Inequality Mastery

Overview

Students will learn what inequality symbols mean, then solve one-step inequalities using inverse operations. They will finish by graphing solution sets on a number line and explaining their reasoning using each step’s justification.

Learning intentions

Students will be able to:

• interpret inequality symbols ( <, >, ≤, ≥ ) and understand the direction of solutions
• solve one-step linear inequalities in one variable using addition and subtraction
• solve one-step linear inequalities in one variable using multiplication and division, including negative coefficients
• graph and justify the solution on a number line with correct open/closed circles

Success criteria

“I can…”

• explain what it means when a solution satisfies an inequality
• solve inequalities and maintain the correct inequality direction at each step
• correctly treat a negative multiplier/divisor by reversing the inequality sign
• graph the solution accurately on a number line (open circle for strict, closed for inclusive)

Curriculum links

• Algebra—Reasoning with Equations and Inequalities: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters (HSA-REI.B.3)
• Algebra—Reasoning with Equations and Inequalities: Explain each step in solving a simple equation as following from equality of numbers (students will transfer the “justify each step” habit to inequality solving) (HSA-REI.A.1)
• Algebra—Creating Equations: Create inequalities from word/real situations and use them to solve (brief set-up check) (HSA-CED.A.1)

Lesson structure (60 minutes)

1. 0–6 min · Hook: Inequality quicksort. Teacher displays four “number statements” and asks students to decide which are true for a sample value (e.g., when x = 3: x < 5, x ≥ 3, x > 4, x + 1 ≤ 4). Students justify each decision with a partner using the meaning of the symbols.

2. 6–15 min · Direct teach: Symbols and solution meaning. Teacher charts the symbols and runs a short example: “Solve x > 2” with a few checks (is 3 a solution? is 2 a solution?). Students underline the boundary number and describe whether it belongs to the solution set.

3. 15–28 min · One-step inequalities (addition/subtraction). Teacher models solving two problems, writing the justification sentence at each step: Example A: Solve x − 5 ≤ 2.

• Add 5 to both sides → x ≤ 7
• Check with a test value (x = 7 works; x = 8 does not). Example B: Solve x + 3 > 10.
• Subtract 3 from both sides → x > 7 Students complete a third problem in pairs and share their “each step follows because…” reasoning aloud.

4. 28–40 min · One-step inequalities (multiplication/division). Teacher highlights the key rule: multiplying/dividing by a negative flips the inequality sign. Example C: Solve 3x ≥ 12.

• Divide by 3 → x ≥ 4 Example D: Solve −2x < 6.
• Divide by −2 and flip → x > −3 Students do a “Sign-Swap” mini-practice: each student solves one problem card; classmates confirm the inequality direction using a fast check.

5. 40–52 min · Graphing on a number line. Teacher demonstrates graphing:

• x ≤ 7 → closed circle at 7, shade left
• x > −3 → open circle at −3, shade right Then uses one mixed problem: “Solve 5 − x ≥ 1”
• Solve: −x ≥ −4 → multiply by −1 flips → x ≤ 4 Students graph the corresponding solution on their own number line (they must choose open vs closed correctly).

6. 52–58 min · Whole-class reasoning check (guided). Teacher projects a common error: forgetting to flip when dividing by a negative (e.g., −2x < 6 turned into x < −3). Students vote, explain why it’s incorrect, and correct the inequality.

7. 58–60 min · Exit ticket. Students complete two items independently and submit:

• Solve: x + 2 ≥ 9
• Solve and graph: −3x > 6 (write the inequality solution and mark it on a number line)

Resources

• Inequality symbol cards (<, >, ≤, ≥)
• Number line handouts (with blank shading areas)
• One-step inequality problem sets (addition/subtraction, multiplication/division, negative cases)
• “Sign-Swap” practice cards
• Markers/colored pencils for shading left/right
• Projector/board for teacher worked examples
• Exit ticket slips

Assessment

• Formative checks during pair work: monitor explanations and ensure inequality direction is correct
• Teacher observation during practice cards: look specifically for sign-flip errors when multiplying/dividing by negative
• Exit ticket: verify both the algebraic solution and the correct graph (open vs closed circle)

Differentiation

• Support: Provide a two-column scaffold (“Inverse operation I apply” / “New inequality statement”) and sentence starters: “I changed the inequality because I added/subtracted/multiplied/divided both sides…”
• Support: Offer a “test value” checklist so students confirm solutions quickly (especially after negative sign changes)
• Extension: Challenge a “create and solve” item (e.g., “Write an inequality for ‘at least 5 dollars’ and solve for m”) to connect inequalities to real contexts
• EAL/SEN: Allow students to verbalize reasoning with a partner first; emphasize symbol meaning with consistent gestures (open circle = strict, closed circle = inclusive)