Summary
This lesson focuses on the properties of real numbers, properties of equality, and inverse operations to help students deepen their understanding of solving linear equations. Students will learn to isolate variables and apply this knowledge to more complex problems. By the end of the lesson, students will solve multi-step equations using properties of rational numbers and algebraic properties. This is the second lesson in the “Journey of the Isolated Variable” series.
Essential Question(s)
How do I isolate a variable in a multi-step equation?
Snapshot
Engage
Students activate prior knowledge by creating Picture Notes for key algebraic vocabulary terms.
Explore 1
Students use a Desmos Classroom activity to investigate how to manipulate an equation to create the smallest solution possible.
Explain 1
Students reason and abstractly argue that their expression creates the smallest possible solution through a Think-Pair-Share activity.
Explore 2
Students work in pairs to solve multi-step equations and peer-review each other's work using the Pass the Problem strategy.
Explain 2
Students review their equation-solving strategies through a Flowchart and practice solving problems using the GUS Method.
Extend
Students create word problems based on items bought and sold in a theater during a station-based Drive-in Theater activity.
Evaluate Students demonstrate understanding through an Exit Ticket.
Materials
Lesson Slides (attached)
Picture Notes (attached; one per student)
Note Catcher (attached; one per student)
Just Give Me a Reason (attached; one set per pair)
Flowchart (attached; one per student)
Create Your Own Problem (attached; one set per 5 stations; front only)
Exit Ticket (attached; one-half sheet per student)
Pencils
Paper
Chromebooks or student devices with internet access
Student dry-erase boards (optional)
Engage
10 Minute(s)
Introduce the lesson using Lesson Slides. Display slide 3 to share the essential question: “How do I isolate a variable in a multi-step equation?” Display slide 4 to review the learning objective. Discuss these slides as needed.
Display slide 5 and distribute Picture Notes handout. Instruct students to independently create Picture Notes for different algebraic vocabulary terms (e.g., associative property, inverse property, like terms, and coefficient).
Give students five minutes to work independently. Walk around the classroom to assess prior knowledge and identify areas where students may need additional guidance. Once students have completed their Picture Notes, have them set the handout aside. Inform students that they will revisit this handout later in the lesson.
Explore 1
15 Minute(s)
Display slide 6 and provide students with your Desmos session code. Ask students to go to student.desmos.com and enter the session code.
Distribute the Note Catcher handout to each student. Explain that this handout will provide them with space to record their findings and equations during the activity. Alternatively, students may use a piece of notebook paper if they prefer.
Instruct students to work individually through six screens in the Desmos activity. Each screen requires them to explore how to manipulate an equation to produce the smallest possible solution for xx. Explain that "smallest" refers to the value of xx after applying the absolute value (ignoring the sign).
Ask students to record the equations they create on their Note Catcher so they can refer to their work later. This will help them build evidence to support their reasoning during the next activity. Remind students that there is no right or wrong answer for this activity and that they should explore independently. At this stage, they should not seek assistance from their peers.
Explain 1
15 Minute(s)
In this activity, have students use the strategy Think-Pair-Share to reason abstractly and structurally why they believe their expression produces the smallest solution.
Display slide 7. Have students individually write down why they believe their equation produces the smallest solution on their original piece of paper or their Note Catcher. Give them a few minutes to process their thoughts.
Once all students are done writing their arguments, have them turn to a partner and take turns sharing their equations and why they believe their equation produces the smallest value. During that time, they also demonstrate how they got the solution. In pairs, instruct students to eliminate any misconceptions or mistakes and pick an equation they would like to share with the whole class.
Have each pair then share the equation they chose with the class. After every pair has presented their equation, have students vote on which equation produces the smallest solution.
Explore 2
20 Minute(s)
Display slide 8. Have students find a partner or assign partners. Distribute a copy of the first two pages of the attached Just Give Me a Reason handout: Problems 1–2, to each pair of students.
Explain to students how to complete the handout using the Pass the Problem strategy. Begin by instructing each student to complete the first step of their assigned problem by modeling the algebraic equation. This involves drawing the number of variables and keeping the constant written in its algebraic form. Use slide 9 to provide an example of this step.
Once students complete step 1, explain that they are to write their reasoning for their step in the second column of that row. Note that the reasoning for step one has already been completed in the handout. Take time to ensure students understand the procedure for this activity.
Move to slide 10 and instruct students to trade papers with their partners. Guide students as they check the work completed by their partner and proceed to complete the second step. If students have difficulty articulating their reasoning, encourage them to reference the vocabulary activities from this lesson or the "Journey of the Isolated Variable, Part 1".
Once students have completed Problems 1–2, display slide 13. Provide each pair of students with a copy of the third page of the Just Give Me a Reason handout. Direct students to work collaboratively to solve Problem 3.
