Crafting Inequalities

Grade Level

11th Grade

Duration

60 Minutes

Common Core Standard

CCSS.MATH.CONTENT.HSA-REI.B.3
Solve linear inequalities and represent solutions on a number line.

Additional Alignment:
CCSS.MATH.PRACTICE.MP1 - Make sense of problems and persevere in solving them
CCSS.MATH.PRACTICE.MP4 - Model with mathematics
CCSS.MATH.PRACTICE.MP6 - Attend to precision

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Learning Objectives

By the end of this lesson, students will be able to:

• Construct one-variable linear inequalities from real-world scenarios.
• Solve these inequalities using algebraic methods.
• Graph solutions on a number line to visually represent solution sets.
• Interpret the solution sets in context of the given problems.

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Materials Needed

• Whiteboard and markers
• Student notebooks
• Graph paper or number line templates
• Index cards with problem scenarios
• Mini-whiteboards or laptops/tablets (optional for student work)
• Stopwatch or timer

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Lesson Breakdown

Introduction (10 minutes)

1. Hook / Engage: Present a relatable real-world scenario — "You have $50 to spend on snacks that cost $2 each. How many snacks can you buy without going over budget?"
2. Ask students to brainstorm possible inequalities that represent this situation.
3. Write and discuss a sample inequality on the board (e.g., 2x ≤ 50).
4. Highlight the standard form of one-variable inequalities and review inequality symbols (>, <, ≥, ≤).

Pedagogical tip: Use think-pair-share to encourage student engagement and verbalization of ideas.

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Guided Practice (15 minutes)

1. Modeling:

   • Create a few different inequalities from sample problems (e.g., age restrictions, budget limits, speed limits).
   • Solve each inequality on the board step-by-step, emphasizing algebraic manipulation and maintaining inequality relationships.
   • Show how to graph solution sets on a number line, noting open vs. closed circles to represent strict vs. inclusive inequalities.

2. Check for Understanding:

   • Use quick questioning or polling (e.g., thumbs up/down) on inequality signs and solution correctness.

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Independent or Group Activity (20 minutes)

Inequality Scenario Stations

• Split students into 5 groups of 6.
• Each group receives index cards with 2 unique real-world inequality scenarios.
• Tasks:
  1. Write the inequality for each scenario.
  2. Solve the inequality.
  3. Graph the solution on provided number line templates.
  4. Prepare to present one solution to the class clearly explaining reasoning and solution.

Examples of scenarios:

• "You want to work less than 30 hours but earn at least $250 with $10/hr pay."
• "A concert hall seating limit is 300. Ticket sales so far are x; define allowable ticket sales remaining."

Teacher Role: Circulate, offer targeted questions, and check for understanding. Encourage groups to explain their inequality formation clearly.

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Presentation and Discussion (10 minutes)

1. Each group presents one inequality, its solution, and its graph.
2. The class discusses if the inequality and graph are correct, focusing on refining interpretation and precision.
3. Teacher provides corrective feedback and highlights best practices for clarity in writing and graphing inequalities.

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Closing and Assessment (5 minutes)

• Quick Exit Ticket on one card per student:
  • Write and solve one inequality from a short given scenario (e.g., “You have at most $20 to spend on shirts costing $4 each. Write and solve the inequality representing how many shirts you can buy.”).
• Collect exit tickets to assess individual mastery.

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Differentiation Strategies

• For learners needing support: Provide scaffolded sentence starters (“Let x be...”), number line templates with key points marked, and additional examples.
• For advanced learners: Challenge with compound inequalities or inequalities involving absolute value contexts. Encourage them to create two different inequalities from one scenario and compare.

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Reflection & Next Steps

• Encourage students to reflect in their notebooks on how inequalities can be useful in everyday decisions.
• Preview: Next class will build on this by introducing compound inequalities and systems involving inequalities.

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Teacher Notes

• Emphasize precision in language and symbols per CCSS.MATH.PRACTICE.MP6.
• Use real-world, diverse contexts relevant to students’ experiences to increase engagement per CCSS.MATH.PRACTICE.MP4.
• Encourage peer discussion throughout to satisfy MP1 and build confidence in problem-solving communication.