Lesson 5: Systems of Inequalities & Real-World Applications

• How do we solve a system of inequalities?
• What does the solution region represent?
• How do we shade the solution?
• Where do systems appear in real life?

System of inequalities, solution region, boundary line, shade, test point

CCSS.MATH.9.A.REI.D.12

Description: Students graph systems of inequalities by graphing each inequality and shading the solution region (where both are true). They use test points to verify which region to shade. Real-world applications (budgets, constraints, optimization) show relevance. Purpose: To extend system-solving to inequalities and show real-world applications. DOK Level: 2-3 (Application)

• Real-world contexts: Budgets, constraints, resource allocation
• For struggling learners: Use simple inequalities; provide pre-drawn boundary lines
• For advanced learners: Explore optimization within constraints
• Color-coding: Use different colors for each inequality's shading

• Observation: Can students graph inequalities and identify solution regions?

• Worksheet: Graph 2 systems of inequalities

• Test-point task: Use test points to verify solution regions

• Real-world problem: Solve a context-based system of inequalities

• System of inequalities graphing worksheets

• Test-point strategy guides

• Real-world context cards

• Coordinate plane worksheets

• Resource: Khan Academy "Systems of Inequalities" (adapted)