Grade 8: Solving Linear Equations in One Variable


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Content Standards

8.EE.7 Solve linear equations in one variable.

8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Standards for Mathematical Practice

MP.1 – Make sense of problems and persevere in solving them.

MP.3 – Construct viable arguments and critique the reasoning of others

MP.7 – Look for and make use of structure


In this lesson titled “Solving Linear Equations in One Variable” from, students begin by completing a pre-assessment where students begin to examine what it means for an equation to be true. Students are asked to critique two sample students’ work for this assessment. The lesson moves to discussing how to know an equation is true and determining values to make an equation true. Students collaborate to determine whether an equation will always, sometimes, or never be true, which represents the three possible solutions to a linear equation (one solution, no solution, infinitely many solutions).  The lesson also includes a card matching activity, where students match different equations with other equations with the same solution. The lessons a wealth of information for guiding questions for to promote reasoning and develop conceptual understanding.


Some of the cautions of this lesson include a lack of support for English language learners. There is also a lack of cultural diversity support. The lesson is lacking in additional supports for students working both above and below grade level. There are sample solutions but there is no rubric for providing unbiased assessments. There is a lack of application to real-world scenarios and opportunity to promote transfer. There should also be an addition of some way to adjust this for more multicultural students.


The lesson provides a rich lesson that has students working at the level of rigor of the CCSS. Students are actively engaged in the activity, using hands-on manipulatives to match different cards and using multiple representations of the concept.  There is a balanced approach to working with concepts and procedures. Students are required to communicate their understanding in multiple formats, justify their reasoning, and critique the reasoning of others. The lesson’s most valuable resource is questions provided to teachers that promote reasoning for students. These questioning strategies, as well potential areas of misunderstanding, are valuable to teachers, helping them anticipate and correct student misunderstanding.