Solving Literal Equations

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SWBAT solve a literal equation for a specified variable.

Big Idea

Students will use Algebraic reasoning and inverse operations to isolate a variable.


10 minutes

Students will complete the Do Now in their notebooks. Four students will come up to the board to show their work and solutions on the whiteboard for the class to review.

Next, a student will read the objective to the class: SWBAT solve a literal equation for a specified variable.

I will ask a few volunteers to give their own definition of the word literal. I will then ask students to compare the meaning of the expressions  "it's raining cats and dogs" vs. "it's literally raining cats and dogs".

I will then ask the class to brainstorm the definition of a literal equation. 

Guided Notes + Practice

40 minutes

In today's Guided Notes we spend some time developing students' understanding of the term 'literal' in different contexts. The Literal Equations presentation begins with some fun, but meaningful, slides and then progresses into the meaning of literal equations in the context of Algebra 1.

Slides 2 and 3: The fun, but meaningful part.

I will tell students that a literal equation is an equation that has more than one variable. Since there are multiple variables, it is impossible to get a numerical response because we have so many unknown values that are being represented with letters all within the same problem. The best we can do is to literally solve the equation, meaning manipulate the terms using inverse operations as if they were constants and like terms.

Slide 6:  I will ask students to decide me what number x is equal to in the equation x + y = 7, and to call their answer aloud. I will then begin to advance the slide forward to show 15 possible values of x and y. I will ask the class to brainstorm how many more solutions could be created to justify this equation.  I will then ask them to decide what is problematic with the situation we are in. Once we realize that the possibilities are limitless, I will assure them that it is okay that we do not know the value of each variable, because we know that x + y = 7. If we know that x + y = 7, then 7 – y has to equal x, which is our answer. I will use a few test values to demonstrate that x = 7 – y will always work if x + y = 7. We have solved our first literal equation!

Slide 7 and 8: I will solve these problems side by side to increase student’s comfort levels with seeing an equation that has all variables. (Most were initially intimidated by these examples). I will focus on having student undo inverse operations:

  • Our goal is to isolate x, so we want to move everything else away from it.
  • We don’t know what a or x represent, but we know that they are being multiplied together because they are side by side.
  • How can we undo multiplication?
  • Since we only want a and not x, lets divide away the term that we don’t want.

Partner Activity

20 minutes

Students will practice solving literal equations with this handout using the ETA Hand to Mind product VersaTiles. Students will match correct responses to the numbered tiles in the black VersaTile case. If you do not have a VersaTiles classroom set, the assignment can still be completed by having students match questions and responses with pencil and paper.


10 minutes

To close our lesson, I will ask students to brainstorm a situation where solving a literal equation could be helpful.  Then I will challenge the class to think about how a literal equations can help you graph a line on a coordinate plane. Students will complete then complete the exit card.