To introduce the new unit on Solving Equations and Inequalities in two variables, I begin with an Entry Ticket problem set in the context of running a donut shop.
This entry ticket reviews how to create equations and graphs of linear functions from a word problem. In the instructions I break the problem down statement by statement on purpose to help highlight the different aspects and skills that go into solving a system. I also want students to have access to the unit from the beginning and not feel overwhelmed.
For the next 20 minutes or so, the goal for the class is to better understand how to define variables and create equations in the context of describing a system of equations. I will lead the class through Class Slides: Defining Variables and Creating Equations to Solve Systems as they take notes on the steps used to solve systems. As an easy extension for more advanced/honors sections, I typically ask students to try and go ahead and solve each example and to explain the strategies used to solve the system.
I let students know that I spend an entire class on this topic because of how important I think it is. We go through some examples of why we need to define variables.
I want to approach solving and interpreting systems holistically. A unit on solving systems can be a lot like shopping at Home Depot. It is easy to acquire a collection of housing materials. My goal is to enable students to build a sturdy house as we learn about strategies for solving systems of equations using graphing, substitution, etc.
After reviewing the class notes for the day, students work in collaborative groups to complete 1-2 problems assigned from Collaborative Work: Creating Systems of Equations. Each problem describes a situation that can be modeled by a system of linear equations. The modeling (MP.4) in these problems help make the math more tangible, and I try to use examples that students can relate to in the here and now.
I find that assigning groups a small number of problems with high expectations of completeness helps students understand the concepts at a deeper level as opposed to having every students complete every problem in class.
Each group is asked to document their work on one of the white boards in the room. I let the class know that we will be celebrating each other's work with a gallery walk after the group work.
When each group is completed documenting their work on the white boards, I have the class rotate between the different problems in a Gallery Walk. I like to provide structure to make it time efficient - if there are 6 problems to present, give each group 3 minutes to review and provide feedback to one problem and then rotate. Check out the pictures of the gallery walk in action (gallery_walk_pic_1, gallery_walk_pic_2, and gallery_walk_pic_3)!
One way to quickly generate constructive feedback from classmates is to have each group put their feedback on sticky notes. I like to give different groups different colored sticky notes so I can assess the detail and level of feedback each group is giving (and to be able to know which group made any inappropriate comments!).
I like the structure of this instructional activity because it gives students an opportunity to interact with MP.3. Having to present work on the white board pushes students to construct an argument in writing. The sticky notes gives students the perspective of their classmates on how they interpreted not only the problem, but how they thought about the problem.
To conclude the lesson I have students complete an Exit Ticket as a formative assessment. I want to assess where each student is at in his/her thinking about defining variables and creating equations. I provide structure and cues for students to try to solve the system by guess and check (organized with a table) and/or by graphing.
I am happy with this lesson if the majority of students can define variables and create equations from a word problems. I put in the time and effort into this skill because I believe it helps students better understand what we are working on, and will help them solve more complicated systems as we move forward in this unit of instruction.
For homework I ask students to create their own word problem that can be solved with a system of equations. As part of the assignment, students need to have:
I like having students create their own equations because it gives them a chance to think about areas in their own lives where math can help model different scenarios and be helpful in understanding the world around us.