In the previous lesson, students learned that sometimes an equation has one solution, sometimes no solution, and sometimes infinitely many solutions. The purpose of this lesson is to help students identify structural features of an equation that tell them which of these outcomes will occur when they solve it. They also learn to stop solving an equation when they have reached a point where it is clear which of the outcomes will occur, for example when they reach an equation like \(6x+2=6x+5\) (no solution) or \(6x+2=6x+2\) (infinitely many solutions). When students monitor their progress in solving an equation by paying attention to the structure at each step, they engage in MP7.
Lesson overview
 8.1 Warmup: Matching Solutions (5 minutes)
 8.2 Activity: Thinking About Solutions Some More (25 minutes)

8.3 Optional Activity: Make Use of Structure (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 8.4 Cooldown: How Does She Know? (5 minutes)
Learning goals:
 Describe (orally) a linear equation as having “one solution”, “no solutions”, or “an infinite number of solutions”, and solve equations in one variable with one solution.
 Describe (orally) features of linear equations with one solution, no solution, or an infinite number of solutions.
Learning goals (student facing):

Let's solve equations with different numbers of solutions.
Learning targets (student facing):
 I can solve equations with different numbers of solutions.
Required materials:
 preprinted slips, cut from copies of the blackline master (See Additional Materials section of this lesson)
Required preparation:
 Make 1 copy of the Make Use of Structure blackline master for every 3 students, and cut them up ahead of time.
Glossary:
 constant term  In an expression like \(5x+2\), the number 2 is called the constant term because it doesn't change when \(x\) changes. In the expression \(7x+9\), 9 is the constant term. In the expression \(5x+(\text8)\), 8 is the constant term. In the expression \(124x\), 12 is the constant term.
 coefficient  A coefficient is a number that is multiplied by a variable. For example, in the expression \(3x+5\), the coefficient of \(x\) is 3. In the expression \(y+5\), the coefficient of \(y\) is 1, because \(y=1 \cdot y\).
 Access the complete Grade 8 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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