Unit Plan 9 (Grade 4 Math): Division Concepts—Quotients & Remainders
Divide up to 4-digit by 1-digit using area/array models and partial quotients; estimate to check reasonableness and interpret remainders based on context and units.
Focus: Use place value and area/array models to divide up to 4-digit ÷ 1-digit; apply partial quotients; interpret remainders in context with estimation and reasonableness.
Grade Level: 4
Subject Area: Mathematics (Number & Operations in Base Ten • Operations & Algebraic Thinking)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students build meaning for division using arrays and the area model, then connect to partial quotients and place-value decomposition for efficient computation. They practice choosing what to do with a remainder (use as a fraction, round up, drop, or report remainder) based on the story’s units and question.
Essential Questions
- How do area/array models show the meaning of quotient and remainder?
- How does place value help me break a big dividend into manageable chunks (partial quotients)?
- In word problems, how do I decide what to do with the remainder to give an answer that makes sense?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Represent division situations with arrays/area models and explain dividend, divisor, quotient, and remainder.
- Use place-value decomposition and partial quotients to divide up to 4-digit by 1-digit.
- Estimate with compatible numbers to predict/verify a quotient and check reasonableness by multiplication.
- Decide how to interpret a remainder (keep, drop, round up, or as part of a mixed unit) using context and units.
- Write equations that match division stories and explain strategy choices.
Standards Alignment — CCSS Grade 4 (spiral across the unit)
- 4.NBT.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using place value, 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.
- Connections: 4.OA.3 (solve multistep word problems, represent with equations with a letter for the unknown, assess reasonableness using estimation/rounding).
- Mathematical Practices (MP.1–MP.8) threaded throughout.
Success Criteria — Student Language
- I can use an array/area model to show my dividend, divisor, quotient, and remainder.
- I can divide using partial quotients and place value and explain each step.
- I can estimate first and check by multiplication that my answer is reasonable.
- I can choose what to do with the remainder based on the context and units.