F Inequalities, Lesson 4, Graphing Linear Inequalities (r. 2018) – INEQUALITIES Graphing Linear Inequalities Common Core Standard Next Generation Standard A-REI.12 Graph the solutions to a linear inequality AI-A.REI.12 Graph the solutions to a linear inequality in in two variables as a half-plane (excluding the two variables as a half-plane (excluding the boundary in boundary in the case of a strict inequality), and the case of a strict inequality), and graph the solution set graph the solution set to a system of linear to a system of linear inequalities in two variables as the in two variables as the intersection of the intersection of the corresponding half-planes. half-planes. Note: Graphing linear equations is a fluency for Algebra I. Students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems involving linearity; as well as modeling phenomena (including modeling using systems of linear inequalities in two variables). LEARNING OBJECTIVES Students will be able to: Graph a single inequality involving two variables on a coordinate plane. Determine if the boundary line is a solid line or a dashed line. Determine if the solution set is shaded above or below the boundary line. Overview of Lesson Teacher Centered Introduction Student Centered Activities Overview of Lesson guided practice anticipates, monitors, selects, sequences, and Teacher: connects student work - prior knowledge activate students’ - developing essential skills - vocabulary - Regents exam questions - learning objective(s) - formative assessment assignment (exit slip, explain the math, or journal - big ideas: direct instruction entry) - modeling VOCABULARY boundary line shading testing a solution dashed line solid line linear inequality solution set BIG IDEAS A linear inequality describes a region of the coordinate plane that has a boundary line. Every point in the region is a solution of the inequality.
F – Inequalities, Lesson 4, Graphing Linear Inequalities (r. 2018) INEQUALITIES Graphing Linear Inequalities Common Core Standard A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear in two variables as the intersection of the half-planes. Next Generation Standard AI-A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Note: Graphing linear equations is a fluency for Algebra I. Students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems involving linearity; as well as modeling phenomena (including modeling using systems of linear inequalities in two variables). LEARNING OBJECTIVES Students will be able to: Graph a single inequality involving two variables on a coordinate plane. Determine if the boundary line is a solid line or a dashed line. Determine if the solution set is shaded above or below the boundary line. Overview of Lesson Teacher Centered Introduction Overview of Lesson - activate students’ prior knowledge - vocabulary - learning objective(s) - big ideas: direct instruction - modeling Student Centered Activities guided practice Teacher: anticipates, monitors, selects, sequences, and connects student work - developing essential skills - Regents exam questions - formative assessment assignment (exit slip, explain the math, or journal entry) VOCABULARY boundary line dashed line linear inequality shading solid line solution set testing a solution BIG IDEAS A linear inequality describes a region of the coordinate plane that has a boundary line. Every point in the region is a solution of the inequality.