Unit Plan 11 (Grade 7 Math): Equations—Solve and Explain
7th graders master solving multistep equations with rational numbers by applying properties, distributing, and combining like terms. They justify each step, check with substitution and estimation, and interpret solutions clearly within real-world contexts.
Focus: Solve multistep equations with rational numbers; justify steps and check solutions for reasonableness.
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 develop fluency solving single-variable, multistep linear equations with rational numbers. They translate contexts to equations, use properties (distributive, combining like terms, inverse operations), and write step-by-step justifications. They also build habits of mental estimation, unit checks, and substitution to confirm solutions make sense.
Essential Questions
- How do I move from a real-world situation to an equation that models it?
- Why do the properties of operations justify each step when solving?
- How do I check whether my solution is reasonable and answers the question asked?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Represent word problems with equations of the form px + q = r or p(x + q) = r where p, q, r are rational.
- Solve multistep equations that may include fractions/decimals, distribution, and combining like terms.
- Justify each solving step by naming the property or operation used.
- Check solutions by substitution and with estimation/units to assess reasonableness.
- Write concise conclusion statements in context (state what the solution means).
Standards Alignment — CCSS Grade 7
- 7.EE.4a: Use variables to represent quantities; solve word problems leading to equations of the form px + q = r and p(x + q) = r with rational numbers; assess reasonableness of answers using mental math.
- 7.EE.3 (spiral): Solve multistep real-life problems with positive and negative rational numbers; use estimation/benchmarks to assess reasonableness.
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can write an equation that matches the story (define variables and units).
- I can solve a multistep equation and name the property or operation for each step.
- I can substitute my solution to check and do a quick estimate to see if it is reasonable.
- I can explain what the solution means using the context and units.