# 1. Understand that linear equations in one variable may have one solution, no solution, or infinitely many solutions (C)

teaches Common Core State Standards CCSS.Math.Content.8.EE.C.7 http://corestandards.org/Math/Content/8/EE/C/7
teaches Common Core State Standards CCSS.Math.Content.8.EE.C.7a http://corestandards.org/Math/Content/8/EE/C/7/a
teaches Common Core State Standards CCSS.Math.Content.8.EE.C.7b http://corestandards.org/Math/Content/8/EE/C/7/b
teaches Common Core State Standards CCSS.Math.Practice.MP2 http://corestandards.org/Math/Practice/MP2

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Lesson objective: Students understand that not every equation has a solution; some have one, some have none, and some have infinitely many solutions.

Students bring prior knowledge of solving equations from 7.EE.A.1 and 7.EE.A.2. This prior knowledge is extended to solving linear equations in one variable as students explore linear equations in one variable with one, none, or infinitely many solutions. A conceptual challenge students may encounter is understanding the difference between what the solutions to equations with no solution and those with infinitely many solutions look like.

The concept is developed through examination of equations that illustrate the differences between equations with one, none, and infinitely many solutions.

This work helps students deepen their understanding of operations because they will apply properties of operations to a variety of equations.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they examine equations and their solutions.

Key vocabulary:

• infinitely many solutions

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