The objective of this lesson is to solve a system of inequalities, so I begin by accessing the students' prior knowledge of solving a linear equation and a linear inequality in one variable. I allow the students 5 minutes to complete the Warm-Up. I review the warm up with the class to introduce the lesson.
I discuss today's warm-up in the video below:
After the warmup, the main purpose of today's lesson is to build on known concepts by making connections. First, to solving a linear inequality in two variables and then to solving a system of linear inequalities in two variables. I discuss with the students how inequalities place restrictions on the problem, but there are many solutions. These restrictions I refer to as boundaries or constraints.
In the Guided Notes I discuss:
I set up the notes for students. My plan is for them to develop an understanding of how the symbols are related to the solutions of the inequality. We will also review the meaning of this relationship. After completing the Guided Notes, students should recognize that solutions are contained in the intersection of the shaded regions, and, on the solid boundary lines in some cases.
Students are also required to be able to apply the following skills:
Throughout the warm up, guided notes, practice, and lesson, students should gain a conceptual understanding of why these different methods for solving a system of equations work. I ask the following questions throughout the lesson.
While students are working the Independent Practice, they are allowed to talk with their assigned elbow partner for math questions, but they must stay on task. I walk around the room while students are working to monitor progress and to assist students one on one or in pairs as needed. I use these questions continue to guide students forward in their productive struggle.
In the last problem, students have not been introduced to graphing quadratic functions this year. Some students do remember graphing quadratics previously in 8th grade. This provides a good teaching moment to discuss a strategy to use when graphing an unfamiliar function. A t-table is a strategy to use to substitute random numbers for x and solve for y to determine the points of the graph and the shape of the function.
In closing, we discuss how a linear inequality in one variable can be graphed on the number line or on a coordinate plane.
I also have students check their work by entering into an online graphing tool. I instruct students that the equations or relations should be entered in standard form Ax + By = C. If the inequality has only one variable, a 0 must be entered as the coefficient for the other variable.