Authentic Lessons for 21st Century Learning

Journey of the Isolated Variable, Part 1

Solving Two-Step Equations

Matthew McDonald, Brittany VanCleave | Published: April 19th, 2021 by K20 Center

Summary

This lesson focuses on the properties of real numbers, properties of equality, and inverse operations to help students solve linear equations. The goal is for students to understand the fundamentals of isolating a variable. Students will then be able to solve two-step equations by applying properties of rational numbers. The next lesson in this series focuses on isolating variables in multi-step equations.

Essential Question(s)

How do I isolate a variable in a two-step equation?

Snapshot

Engage

Students reflect on their knowledge of algebraic properties through a card sort.

Explore

Students investigate how to isolate the variable x using the weighted scale method.

Explain

Students analyze their understanding through a foldable.

Extend

Students use dice as a randomizer to create and comprehend harder equations.

Evaluate

Students' new knowledge is evaluated through an exit ticket.

Materials

  • Lesson Slides (attached)

  • Algebraic Properties Card Sort (attached; one per group)

  • Weighted Scale and Variable Cards (attached; one per group)

  • Weighted Scale Activity handout (attached; one per group)

  • Foldable (attached; one per student)

  • Extend Activity handout (attached; one per group)

  • Practice handout (attached; one per student)

  • Exit Ticket (attached; one half-sheet per student)

  • Extend Cards (attached; optional)

  • Desmos Activity Step-by-Step Guide (attached; optional, for teacher use)

  • Paper

  • Pencils (one per student)

  • Polyhedral dice (three per group, including one die of a different color)

  • Chromebooks (optional)

  • Scissors (optional)

  • Glue Stick (optional)

Engage

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? 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. Students will analyze their understanding of algebraic properties using a Card Sort. Place students in groups of two or three, and provide each group with the cut-out cards from the attached Algebraic Properties Card Sort. The card sort has three different categories: the word or expression, the definition, and an example. In their groups, invite students to match the word/expression, definition, and example provided. As they are matching, have students discuss why they believe the cards fit together based on their previous knowledge.

After the groups have had time to discuss, invite them to share their answers with another group. As a class, define each property and eliminate any misunderstandings students may have about the card sort or definitions by revealing the answers. The more students can process why the definitions matter, the easier solving equations will be.

Explore

Display slide 6. As a class, discuss what the different variables mean, but don't use this slide to show students how to solve the equation just yet. Simply show students there is a weighted scale with variable pieces on the scale, as well as an equation at the base of the scale. To the right of the scale, there are the four different symbols students can use to create an equation. The squares represent positive and negative variables, which don't always have to be x, and the circles represent positive and negative numbers.

Pass out the attached Weighted Scale Activity handout, the first page of the attached Weighted Scale and Variable Cards, and the cut-out Variable Cards. One student will use the weighted scale and variable cards to solve, and the other will draw out the process on the Weighted Scale Activity handout.

Once each partner completes the first problem, they will check to see if they got the same answer. They will analyze how they solved the problem using their manipulative (either moving the cards physically on the scale or drawing their pieces on the handout), and then they will discuss the process with their partner.

After each partner has talked about how they solved the problem, they will switch materials. By the end of this activity, each person will have had an opportunity to use both the cards and the handout to solve the problems.

Explain

Display slide 7. Pose the question: How do you isolate a variable?

Have students use the strategy Think-Pair-Share to communicate to the class how they solved the problems using the weighted scale. At this point in the lesson, it is time to eliminate any misconceptions students may have and bring back the properties discussed in the Engage section of the lesson to begin using academic vocabulary to discuss the concepts.

Display slide 8. Provide each student with a copy of the attached Foldable. Using the example provided on the slide and the foldable steps, teach students how to follow the steps to solve an equation. The first example will be easier for them because they can answer “no” to the first step.

Go to slide 9. As students are comprehending how to follow the steps of solving equations using the foldable as a guide, begin to introduce harder problems that require a “yes” on each foldable step, such as the example provided on this slide. Feel free to add, delete, or modify the equations given to best fit students’ needs.

Extend

For this activity, invite students to work together in pairs, but make sure each partner has their own copy of the attached Practice handout to work on. Also pass out a copy of the attached Extend Activity handout to each student pair. If you do not want to print out the Practice handout, students can always use a piece of paper to show their work.

Give each pair of students three polyhedral dice—two dice should be the same color and the third a different color. The different colored die represents a negative number. Ask the pairs to identify one partner to go first, “Student A.” This student should begin with the first equation on the Extend Activity handout (or the first strip if the cards are halved and being solved in random order).

Go to slide 10. Invite the partner who is going first to follow the steps on the slide:

  1. Roll a polyhedral die. Place the resulting number in the first slot of the equation.

  2. Roll a different polyhedral die. Place the resulting number in the second slot.

  3. Roll the last polyhedral die. Place the resulting number in the third slot.

Ask both students in each pair to write this randomized equation down on their Practice handout, under the “Student A” column in the first row. Next, ask each pair to work together to solve for x. Allow enough time for every pair to finish 10 rounds of solving their randomized equations, alternating between Student A and Student B rolling the dice.

Evaluate

Display slide 11. Students will 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, they will 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