Unit Plan 9 (Grade 7 Math): Rational Number Problem Solving
7th graders apply all four operations with rational numbers to solve multistep real-world problems. They plan, estimate, and compute using fractions or decimals, track units and signs, and verify results with error checks and clear, context-based conclusions.
Focus: Integrate all four operations with rational numbers in multistep contexts; estimation and error checks.
Grade Level: 7
Subject Area: Mathematics (The Number System • Expressions & Equations • Problem Solving)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This unit is a capstone for rational-number arithmetic: students apply addition, subtraction, multiplication, and division with signed fractions and decimals to solve multistep, real-world problems. They plan solutions, choose efficient representations (fractions or decimals), track units and signs, and build in estimation and error checks. Emphasis: communicating a plan, showing structure, and verifying reasonableness.
Essential Questions
- How do I choose a strategy (fraction vs decimal, equation vs step list) for a multistep rational-number problem?
- How do estimation, units, and sign checks help me catch errors before and after I compute?
- How can I clearly justify my solution path so another person can follow it?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Translate contexts into expressions or step plans that combine all four operations with signed rational numbers.
- Choose efficient representations (fractions/decimals) and use properties to organize work and reduce error.
- Use estimation (benchmarks, compatible numbers, bounds) to predict and to verify results.
- Execute calculations with precision (units, rounding rules, place value, sign management).
- Write clear conclusion statements that interpret answers in context and include an explicit reasonableness check.
Standards Alignment — CCSS Grade 7
- 7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers.
- 7.EE.3 (connection): Solve multistep real-life problems using positive and negative rational numbers; assess reasonableness using mental math and estimation strategies.
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can plan my steps and pick fractions or decimals that make the work easier.
- I can keep signs and units correct through all steps.
- I can give an estimate before I start and a check after I finish.
- I can explain my solution so someone else can follow it.
- I can state a clear conclusion that answers the question with units.