Unit Plan 8 (Grade 7 Math): Multiply & Divide Rational Numbers
7th graders gain fluency with multiplying and dividing signed fractions and decimals through sign rules, reciprocals, and real-world applications. They convert fractions to decimals, identify repeating or terminating forms, and check results for magnitude, sign, and reasonableness.
Focus: Fluency with multiplication/division of signed fractions and decimals; properties and real-world contexts.
Grade Level: 7
Subject Area: Mathematics (The Number System • Problem Solving)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This unit develops conceptual and procedural fluency with multiplication and division of signed rational numbers (integers, fractions, decimals). Students connect sign rules to structure (properties and patterns), use reciprocals for division, convert rational numbers to terminating or repeating decimals via long division, and apply operations in real contexts (rates, area/scale, money, temperature change). Emphasis: precision with signs, units, and reasonableness checks.
Essential Questions
- Why do the sign rules for products/quotients make sense?
- How does division by a rational number relate to multiplying by its reciprocal?
- When do rational numbers produce terminating vs. repeating decimals, and why does that matter in context?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Use properties/patterns to justify and compute products of signed rational numbers (including fractions/decimals).
- Interpret and compute quotients of signed rational numbers; explain reciprocal reasoning and sign of the result.
- Convert fractions to decimals using long division and identify whether decimals terminate or repeat; round appropriately.
- Solve real-world problems requiring multiplication/division of rational numbers, with units and clear statements.
- Estimate before/after computing to assess reasonableness (magnitude, sign, order of magnitude).
Standards Alignment — CCSS Grade 7
- 7.NS.2a–d: Multiply and divide rational numbers; interpret sign rules; understand and compute quotients; use properties; convert rationals to decimals via long division (terminate or repeat).
- 7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers (focus here on multiply/divide; add/subtract spiral).
- Mathematical Practices highlighted: MP.1 (make sense), MP.3 (justify), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can decide the sign of a product/quotient before computing.
- I can divide by a rational number by multiplying by its reciprocal and explain why that works.
- I can turn a fraction into a decimal with long division and tell if it terminates or repeats.
- I can solve context problems with correct units and a clear final statement.
- I can estimate and check if my answer makes sense.