
Student devices with access to internet
Lesson Slides (attached)
Step-by-Step Desmos Activity handout (attached, for teacher use)
Absolute Value Equations Flowchart (attached, 1 per student)
Explain Example Answers (attached, for teacher only)
Engage handout (attached, 1 per student)
Explore Record Sheet (attached, 1 per student)
Extend handout (attached, 1 per student)
Extend Answer Key (attached, for teacher only)
Exit Ticket (attached, 1 per student)
Engage
Introduce the lesson using the attached Lesson Slides. Go to slide 3 to display the lesson’s essential question: How can I solve for absolute value equations with one variable? Go to slide 4 to share the lesson’s learning objective with students. Review this with your class to the extent you feel necessary.
Go to slide 5. Students will complete a Collective Brain Dump activity. Give students the Engage handout. During this activity, students will individually write down everything they know about equations and absolute value in the columns on their handout. Give the students about two minutes to have time to write what they might know.
Next, invite students to get into small groups of 2-3 students. You can either already have groups created or let students choose their groups. Within their groups, have students compare their lists of information. Students should add items to their list as their peers share within their group.
Once all students have had the chance to share in their groups, go to slide 6. Create a class list of knowledge the class has about equations and absolute values.
Explore
To introduce the explore activity, refer to the absolute value list created in the engage. Highlight some of the key items the students stated from their knowledge.
Go to slide 7. Students will work through the Desmos activity to see how numbers inside of absolute value equations can be different in order to equal a specific distance. Give students the Explore Record Sheet. Invite them to write their process for solving slides #11-15. Slide numbers are in the top right corner of the Desmos activity. This activity will help with the Explain portion of the lesson.
Explain
Once students have completed the Desmos activity, go to slide 8. As a whole class, discuss how the students determined their answers for the Desmos activity. Ask the following questions:
What key items helped you determine where the sliders should be moved to?
Why do you think those items are important?
How might one solve the problems in a different way?
Go to slide 9. Provide an Absolute Value Equations Flowchart to each student. Using the example provided on the slide and the flowchart steps, show students how to follow the steps to solve an absolute value equation. The first example will be an easier problem for them because they can answer "no" to the first step.
Go to slide 10 for another simple absolute value equation. As students begin to comprehend how to follow the steps of solving absolute value equations using the flowchart as a guide, begin to introduce harder problems that require a “no” on each flowchart step, such as the examples provided on slides 11-13. Feel free to add, delete, or modify the equations given to best fit your students' needs.
Extend
Go to slide 14. Provide an Extend handout to each student. Each of the three problems is an example of an error another "student" made in their steps while solving the absolute value equation. Students are to complete all four steps for each of the problems.
Step 1: Identify the error in solving the absolute value equation. Students can complete this step a variety of ways. Students can circle, highlight, or star where the error occurred.
Step 2: Correct the error by showing correct steps. Students may complete the correction on the handout or a separate sheet of paper to be attached to the handout at the end.
Step 3: Explain how/why the student might have made the error. This step allows students to think about what the common mistakes are when solving absolute value equations in order to be less likely to make the same mistakes in the future.
Step 4: Justify the correct answer and steps taken. Students need to be able to communicate their mathematical thinking. By justifying their answer and steps, students are using math vocabulary and process skills to communicate their understanding.
After students have completed the handout individually, go to slide 15. Either place students in groups of three or let students choose their group of three. Within the group, each of the students will pick one of the absolute value equations to verify the four steps as identified above.
Evaluate
Go to slide 16. Students will complete an Exit Ticket to close this lesson. Provide each student with an Exit Ticket handout. They will use the handout to solve an example of each type of equation. Students will also justify how they solved the equation and explain what is unique about that equation type. Encourage the students to go beyond the idea that numbers or operations are unique for each equation type.
Resources
Desmos. https://teacher.desmos.com/activitybuilder/custom/5ec2d10f4748f47be91b6681
K20 Center. (n.d.). Bell ringers and exit tickets. Strategies. Retrieved from https://learn.k20center.ou.edu/strategy/d9908066f654727934df7bf4f505d6f2
K20 Center. (n.d.). Collective brain dump. Strategies. Retrieved from https://learn.k20center.ou.edu/strategy/baee4e90c5fa1a7060ca04dd8b00450e