Inequalities & Modeling

Grade 7 | 30-Minute Session

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Common Core State Standards Addressed

7.EE.B.4

• Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems.
• Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.

7.EE.B.4a

• Solve inequalities and represent solutions on a number line.

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Learning Objectives

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

• I can write one-step inequalities from word problems.
• I can correctly use inequality symbols (>, <, ≥, ≤).
• I can model one-step inequalities on number lines.
• I can explain the difference between an inequality and an equation.

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Success Criteria

Students will demonstrate success by:

• Accurately translating verbal statements into one-step inequalities.
• Correct use of inequality symbols in writing and interpreting problems.
• Correctly graphing solution sets of one-step inequalities on number lines.
• Explaining orally or in writing the conceptual difference between an inequality (range of solutions) and an equation (single solution).

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Materials Needed

• Whiteboard and markers
• Number line printouts (dyslexia-friendly version with larger font and clear spacing)
• Inequality symbol cards (> , < , ≥ , ≤)
• Mini whiteboards for student work
• Word problem task cards
• Colored pencils or markers

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Lesson Breakdown

1. Introduction & Review (5 minutes)

• Begin with a quick review of what an equation is (one solution, equality symbol =).
• Introduce inequalities: Explain these represent ranges of values, not just one value. Write examples on board:
  • Equation: x + 3 = 7
  • Inequality: x + 3 > 7
• Display inequality symbols and explain their meaning with simple, relatable phrases (e.g., > means “greater than”).
• I can statement: I can recognize and use inequality symbols.

2. Guided Practice: Writing Inequalities (8 minutes)

• Read aloud a short word problem as a class, e.g.:
  “Luis has $10. He wants to buy a book that costs more than $6. Write an inequality to represent the amount of money Luis can spend.”
• Model how to translate this into an inequality: x > 6.
• Write the inequality on the board and ask: “What does ‘>’ mean here?”
• Hand out task cards with similar word problems. Students work in pairs to write inequalities.
• Circulate and provide support; use inequality cards as manipulatives for kinesthetic learners.
• Dyslexia-friendly tip: Use bullet points or numbered steps to break down word problems on cards.

3. Modeling Inequalities on Number Lines (7 minutes)

• Draw a number line on the board and model graphing x > 6: open circle at 6, shading to the right.
• Explain open vs. closed circles for <, >, ≤, ≥.
• Students use mini whiteboards to graph inequalities from their task cards.
• Invite volunteers to share their graphs, explaining their choices of circle and shading.
• I can statement: I can model inequalities using number lines.

4. Discussing Differences: Equations vs. Inequalities (5 minutes)

• Guide students to articulate how inequalities differ from equations in terms of solutions and graphing.
• Use a Venn diagram on the board to organize differences and similarities.
• Ask students to pair-share an explanation sentence, then randomly call on several to share aloud.

5. Extension Activity & Wrap-Up (5 minutes)

• For advanced learners: Challenge them to create and solve one-step inequalities involving multiplication/division, e.g., 3x < 12.
• Dyslexia-friendly written summary on a handout reinforcing key points with icons and color coding.
• Quick formative assessment: Each student writes one inequality and graphs it on a mini whiteboard for immediate feedback.

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Differentiation Strategies

• Visual learners: Use color-coded inequality symbols and shaded number lines with clear, large fonts.
• Kinesthetic learners: Use movable inequality symbol cards and physical number line strips on desks.
• Students with reading difficulties or dyslexia: Provide dyslexia-friendly formatted task cards and handouts with spacing, larger font, and sans-serif typeface. Use auditory instructions and partner reading.
• English Language Learners (ELL): Pair with strong English speakers; pre-teach key vocabulary (greater than, less than, equal to). Use visual aids extensively.

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Assessment

• Formative through observation during partner work and graphing.
• Checking mini whiteboard responses ensures understanding in real time.
• Venn diagram verbal discussion checks conceptual grasp.

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Teacher Reflection Prompts

• Did students use inequality symbols correctly and confidently?
• Were students able to explain the difference between inequalities and equations?
• Were the number line models accurate and consistent?
• Did differentiation strategies support diverse learners effectively?
• How engaged were students with the extension activity?

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This lesson plan is designed to meet CCSS 7.EE.B.4 with a focused, interactive, and scaffolded approach that encourages clear understanding of inequalities as a foundation for future algebra work.