Solving Literal Equations

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Objective

SWBAT solve a literal equation for a specified variable by rewriting a given equation in an equivalent form.

Big Idea

The process of rewriting equations in equivalent forms is the same whether the equations contain variables, integers, or a mix of both.

Investigation

20 minutes

At the start of today's lesson, students will work on Literal Equations Investigation in pairs without any prior instruction. I want students to make an informal, initial investigation of solving literal equations by asking them to work through examples. I encourage student ownership by moving students through cycles of individual work, class time, and peer discussion.

See Classroom Video: Discourse and Questioning to visit my classroom for this part of the lesson. 

The goal is for students to engage in cycles of reasoning and abstraction as they explore the questions (MP2). I provide about 10 minutes for students to work on the investigation. Then, we will spend about 10 minutes reviewing each question and discussing students' ideas and solutions.

See Classroom Video: Shared Expectations to visit my classroom for this part of the lesson. 

I want to guide the class toward the understanding that solving literal equations is all about inverse operations.  Sometimes, this idea is difficult for students because literal equations are more abstract.  

  • Question 1: Students will compare and contrast a linear equation and a literal equation. My goal is for them to observe how the steps for solving each equation for a single variable are similar.  In the "another approach"  section, students will use substitution to see that the two equations produce the same result. This discovery will help them to recognize that the literal equation is a model for the linear equation. Solving the literal equation for x produces a formula that can be used to solve all literal equations.
  • Questions 2-3: Students will continue to investigate solving linear equations.  By plugging in values, students learn to use numerical values to check their solutions.
  • Question 4:  Students will see that, as with linear equations, literal equations can be solved in different ways.  Students can show that both solutions are the same by finding a common denominator for the two fractions under method 1.  Students could also determine values for a, b and c and show that when these values are substituted in each solution is the same. 

Throughout, I will be on the lookout for student mistakes that show a lack of conceptual understanding such as:

"a + b = ab"

I will remind my students about the concept of "like terms" in order to convince students that statements like this are not true. If necessary, we can also substitute values for each variable and use arithmetic to disprove this result.

Practice

15 minutes

During this section of the class, I give students time to work in pairs on the Literal Equations Practice worksheet.  I continue to remind students that they are trying to take apart the equation and isolate the variable by using inverse operations.  Encourage students to think out loud while they are working with their partner so that they can critique each other's reasoning on the various exercises (MP3).

As students are finishing this series of questions, I will ask them to post their work on the board. I want them to share their ideas and solutions. I want to be able to review the problems on the worksheet quickly.

See Classroom Video: Student Ownership to visit my classroom for this part of the lesson. 

Closure

5 minutes

Literal Equations Close is a great Ticket Out the Door at the end of this lesson because it allows students to see that one literal equation can be solved in a variety of ways based on the variable you are trying to isolate.

After handing out the worksheet, I will have students do a Turn-and-Talk with their partner around the example given.  I will have each partner take turns (two each) explaining how the original equation is manipulated to become the solution for each variable.  Next, I will have students solve the equation y = mx + b for each variable.  This should be done individually and student's work can be collected as a formative assessment of the day's lesson. 

To see this part of the lesson unfold, watch: Classroom Video: Exit Ticket