Summary
This lesson introduces students to properties of real numbers, equality, and inverse operations for solving linear equations. The objective is for students to understand how to isolate a variable in two-step equations by applying properties of rational numbers. In the next lesson, students will advance to multi-step equations. This is the first of four lessons in the “Journey of the Isolated Variable” series.
Essential Question(s)
How do I isolate a variable in a two-step equation?
Snapshot
Engage
Students explore algebraic properties through a card matching activity.
Explore
Students practice isolating the variable x using a weighted scale.
Explain
Students analyze their understanding through a foldable.
Extend
Students create more challenging equations using dice as a randomizer.
Evaluate
Students' new knowledge is evaluated through an Exit Ticket.
Materials
Lesson Slides—Journey of the Isolated Variable, Part 1 (attached)
Algebraic Properties Card Matching (attached; one per group)
Weighted Scale and Variable Cards (attached; one per group)
Weighted Scale Activity (attached; one per group)
Foldable (attached; one per student)
Extend Activity (attached; one per group)
Practice (attached; one per student)
Exit Ticket (attached; half-sheet per student)
Extend Cards (optional)
Polyhedral dice (three per group, one of a different color)
Paper, Pencils, Scissors, Glue Stick
Student devices with internet access (optional)
Engage
15 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 two-step equation? Then, display slide 4 to review the lesson’s learning objective. Adjust your presentation of these slides based on student familiarity.
Move to slide 5. Have students analyze their understanding of algebraic properties through the Card Matching strategy. Group students in pairs or trios and provide each group with a set of cut-out cards from the Algebraic Properties Card Matching Activity. The cards include three categories: terms, definitions, and examples. Ask students to match each term with its correct definition and example, encouraging discussion on why each match is correct based on their prior knowledge.
After groups have discussed and completed their matches, invite each group to share their answers with another group. As a class, review each property to clarify definitions and address any misunderstandings by revealing the correct answers. Reinforce the importance of these definitions as foundational to solving equations.
Explore
20 Minute(s)
Display slide 6. Begin with a discussion on what the different variables mean without yet explaining how to solve the equation. Show students the weighted scale, variable pieces, and the equation displayed at the base of the scale. Explain the function of each symbol, emphasizing that the squares represent variables (positive and negative), while circles represent numbers (positive and negative).
Distribute the Weighted Scale Activity handout along with the first page of the Weighted Scale and Variable Cards and the bagged variable cards. One partner will manipulate the scale and cards, while the other will draw the process on the handout.
After each partner solves the first problem, they should verify their answers. Have partners discuss their processes, then switch roles. Each student will complete problems using both the cards and handout by the end of the activity.
Explain
25 Minute(s)
Display slide 7 and pose the question: How do you isolate a variable? Use the Think-Pair-Share strategy to facilitate class discussion on solving equations using the weighted scale. Address any misconceptions and reintroduce academic vocabulary discussed in the Engage section to help students build a conceptual understanding of equation-solving.
After assembling, display slide 8. Use the provided example and foldable steps to demonstrate solving an equation. The first example will allow students to answer "no" to the first step.
Proceed to slide 9. As students gain familiarity with the foldable, introduce more challenging problems requiring "yes" responses for each step, such as the example on this slide. Adjust problems to best meet student needs.
Extend
10 Minute(s)
Instruct pairs to work togetherbut make sure each partner has their own copy of the attached Practice handout to work on. Each pair also receives a copy of the Extend Activity handout. If printing the handout is not preferred, students may use blank paper.
Provide each pair with three polyhedral dice—two of the same color and one of a different color to represent a negative number. Have “Student A” roll first to generate an equation.
Display slide 10 and outline the following steps:
Roll a die and place the number in the first equation slot.
Roll a second die and place the number in the second slot.
Roll the final die and place the number in the third slot.
Both students should write the equation on their Practice handout under the “Student A” column. Have pairs work together to solve for x, alternating roles after each round. Encourage students to complete 10 rounds.
Evaluate
10 Minute(s)
Display slide 11. Have students complete an Exit Ticket to close this lesson. Provide each student with a half-sheet from the attached Exit Ticket handout and have them respond to the following prompt: Create two different equations that will give you a solution of x = -7.
Encourage students to be creative when writing their equations instead of picking easy equations just to get the assignment finished. Once they pick their equations, have them justify their answers by solving the problems and describing their steps. This quick assessment will give you a good indication that students are understanding the concept if they can create their own problem, solve it, and give an explanation of the process.
Resources
Getting Started. (n.d.). Polypad. https://polypad.amplify.com/help
K20 Center. (n.d.). Bell Ringers and Exit Tickets. Strategies. https://learn.k20center.ou.edu/strategy/125
K20 Center. (n.d.). Card Matching. Strategies. https://learn.k20center.ou.edu/strategy/1837
K20 Center. (n.d.). CPM Probability Generators. Tech Tools. https://learn.k20center.ou.edu/tech-tool/2317
K20 Center. (n.d.). Desmos Classroom. Tech Tools. https://learn.k20center.ou.edu/tech-tool/1081
K20 Center. (n.d.). Journey of the Isolated Variable, Part 2. 5E Lessons. https://learn.k20center.ou.edu/lesson/1255
K20 Center. (n.d.). Think-Pair-Share. Strategies. https://learn.k20center.ou.edu/strategy/139
Mathigon. “Using the Balance Scale - Polypad Pointers.” YouTube, 20 Feb. 2023, www.youtube.com/watch?v=1pz-jB0ayFM.
Stokes, A. (n.d.). Journey of the Isolated Variable, Part 1 [Interactive activity]. Desmos Classroom. https://teacher.desmos.com/activitybuilder/custom/5ec289300ddf040f35680d93