As students complete Problem 3, bring the class together for a whole-group discussion. Ask students, "What is different about Problem 3?" Encourage students to share their observations and reasoning as part of the discussion. Use this conversation to transition into the next portion of the lesson, where you introduce a flowchart.
Explain 2
30 Minute(s)
Display slide 14 and pass out the attached Flowchart. Direct students to insert the equation shown on the slide into the top box of the flowchart. Walk students through the procedure for using the flowchart, explaining how their "Yes" or "No" responses lead them step by step to the final answer.
Move to slide 15. Using the GUS Method, give students an opportunity to practice solving equations while using the flowchart. Provide students with either a piece of paper or student dry-erase boards for this activity.
Instruct students to solve the equation displayed on the slide. Ask students to label their work in the top-right or top-left corner of their paper or board with one of the following:
G: Guessed the answer and have no clue how to solve the problem.
U: Unsure if they completed all the steps correctly.
S: Sure they understand and completed all steps correctly.
Display slides 16 and 17 to give students two more equations to solve using the flowchart and the GUS Method.
Display slide 18. Instruct students to retrieve their Picture Notes handouts from the Engage section of the lesson. Ask students to review their notes and identify if there is anything they need to add or revise based on what they have learned during the lesson.
If students have any words they are still not sure about, allow them to ask questions of you or their classmates. You may choose to provide formal definitions at this time if students have any missing definitions or parts they don’t fully understand.
Extend
40 Minute(s)
Display slide 19 and show students the video on the slide, "Winchester Drive-In Theatre [Oklahoma City]." After the video, ask students:
"If you were the owner of a drive-in theater, what would you spend money on?"
"What might be good things to offer to customers?"
"If you were a customer, what would you spend money on?"
Have students brainstorm ideas. Encourage them to think of expenses that the owner pays and to not just consider what the customers buy.
Display slide 20 and walk students through solving the word problem shown on the slide. Explain that they will create their own story problems and should consider how to solve a problem when writing it.
Display slide 21 and have students get into groups of three at each station. Explain that they will write their own story problems and solve their peers’ story problems in a process similar to the earlier Pass the Problem activity. This time, however, students will rotate between stations rather than passing papers.
Activity Procedure:
Round 1: Students write the first story problem on page A (e.g., 1A, 2A, 3A, 4A, or 5A). Allow a few minutes for students to fill in the story problem template.
Round 2: Students leave their pages at their current station and rotate to the next station. At the new station, they write their second story problem on page B (e.g., 1B, 2B, 3B, 4B, or 5B). Allow five minutes for this round.
Round 3: Students rotate to the next station, where they read both story problems (A and B) left at the station. Students write the algebraic equation they would use to solve one of the problems but do not solve it. Allow five minutes for this round.
Round 4: Students rotate again. At this station, they read the story problems, check the equation written by the previous group, and solve it. Allow ten minutes for this round.
Round 5: Students rotate to the next station, where they substitute the solution back into the equation to check the work done by their peers. If the solution is incorrect, they should review the steps, identify the mistake, and circle it. Allow five minutes for this round.
Round 6: Students return to their original station to review the work done by their peers. Have the group discuss whether the final solution aligns with their expectations. If they find a circled mistake, they should correct it and verify the solution.
After all rounds, encourage volunteers to share their group discussions and findings with the whole class. Students can explain mistakes they encountered, how they resolved them, and what the correct process should have been.
If time allows, use this discussion to review key concepts and reinforce problem-solving strategies.
Evaluate
5 Minute(s)
Display slide 22 and use the Exit Ticket strategy to individually assess what students have learned. Distribute the Exit Ticket handout to each student. Direct students to read the question carefully and to write a sentence for their final answer.
Resources
Desmos Classroom. (n.d.). Smallest Solution [Interactive activity]. Desmos. https://teacher.desmos.com/activitybuilder/custom/582615b63e43a0e4058569c6
K20 Center (n.d.). Bell Ringers and Exit Ticket. Strategies. https://learn.k20center.ou.edu/strategy/125
K20 Center. (n.d.). Desmos Classroom. Tech tools. https://learn.k20center.ou.edu/tech-tool/1081
K20 Center. (n.d.). GUS Method. Strategies. https://learn.k20center.ou.edu/strategy/76
K20 Center. (n.d.). Pass the Problem. Strategies. https://learn.k20center.ou.edu/strategy/151
K20 Center. (n.d.). Picture Notes. Strategies. https://learn.k20center.ou.edu/strategy/104
K20 Center. (n.d.). Think-Pair-Share. Strategies. https://learn.k20center.ou.edu/strategy/139
Spielventure. (2020). Winchester drive-in theatre [Oklahoma City]. [Video]. YouTube. https://youtu.be/S5FP28yDChI?si=k5zajTEF9VSKE8zT
