Unit Plan 28 (Grade 5 Math): Fractions & Decimals—Multi-Step Decisions
5th graders solve real-world problems using fractions and decimals, choosing the most efficient form for each task. They justify methods with models, estimate for reasonableness, and communicate reasoning clearly.
Focus: Solve real-world problems requiring fraction and decimal operations; choose efficient representations (fraction vs decimal), justify methods, and check reasonableness with benchmarks and estimates.
Grade Level: 5
Subject Area: Mathematics (Number & Operations—Fractions; Number & Operations in Base Ten)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This unit braids together fraction and decimal computation in authentic, multi-step contexts (recipes, budgets, measurement, data displays). Students decide when to keep fractions and when to convert to decimals, structure their plan, then defend their choices with models, properties, and estimation checks. Emphasis is on method selection, accuracy, and clear mathematical communication.
Essential Questions
- Should I solve this with fractions or decimals—and why?
- How do benchmarks and estimation tell me if an exact answer is reasonable?
- What models (area, number line, tape diagram) best explain my method?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Add and subtract fractions with unlike denominators, including mixed numbers, and interpret results in context.
- Multiply fractions × fractions and fractions × whole numbers using area/array models and scaling reasoning.
- Divide unit fractions by whole numbers and whole numbers by unit fractions; explain meaning with tape diagrams or sharing/measurement contexts.
- Add, subtract, multiply, and divide decimals to hundredths; flexibly convert between fractions and decimals when helpful.
- Solve multi-step word problems that blend fraction/decimal operations, including estimation and justification of method choice.
Standards Alignment — CCSS Grade 5
- 5.NF.1–2: Add/subtract fractions with unlike denominators; solve word problems with fraction addition/subtraction (including mixed numbers) using visual fraction models and equations.
- 5.NF.4–6: Multiply a fraction by a fraction/whole number; interpret multiplication as scaling; apply multiplication to real-world problems.
- 5.NF.7 (a–c): Divide unit fractions by whole numbers and whole numbers by unit fractions using visual models and equations.
- 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths using place-value strategies and models.
Success Criteria — Student Language
- I can choose fractions or decimals and explain why that choice is efficient.
- I can add/subtract fractions with unlike denominators and show how I found an equivalent form (LCD).
- I can multiply fractions and tell whether the product should be greater or less than each factor (scaling).
- I can divide unit fractions and whole numbers and explain what the quotient means in the situation.
- I can estimate before and check after to confirm that my result is reasonable.