Unit Plan 6 (Grade 5 Math): Whole-Number Division—Up to 2-Digit Divisors
5th graders divide multi-digit numbers using area and partial-quotients models before mastering the standard algorithm. Students estimate, align place values, interpret remainders in context, and explain reasoning with precision and real-world problem-solving clarity.
Focus: Divide whole numbers with up to four-digit dividends and two-digit divisors using partial quotients, area/array models, and the standard algorithm; interpret remainders in context.
Grade Level: 5
Subject Area: Mathematics (Number & Operations in Base Ten — Whole-Number Division)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students extend division from simpler cases to 4-digit ÷ 2-digit problems. They use place-value reasoning, compatible-number estimation, and partial-quotients (a.k.a. chunking) to make sense of large quotients. Visuals (arrays/area rectangles) connect to equations and then to the standard algorithm. Word problems emphasize units and remainder interpretation (drop, round up, share as a fraction, or report remainder).
Essential Questions
- How do area/array models and partial quotients show what division means?
- How does estimation help choose good “chunks” and check reasonableness?
- How does the standard algorithm relate to the partial-quotients method?
- What does a remainder mean in different contexts, and how should we report it?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Represent 4-digit ÷ 2-digit division with area/array models and equations, then compute using partial quotients.
- Connect partial quotients to the standard long-division algorithm; align place values and use regrouping accurately.
- Use compatible numbers and front-end estimation to predict results and check reasonableness.
- Interpret remainders appropriately (ignore, round up, report as fraction of divisor, or state remainder) depending on context.
- Explain and critique solutions using precise vocabulary, units, and clear notebook organization.
Standards Alignment — CCSS Grade 5
- 5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on 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.
- Mathematical Practices emphasized: MP.1 (make sense/persevere), MP.3 (justify/critique), MP.4 (model), MP.6 (precision), MP.7 (structure), MP.8 (regularity).
Success Criteria — Student Language
- I can show a division problem with an area/array model or partial quotients and explain each chunk I took.
- I can use the standard algorithm with correct alignment and regrouping, and my answer matches the model.
- I can estimate my quotient and compare it to the exact answer to check reasonableness.
- I can interpret the remainder and report the answer in a way that fits the situation.
- I can explain my steps clearly and include units.