Grades 9-12: Algebra 2 – Defining Regions Using Inequalities


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Content Standards

HSA-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve.

HSA-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately.

HSA-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Standards for Mathematical Practice

MP 1 Make sense of problems and persevere in solving them.

MP 6 Attend to precision.


This lesson titled “Algebra 2 – Defining Regions Using Inequalities” from University of Nottingham and UC Berkeley asks students to find the location of a point on a given coordinate grid based on clues provided by the teacher. These clues come in the form of linear inequalities. Students are required to draw conclusions from the inequalities, such as paying close attention to whether the inequality includes the possibility of equals. Students continue to play another game, using linear inequalities to eliminate possible points. Students are then asked to create the clues for a given point, providing as few clues as possible. By the end of the lesson, students will be able to discern how combining a set of linear inequalities restricts a solution space, as well as determine how to appropriately show a linear equality’s solution set.


Some of the major cautions for this lesson are the lack of differentiation supports, as well as supports for English-deficient students. The lesson activities do not provide the teacher with information about how to help support struggling learners, or to extend this content for an advanced learner. Likewise, there are no suggestions for teachers with ELL students. There are no rubrics or student work samples provided.


This lesson attends to the rigor of the Common Core, requiring students to use precision and to persevere in solving this problem. The lesson takes on a real-world context; while most people are not graphing linear inequalities, it adds a competitive nature and game-like quality to the lesson. The instructional support in the lesson plan is extensive and there are a multitude of resources presented to properly assess student progress. The lesson also provides redirect questions for common misconceptions regarding linear programming.