Diagrams of Two-Step Equations

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SWBAT solve two-step equations using models

Big Idea

Remember how to diagram a sentence? Me either. This method for diagramming two-step equations is unforgettable.


10 minutes

I'll begin the lesson with the essential question:  How can you use inverse operations to solve a two-step equation?  The sentence diagrams that we create today are a useful tool (MP5) that we will use to answer this question.  

Here is a video that explains how to diagram an equation.


I will model the first two diagrams step by step.  The model always starts with the unknown value and then the operations that lead to a value.  For example,  -3x + 7 = -5 is presented as x being multiplied by -3 and then being added by 7 to get -5.  This is perhaps counter to the idea modeled in a pan balance, but I think this method is helpful for getting to the idea of inverse operations.

Once we have two good models, the students get to work through four problems.  This is a way for me to check whether or not they understand how to diagram the equations.  Students sometimes make simple errors with the model.  Make it clear that they label the first circle with the variable and all operations go under the lines that connect the circles.  

Guided Problem Solving

15 minutes

The purpose of this section is to get students to focus in on how to use inverse operations to solve equations.  The previous section had equations that a student with strong integer number sense could probably solve using a bit of mental math.  I have purposely made the problems in this section a bit less friendly for mental math so that students have to focus on how the inverse operations are applied and in what order.  Calculator use will be encouraged.

By the end of the page we conclude that first we undo addition or subtraction and then multiplication or division.

Independent Problem Solving

20 minutes

Students now work independently on 10 problems.  The first 5 problems only focus on how to apply inverse operations.  Some students will be tempted to find the unknown value in problems 2-5, make sure to let them know this is not necessary or even desirable.  The point is for them to see an equation and know how they would go about solving it.  If they really want to solve them, ask them to wait until they have completed all 10 problems.

Problem 10 is a word problem that can be solved by working backwards.  That is what is required for part i.  This problem is presented to show the connection between solving problems and solving equations.

Exit Ticket

5 minutes

Before beginning the exit ticket we will summarize how to solve equations.  I may write an equations like -7.2m - 15 = -3.5.  I will ask students to discuss how they would solve the equations.  An acceptable response would be first add 15 and then divide by -7.2.  An even better answer would say first add 15 to -3.5 and then divide that sum by -7.2.

The exit ticket has only two parts.  Because I am required to enter exit ticket results into SchoolRunner (a grading system) I will assign points.  The first problem will be worth 4 points: 2 points for the correct operation in the correct order:  add 8 to 55 and then divide the sum by -7.   One point is awarded in problem 2 for the solution.  I will explain this to my students before taking the exit ticket.  Notice that the emphasis is on the order of inverse operations and not just a solution.