This is an exploration lesson for students to discover the properties of linear inequalities in two variables. The link will download a copy of the files that I print out for students as well as a possible facilitation guide. The general idea behind the lesson is that students are taking a piece of a Cartesian plane and identifying whether points on the graph are or are not solutions to the inequality. If it is a solution, the point gets a "closed circle" sticker. If it's not, the point gets an "open circle" (a reinforcement sticker). Students work in small groups to fill up the plane with open and closed circles. I verify and ask questions as I walk around.
When they are finished I pair up the groups and have them note things their graphs and inequalities have in common. There are 8 groups, but they are strategically paired. For example in the first rotation students are comparing inequalities that both have a boundary line with the same slope and y-intercept, but one is greater than or equal to, and one is less than or equal to. By the end of the discussion students should be able to identify solutions to inequalities in two variables, understand the concept of a boundary line, and connect what they know about slope and y intercept to the boundary line.
The third part of the lesson is a set of cards for students to match up to inequalities. The purpose of this is to introduce the different boundary lines when the inequality is just less than instead of less than or equal to.
For example, in the first pairing, all groups have inequalities with the same slope and y-intercept, but different inequality symbols.
Graphing Linear Inequalities Exploration Lesson