Unit Plan 31 (Grade 4 Math): Multi-Digit Multiplication & Division—Applied

Focus: Solve multi-step problems requiring multi-digit multiplication and division; attend to reasonableness, estimation, and remainder interpretation in real contexts.

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 deepen fluency with multi-digit multiplication and division and apply both in multi-step word problems. They choose among area/array models, partial products, place-value strategies, and the standard algorithm, check answers with estimation/compatible numbers, and decide how to interpret remainders based on context.

Essential Questions

• How can I choose an efficient strategy for multi-digit multiplication or division?
• How do I know if my answer is reasonable?
• What does the remainder mean in this situation—ignore, round up, use as a fraction, or report as leftover?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Multiply multi-digit numbers using area models, partial products, and the standard algorithm.
2. Divide up to four-digit numbers by one-digit divisors using place-value reasoning and interpret the remainder.
3. Plan and solve multi-step problems that require both operations; record a clear equation and representation.
4. Use estimation/compatible numbers to check reasonableness and verify results.
5. Communicate and justify remainder interpretations tied to the context and units.

Standards Alignment — CCSS Grade 4

• 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and two two-digit numbers, using strategies based on place value and the properties of operations; illustrate and explain the calculation by using equations, rectangular arrays, and/or area models; relate strategies to the standard algorithm.
• 4.NBT.6: Find whole-number quotients and remainders with up to four-digit dividends and one-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.
• 4.OA.3 (connection): Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems where remainders must be interpreted; represent these problems using equations with a letter standing for the unknown quantity; assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Success Criteria — Student Language

• I can pick a strategy (area model, partial products, standard algorithm) that fits the numbers.
• I can check my work with estimation/compatible numbers and explain why my answer is reasonable.
• I can interpret the remainder correctly and explain what it means in the problem’s context.