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.
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:
- Explain solving an inequality as determining which values make it true; use substitution to test candidates.
- Write inequalities from verbal descriptions, define a variable, and include units.
- Graph solution sets on a number line with correct open/closed circles and direction for <, >, ≤, ≥.
- 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.
- 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.”).