Unit Plan 30 (Grade 5 Math): Division Mastery—Whole and Decimal
5th graders master whole-number and decimal division through place-value reasoning, strategy choice, and remainder interpretation. They estimate, compute, and check for reasonableness while explaining how powers of ten preserve equivalence.
Focus: Consolidate whole-number and decimal division; interpret remainders in context; connect all procedures to place value and reasonableness checks.
Grade Level: 5
Subject Area: Mathematics (Number & Operations in Base Ten)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students pull together their division tools—partial quotients, standard algorithm, and place-value reasoning—to divide whole numbers and decimals with confidence. They choose efficient strategies, interpret remainders (round up, drop, or convert to decimals), and explain why shifting digits by powers of ten preserves equivalence in decimal division. Every solution includes an estimate and a quick unit/context check.
Essential Questions
- How does place value explain the steps of whole-number and decimal division?
- What should I do with a remainder in different real-world situations?
- How do estimation and compatible numbers help me decide if my answer is reasonable?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Divide multi-digit whole numbers (up to four-digit dividends, two-digit divisors) using partial quotients and standard algorithm; interpret remainders.
- Divide decimals to hundredths by whole numbers and decimals using place-value shifts and equivalence (multiplying dividend and divisor by the same power of ten).
- Select and defend a strategy (model, partial quotients, or algorithm) that fits the numbers and the context.
- Use estimation and compatible numbers to predict and check quotients.
- Communicate reasoning with clear units, explanation of remainder decisions, and a final reasonableness statement.
Standards Alignment — CCSS Grade 5
- 5.NBT.6: Find whole-number quotients with up to four-digit dividends and two-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division; illustrate and explain the calculation by using equations, rectangular arrays, and/or area models; interpret remainders.
- 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning.
Success Criteria — Student Language
- I can choose partial quotients or the standard algorithm and explain my choice.
- I can show how moving the decimal in both numbers keeps the quotient the same.
- I can decide what to do with a remainder and give a because statement tied to the problem.
- I always estimate first and check after to make sure my answer makes sense.