Solutions of Linear Equations

Once students are fluent with the order of operations, they are ready to solve linear equations. When teaching the order of operations, I emphasize that we are simplifying numerical expressions. So when I provide the total value of a numerical expression BUT make one of the values in your expression a mystery, then my students have an equation to solve. And the process of solving for the mystery value requires students to use the order of operations in reverse.

2x + 5 = 17

What happened to the mystery value? It was doubled (or multiplied by 2) and then 5 was added for a total of 17. What happened last? The 5 was added to result in a total of 17. So take away (or subtract) 5. Now the total is 12...which is the result when I double the mystery value. So divide the total by 2 and you have revealed the mystery value of 6.

In middle school, students are moving from concrete thinking to abstract thinking...some a little more quickly than others. But our goal is to help all students find success dealing with abstract concepts. Solving linear equations may require the use of manipulatives to support concrete thinkers as they conceptualize this abstract concept.

And then when you add the possibility of multiple mysteries value that would reveal the same total result or no mystery value at all that would yield the total, the abstract becomes more abstract. Sarah over at Everybody is a Genius posted an excellent approach to Solving Special Case Equations. I love the introductory "puzzle" approach with balanced scales. I altered the format to a Showdown activity to provide structure for the discussion with the record sheet.
Balance This! Showdown Activity

Balance This! Record Sheet

Sarah also shared the notes her students created for their Interactive Notebooks to summarize their learning. I created the foldable in PowerPoint so it could be sent to the print shop if you prefer.
Types of Solutions Foldable (Student)

Types of Solutions Foldable (Teacher)

And this tiling activity is a great activity to informally assess student understanding of solution types.

Types of Solutions Tiling Activity
These activities highlight the Common Core State Standard 8.EE.C.7a included in MATH-8 and Accelerated MATH-7.

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