Inequalities & Modeling

Grade 7 | 30-Minute Session

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.

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.

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).

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

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.

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.

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.

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?

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.