Unit Plan 33 (Grade 7 Math): Rational Numbers in the Wild
7th graders solve multistep real-world problems using signed fractions and decimals. They estimate, calculate precisely, and report results with units and error bounds, building accuracy, structure, and real-world quantitative reasoning.
Focus: Solve multistep real-world problems with signed numbers and fractions/decimals; estimation and error bounds.
Grade Level: 7
Subject Area: Mathematics (Number System • Expressions & Equations • Modeling)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week sharpens fluency with rational numbers in lived contexts—temperatures, elevations, budgets, recipes, and time changes. Students add, subtract, multiply, and divide signed fractions and decimals, stringing operations together in multistep problems. They practice estimation before calculation, track units, and write error bounds when rounding or measurement uncertainty is present.
Essential Questions
- How do positive and negative numbers model real changes (gains/losses, up/down, above/below zero)?
- How can I check reasonableness with benchmarks, bounds, and units before and after I compute?
- How do I organize multistep work so signs, fractions, and decimals don’t trip me up?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Interpret and operate with signed rational numbers on number lines and in context (changes, differences, distances).
- Add/subtract/multiply/divide fractions and decimals with negatives using properties and representations.
- Solve multistep real problems with mixed operations and rational coefficients; show a clean structure and units.
- Use estimation to set expectations and error bounds (intervals) when rounding or when inputs are approximate.
- Communicate conclusions clearly with units, context sentences, and brief reasonableness checks.
Standards Alignment — CCSS Grade 7
- 7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.
- 7.NS.2: Apply and extend previous understandings of multiplication and division to multiply and divide rational numbers.
- 7.NS.3: Solve real‐world and mathematical problems involving the four operations with rational numbers.
- 7.EE.3: Solve multistep real‐life and mathematical problems posed with positive and negative rational numbers; use estimation, mental math, and rounding to assess reasonableness.
- Mathematical Practices emphasized: MP.1 (make sense), MP.2 (quantitative reasoning), MP.4 (model), MP.5 (tools), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can model gains/losses and up/down changes with signed numbers.
- I can compute with fractions and decimals (positives and negatives) and explain my sign.
- I can solve a multistep situation with neat work, units, and a final sentence.
- I can estimate first and then bound my answer when I round.
- I can explain why my answer makes sense in the situation.