Unit Plan 30 (Grade 7 Math): Expressions & Equations Power-Up

Focus: Spiral practice with rational-coefficient expressions, multistep equations and inequalities from word problems, and explicit solution checks.

Grade Level: 7

Subject Area: Mathematics (Expressions & Equations • Modeling)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

This power-up week tightens core fluencies for Grade 7 algebra. Students practice rewriting linear expressions with rational coefficients, translating real-world situations to equations and inequalities, solving multistep problems, and checking solutions for correctness and reasonableness. Emphasis: structure (distributive property, combining like terms, factoring), unit-consistent modeling, and clear concluding statements.

Essential Questions

• How can I rewrite an expression to reveal structure that makes a problem easier?
• How do I turn words into a correct equation or inequality with a clearly defined variable?
• How do I check whether my solution actually works and makes sense in context?

II. Objectives and Standards

Learning Objectives — Students will be able to…

1. Add, subtract, expand, and factor linear expressions with rational coefficients (including negatives and fractions).
2. Rewrite expressions in equivalent forms to show relationships or simplify computation.
3. Solve multistep real-world problems with positive and negative rational numbers; choose efficient strategies (distribute, combine, inverse operations).
4. Model and solve equations of the form px + q = r and p(x + q) = r; interpret the solution in context and check it.
5. Model and solve inequalities of the form px + q > r or px + q < r; graph the solution set on a number line and explain it in words.

Standards Alignment — CCSS Grade 7

• 7.EE.1: Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.
• 7.EE.2: Understand that rewriting an expression in different forms can shed light on a problem and how quantities are related.
• 7.EE.3: Solve multistep real-life and mathematical problems posed with positive and negative rational numbers; use tools strategically and assess reasonableness.
• 7.EE.4a: Use variables to represent quantities; write and solve equations of the form px + q = r and p(x + q) = r; interpret solutions.
• 7.EE.4b: Use variables to represent quantities; write, solve, and graph inequalities of the form px + q > r or px + q < r; interpret solutions.

Success Criteria — Student Language

• I can correctly distribute, factor, and combine like terms with fractions and negatives.
• I can write an equation or inequality from a word problem and define my variable.
• I can solve and then check by substitution (does the equation/inequality hold?).
• I can state units and write a clear final sentence answering the question.
• I can explain why my answer is reasonable (estimate, bounds, or context).