Solving Two Step Equations

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SWBAT solve two-step equations and check if solutions are correct..

Big Idea

Students use inverse operations to isolate the variable, then receive feedback from classmates.


10 minutes

This lesson continues the plot that began with yesterday's lesson.  So, I begin by projecting a solved equation, one that demonstrates the technique used in class and on the homework assignment (see Launch). Students are presented with a "story of x" told by using inverse operations to find x's original value. In this case, the task is for students to find the mistakes made in the process.

The two mistakes "Charlie" makes are among the common that my students make when learning to solve equations. In the Launch Task students should see that:

  1. Charlie used the wrong order of operations when going in reverse. He should have subtracted six and then divided by three. 
  2. Charlie added 4 instead of dividing by -4. The mistake of not realizing that -4x means x is being multiplied by -4, is quite common.

I allow my students to discuss the among themselves if they wish. After a few minutes of student work time, I will call on volunteers. Once both mistakes are addressed and discussed, I will ask the class what could Charlie have done to know if he had obtained the correct answer. I hope that this will motivate one of our topics for today's lesson, checking your work by plugging a value for x back into the equation.


New Info

10 minutes

I begin this section of the class assuming that my students now understand how one can work backwards, "undoing" what was "done" to x in writing the equation, in order to find the unknown value for x.  Beginning from this assumption, we will now focus on two points of instruction:

  1. Helping students recognize by using their "undoing" skills each step in the solving process produces a simpler, but equivalent equation
  2. Helping students to become aware of common mistakes that are made and how to avoid them

I project the New Info Equation Cards and I ask students to observe the information on the first card. On the left side of the page, the equation is solved by telling the story and working backwards. The way we began to work on equations yesterday. I then ask a student to read the right side of the card, "What two operations were performed?" I ask my students to look carefully and see if they can plan how they will solve the equations. The goal here is for students to make the connection between problem solving processes and the application of order of operations. 

For the second card I will call on a student and ask that they complete the card on the board in front of the class. I will also have another student go up to the board and check the answer in front of the class, to demonstrate how this can be accomplished. 




25 minutes

Part 3 of this lesson is some practice with equation solving. To get this under way, I pair students up by similar math ability and hand each student a copy of the Solving two step equations worksheet. I instruct students to work independently, one problem at a time. Once an equation is solved, partners should compare answers with each other. I encourage them to discuss any differences in their work. If they come up with different answers, I ask them to come to agreement on the correct answer by identifying where an error was made. If one student finishes a problem, the partner should wait until the other is done.

I will circulate and intervene in a students work if he/she is holding up his/her partner. As I do, I tell the groups that it is very important to get immediate feedback when a mistake is made. So, please speak up when working with your partner.

Students will follow the above procedure throughout the process of completing the worksheet. Part 2 switches from solving equations to finding mistakes in a simulated equation solving process. Students are asked to correct the errors that they find. Checking the new solutions should help them to realize when they have found all of the errors.  


5 minutes

To close today's lesson, I ask students to label their worksheet with a happy, straight, or sad face, depending on how they feel they did on the work (see faces.jpg):

  • Happy face means very well understood. 
  • A straight face means Ok, but I still have some questions.
  • A sad face means "I am confused". 

The faces students write on their sheets will give me an idea of what to review, or what students need more practice with, and I adjust the following lessons accordingly. 

For homework tonight I ask my students to complete Homework solving two step eq.