Unit Plan 8 (Grade 5 Math): Decimal Division—Reasoning with Place Value

Focus: Divide decimals by whole numbers and by decimals using place-value reasoning, models (grids, base-ten blocks, number lines), and estimation; connect strategies to a written method and explain decimal placement.

Grade Level: 5

Subject Area: Mathematics (Number & Operations in Base Ten — Decimal Operations)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

Students deepen decimal understanding by dividing decimal dividends by whole-number and decimal divisors. They begin with measurement and partitive models (how many groups? how much in each group?), then generalize to a place-value algorithm. Throughout, they use estimation and scaling by powers of 10 to justify where the decimal belongs in the quotient—replacing “move the dot” shortcuts with clear place-value logic.

Essential Questions

• How do models (hundred grids, base-ten blocks, number lines) show what decimal division means?
• How does place value help determine where the decimal goes in the quotient?
• Why is estimation essential for checking reasonableness in decimal division?
• When dividing by a decimal, how does scaling both numbers by the same power of 10 keep the value the same but change the units?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Model decimal ÷ whole and decimal ÷ decimal using grids, blocks, and number lines with partitive and measurement interpretations.
2. Use place-value strategies (decomposing, scaling by powers of 10) to compute and explain decimal placement in the quotient.
3. Apply a written method (divide as whole numbers after scaling when needed) and connect it to models.
4. Use estimation (rounding, compatible numbers, front-end) to predict and verify quotient size.
5. Solve word problems that require unit tracking and appropriate precision; communicate reasoning clearly.

Standards Alignment — CCSS Grade 5

• 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 operations; relate strategies to a written method and explain reasoning.
• Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify/critique), MP.4 (model), MP.6 (precision), MP.7 (structure), MP.8 (regularity).

Success Criteria — Student Language

• I can show decimal division with a model and connect it to my written steps.
• I can explain where the decimal point goes in the quotient using place value and estimation, not just a rule.
• I can scale the dividend and divisor by the same power of 10 to make division easier and keep the value the same.
• I can estimate first, compute, then compare to check reasonableness.
• I can solve word problems, label units, and state precision choices.