Solving Inequalities

Learning Context

Purpose/Rationale for Learning Experience:
The purpose of this lesson is to ensure students understand the similarities and differences between linear functions and inequalities. Inequalities also enhance a student’s problem solving abilities.

Enduring Understanding(s):
Students should fully understand that inequalities have more than one numerical solution. They should understand the mathematical steps in finding those solutions. They should also know how to represent those solutions by graphing the linear inequalities on a number line and on a coordinate graph.

Essential Question(s):

• What is an inequality?
• How do you find/represent an inequality’s many solutions?

Guiding Questions:

• When do you use an open/closed circle on a number line?
• When do you shade above or below a solution line?
• Do you add/subtract before you multiply/divide when solving an inequality for one variable?
• When do you flip the inequality symbol?
• What is a graph of a solution?
• Why do we need to shade on a graph?

Overview of what students need to know/ be able to do in order to succeed:

Prior to Learning Experience:
Prior to the learning experience, students should have a basic understanding of inequalities. Students should have a strong background in graphing inequalities on a number line and in graphing a linear function.

During and after the implementation of LE:
Throughout the learning experience, students should make the connections between linear functions and inequalities because graphing linear inequalities are very similar. At the conclusion of the lesson, students should be able to solve linear inequalities for one variable and be able to graph them on a number line. Students should have an understanding that linear inequalities have more than one numerical solution and that is why the graphs of their solutions are to be shaded accordingly.

Key Subject-Specific Vocabulary:
inequality, graph of a solution, less than, greater than, less than or equal to, greater than or equal to, open and closed circles, dashed/dotted line, solid line