Multi-Step Equations

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SWBAT solve equations with the distributive property and integers on both sides.

Big Idea

Students discuss varied solution steps to solve multi-step equations

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. A timer is set for 5 minutes and displayed on the board. Their Do Now assignments are already on their desks.

There are many factors that impact student motivation in December. This is our busiest time of year as we need to schedule time during the school-day for students to practice in the orchestra for our winter show; students have also just endured 2 – 3 weeks of unit tests and interim assessments in ELA and math; winter break is just around the corner, as is the end of the middle quarter when we will send out our progress reports. For these reasons, you will notice multiple opportunities for achievement points on this Do Now assignment. I’m also using it as an opportunity to provide written reminders about graded assignments.

Question #1 is included in the Do Now to reflect needed practice with the distributive property, especially with negative numbers. Data from the mock assessment showed that students needed more practice with these types of problems.

Question #2 is included to improve student mastery of rational number operations and problem solving skills. The rigor of this question is admittedly lower than the rigor posed by question #43 from the mock assessment, a very challenging question for my students, where 73% of them scored 0 points. This Do Now question does not require students to do as much synthesizing and interpreting of information to identify the steps needed to solve. My aim is to give students a situation where they CAN identify the steps needed to solve (add the amounts, then subtract the total given to find the change) so that I can pay attention to the ways in which they show their work. Students NOT showing each step, and instead, trying to do all the work “in my head”, may make calculation errors. In other words, before I can get kids to think critically about what steps to take in a challenging problem, I have to get them to show all their work.

Question #3 is included to continue practicing with rational number operations, another skill identified as needing practice in both the multiple choice and open response sections of the mock assessments. 

Class Notes

15 minutes

In past years I have taught the algebra portion of the year somewhat differently – through the use of prescribed steps students memorized. After the CCSS shifts, I realized that this model would no longer work. Rather than memorizing processes, common core demands that students understand the “why?” behind each step which they must identify on their own. This is why I decide to create four different Class Notes versions each with a different solution to a multi-step equation with variables on both sides. Each worksheet includes some of the steps for solving an equation and students must follow these steps independently. Each series of steps is different. I make sure to elect 4 students to display their four different solutions on the board for other students to see. They are given 5 minutes at the beginning of the class notes section to complete the solution for their given worksheet.

In the document attached, the red lettering is meant to be written in by the students, either through discussion or as a result of me writing it on the board. After the first 5 minutes of this section, I lad a discussion using these questions:  

  • How are all of your equations different? How are they all the same?
  • What does this mean about the steps taken to solve equations?
  • How can you ensure that whatever step you take, you are keeping the equation balanced?

As much as possible, I try to make my only role, one of asking questions and asking students to reconsider if they say something mathematically unsound. The responses to these questions must come from multiple students, with varying levels of academic performance. The understandings I am looking for are:

  • There is no one way to solve all equations
  • There are general ways to get to a solution faster
    • 1st  simplify by distributing or combining like terms
    • Then get all the variable terms on one side of the equation and all the constant terms on the opposite side
    • Steps must be grounded in math properties to keep the equation balanced


Independent Practice

20 minutes

Students are asked to take out a blank sheet of paper, write a heading and copy the aim off the board. Then they are instructed to retrieve a green algebra book from the back of the room (Addison-Wesley, 1994). Students must complete any 5 problems from the range of #1 - #12 on the book. These equations include like terms and variables on both sides. Additionally, students must complete 5 questions elected from the range of #13 – 30. They are also reminded that the odd answers can be found on the back section of the textbook. Achievement points will be awarded to any students who would like to show the solution for #29 and#30 on the board, after solving correctly on their paper. These questions along with other samples are included in the worksheet attached.

Students are allowed to work with neighbors for the first 5 minutes of this section but must work independently and silently for the remaining 15. It is important that they get focused work time to practice these tricky concepts. The video below explains the common errors I expect along with a strategy I teach students to use to check if their steps are mathematically sound. All students will be asked to continually check to make sure the steps they are taking are “allowed in math” (MP8).


10 minutes

Students have 5-8 minutes (given time left in class) to complete the exit ticket. It must be turned in at the door on their way out. This equation will allow me to check for ability to distribute, combine like terms, and solve equations with variables on both sides correctly. 

While students are working silently, I distribute the homework. It includes a seating survey. I want student input with my new seating chart. We have been having a lot on conversations around the privileges students will have once they're in high school. Getting to choose whom to sit next to is one of these privileges. This assignment provides them an opportunity to think about important factors when making this choice.