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.

Unit Plan 9 (Grade 4 Math): Division Concepts—Quotients & Remainders

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:

  1. Represent division situations with arrays/area models and explain dividend, divisor, quotient, and remainder.
  2. Use place-value decomposition and partial quotients to divide up to 4-digit by 1-digit.
  3. Estimate with compatible numbers to predict/verify a quotient and check reasonableness by multiplication.
  4. Decide how to interpret a remainder (keep, drop, round up, or as part of a mixed unit) using context and units.
  5. 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.