Unit Plan 12 (Grade 7 Math): Inequalities—Model, Solve, and Graph
7th graders write, solve, and graph one-variable inequalities to model real-world constraints. They interpret solution sets, use correct symbols and boundary checks, and explain inclusive vs. strict conditions with precise, unit-based reasoning.
Focus: Write and solve inequalities from contexts; graph solution sets on a number line and interpret.
Grade Level: 7
Subject Area: Mathematics (Expressions & Equations • Problem Solving)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students learn to model constraints with one-variable inequalities, solve them (including cases with rational numbers and distribution), and graph the resulting solution sets on a number line. They interpret solutions in context (for example, “at least,” “no more than,” “over,” “under”) and use checks (boundary point and test values) to ensure reasonableness. Emphasis: choosing the correct inequality symbol, understanding open/closed circles, and flipping the inequality when multiplying/dividing by a negative.
Essential Questions
- How do phrases like at least, no more than, and greater than translate into inequality symbols?
- What does the solution set tell us about all the values that make the situation true?
- How do I check an inequality solution on both the number line and in the context?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Define a variable and write an inequality from a real-world constraint (for example, px + q > r or px + q < r).
- Solve one- and multistep inequalities with rational numbers, including distribution and combining like terms.
- Graph solution sets on a number line using open/closed circles and correct arrow direction.
- Use boundary-point checks and test values to verify solutions and determine inclusive vs. strict inequalities.
- Interpret solutions in context (units, what values are allowed) and state conclusions clearly.
Standards Alignment — CCSS Grade 7
- 7.EE.4b: Use variables to represent quantities and construct simple inequalities of the form px + q > r or px + q < r to solve problems; graph the solution set and interpret it in context.
- 7.EE.3 (spiral): Solve multistep real-life problems with rational numbers; assess reasonableness using estimation and checks.
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can translate a context into the correct inequality symbol and form.
- I can solve the inequality and flip the sign when multiplying or dividing by a negative.
- I can graph my solution with the right open/closed circle and arrow direction.
- I can test a value from my graph to confirm the inequality is true.
- I can explain what my solution set means in the real situation (with units).