Unit Plan 16 (Grade 6 Math): Inequalities—Model, Solve, and Graph

6th graders learn to write and solve inequalities from real-world situations, graph solution sets with correct symbols, and interpret results using units. They test values, use substitution for accuracy, and explain what each inequality means in context.

Unit Plan 16 (Grade 6 Math): Inequalities—Model, Solve, and Graph

Focus: Write inequalities from situations, graph solution sets on number lines, and interpret results.

Grade Level: 6

Subject Area: Mathematics (Expressions & Equations – Inequalities)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session


I. Introduction

Students extend “solving” beyond a single value to a set of values that make an inequality true. They translate verbal conditions to inequalities, use substitution to test values, and graph solution sets on number lines using open/closed circles and directional shading. Emphasis: meaning-making, units, and clear interpretation of what the solution set represents in context.

Essential Questions

  • What does it mean for a number to satisfy an inequality?
  • How do I decide which symbol (<, >, , ) fits a real situation?
  • Why does an inequality have many solutions, and how do I graph them?
  • How do I check and interpret an inequality solution set with units?

II. Objectives and Standards

Learning Objectives — Students will be able to:

  1. Explain solving an inequality as determining which values make it true; use substitution to test candidates.
  2. Write inequalities from verbal descriptions, define a variable, and include units.
  3. Graph solution sets on a number line with correct open/closed circles and direction for <, >, ≤, ≥.
  4. Solve one-step inequalities involving addition or multiplication by a positive number (for example, x + p ≤ q, px ≥ q) and interpret the solution set in context.
  5. Identify and correct common errors (wrong symbol, reversed direction on the graph, forgetting closed/open circle, misreading “at least/at most”).

Standards Alignment — CCSS Grade 6

  • 6.EE.5: Understand solving an equation or inequality as determining which values make the statement true; use substitution to check.
  • 6.EE.8: Write an inequality of the form x > c, x ≥ c, x < c, or x ≤ c to represent a constraint or condition; graph the solution set on a number line and interpret in context.

Success Criteria — Student Language

  • I can tell if a number makes an inequality true by substituting it.
  • I can choose the correct symbol and write an inequality that matches a situation.
  • I can graph the solution set with the right circle (open/closed) and arrow direction.
  • I can explain what my solution means with units (for example, “Any time ≤ 30 minutes works.”).