Summary
This lesson focuses on the properties of real numbers, properties of equality, and inverse operations to help students solve linear equations on a deeper level. The goal is for students to understand the fundamentals of isolating a variable and to apply that knowledge to more complex problems. Students will then be able to solve multi-step equations by applying properties of rational numbers and algebraic properties. This is the second lesson of four in the “Journey of the Isolated Variable” lesson 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
In groups, students form strategies to solve more complex multi-step equations and then peer-review their classmates' work.
Explain 2
Students review their equation-solving strategies through a flowchart and then practice solving problems while implementing the GUS Method.
Extend
Students create their own word problems by considering items bought and sold in a theater.
Evaluate
Students demonstrate their understanding through an Exit Ticket.
Materials
Lesson Slides (attached)
Picture Notes handout (attached; one per student; printed front only)
Note Catcher handout (attached; one per student; printed front only)
Just Give Me a Reason handout (attached; one set per pair; printed front only)
Flowchart (attached; one per student; printed front only)
Create Your Own Problem handout (attached; one set per 5 stations; printed front only)
Exit Ticket handout (attached; one-half sheet per student; printed front only)
Pencils
Paper
Chromebooks or student devices with internet access
Student dry-erase boards (optional)
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 isolate a variable in a multi-step equation?" 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. Pass out the attached Picture Notes handout. Individually, have students review their knowledge of different algebraic vocabulary terms (associative property, inverse property, like terms, coefficient, etc.) by creating Picture Notes. Direct students to generate their own definitions by creating a sketch, a statement, or an example to represent each term.
Give students five minutes to work independently and walk around to see how much they know before the lesson begins. Once students are at a stopping point, have them set the handout aside. Let students know they will come back to it later in the lesson.
Explore 1
15 Minute(s)
Display slide 6 and provide students with your session code. Then, have students go to student.desmos.com and enter the session code.
Give each student a copy of the attached Note Catcher handout to use for the Desmos Classroom activity, as they need space to investigate equations. Students could use a piece of notebook paper instead.
Instruct students to individually go through the six screens and create an equation that has the smallest possible solution for x, where "smallest" is intended to mean the value of the number after applying the absolute value (i.e. ignoring the sign of the solution). Make sure they write the equations they create on their Note Catcher so they can remember the equations they believe would create the smallest possible solution for x.
Remind students there is no right or wrong answer and no need to ask for help from their peers at this point. This is a time for them to explore their knowledge and find evidence to prove their argument during the next activity.
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 and give each pair a copy of the first two pages of the attached Just Give Me a Reason handout: Problems 1–2.
Explain to students how to complete the handout using the Pass the Problem strategy. Each student starts the first step of their problem by modeling the algebraic equation by drawing the number of variables, keeping the constant written in its algebraic form. Use slide 9 to give students an example of this step.
After students complete step 1, explain that they are to write their reasoning for their step in the second column of that row. The reason for step one has already been completed, but help students understand the procedure for this activity. Move to slide 10 and have students trade papers. Guide students to check the work of their partner and then complete the second step. If students are struggling to write their reasoning, encourage them to use the vocabulary activities from this and the "Journey of the Isolated Variable, Part 1" lesson.
Once students complete Problems 1–2, display slide 13. Give one copy of the third page of the Just Give Me a Reason handout to each pair of students. Direct students to work together to solve Problem 3.
As students finish Problem 3, bring the class together for a discussion and ask, "What is different about Problem 3?" Use this discussion to transition to 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 on the slide in the top box of the flowchart. Walk students through the procedure of using the flowchart and how their "Yes" or "No" responses lead them to the final answer.
Go to slide 15. Using the GUS Method, give students the opportunity to practice while using the flowchart. Have students use either a piece of paper or student dry-erase boards for this activity. Instruct students to solve the equation on the slide. In the top-right or top-left corner of their piece of paper or dry-erase board, direct them to write a G, U, or S.
G means they guessed the answer and have no clue how to solve the problem.
U means they are unsure if they completed all the steps correctly.
S means they are completely sure and understand the material.
Display slides 16 and 17 to give students two more equations to solve using the flowchart and the GUS Method.
Go to slide 18. Invite students to get out their Picture Notes from the Engage section of the lesson. Have students check to see if there is anything they need to add to their Picture Notes or anything they need to change based on what they have learned so far in 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)
Go to slide 19 and show students the video on the slide, "Drive-In Movie Theaters Make Comeback During COVID-19 Crisis." Ask the class: "If you were the owner of a drive-in theater, what would you spend money on? 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 show students how to solve the given word problem. Tell students that they will be creating a story problem and need to consider how to solve one when writing story problems.
Show slide 21 and have students get into groups of three at each station. Explain to students that they will be writing their own story problems and solving their peers’ story problems. Explain that this will be similar to the Pass the Problem activity from earlier in the lesson, except this time, they will be moving instead of their papers. Explain the following procedure for the activity:
Round 1: Students write two story problems—one on each of the pages at their station. This round is approximately ten minutes.
Round 2: Students leave their story problems at that station, get up, and move to the next station. Here, students read the story problems at this station and write the algebraic equation that one could use to solve the story problem. They are not solving the problem. This round is approximately five minutes.
Round 3: Students leave their papers at that station, get up, and move to the next station. Here, students read the story problems, check the equations written by the previous group, and then solve the equations. This round is approximately ten minutes.
Round 4: Students leave their papers at that station, get up, and move to the next station. Here, students take the answer and use substitution to check the work done by their peers. This round is approximately 5 minutes.
Round 5: Students leave their papers at that station, get up, and move back to their original station. Here students review the work done by their peers. This round should take approximately 5 minutes.
After reviewing the procedure, give each group two pages of the Create Your Problem handout such that each group has a Question A page and a Question B page. For example, group 1 should get pages 1A and 1B; group 2 should get pages 2A and 2B, etc. If you have more than five groups, give the sixth group pages 1A and 1B, etc.
Begin Round 1, and encourage students to start with the template pages (pages 1A, 2A, 3A, 4A, or 5A). Have them complete the story problem template for their first question. Then have students create a second story problem on the second page (pages 1B, 2B, 3B, 4B, or 5B). Tell students that they can use the template question as a guide but they should try to be creative with their second story problem.
Begin Round 2, and remind students to leave their papers at their station and move to the next station. Remind students that they are only writing the equation. They are not solving the equation during this round.
Begin Round 3, again, reminding students to leave their papers at the station before moving to the next station. Tell students that they need to check the equation before solving the equation.
Begin Round 4, and remind students that they are plugging in the solution into the equation to check the work of their peers. If they find that the solution is not the correct solution, encourage students to look through the work of their peers and circle the mistake.
Begin Round 5, and have students go back to their original station to review the work done by their peers. Have the group discuss if what they see written on their paper is what they expected. And if they see a circled mistake, have them correct the mistake and find the solution.
If time allows, have volunteers share with the whole class what they discussed in their smaller groups and to share any mistakes that were made and what the correct process should have been.
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
NBC News. (2020, May 5). Drive-in movie theaters make comeback during COVID-19 crisis [Video]. YouTube. https://www.youtube.com/watch?v=Czzt9l9qnZ4
