Unit Plan 15 (Grade 5 Math): Fraction Multiplication in the Real World
5th graders apply fraction multiplication to real-world problems, using models like tape diagrams, arrays, and number lines. Students write matching equations, label units, and justify answers with benchmarks, scaling logic, and clear reasoning.
Focus: Apply fraction-by-fraction and fraction-by-whole multiplication to solve word problems, choosing and justifying models (tape diagrams, arrays/area, number lines) and equations that match the situation.
Grade Level: 5
Subject Area: Mathematics (Number & Operations—Fractions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Building on fraction multiplication concepts and scaling, students now apply them to real contexts: recipes, measurement, area, rates, and portion-of-a-portion situations. Emphasis is on model–equation–solution coherence, units, and reasonableness checks. Students select a representation, solve, interpret the product, and explain why their method fits the story.
Essential Questions
- How do I decide which model (tape diagram, area/array, number line) best fits a fraction multiplication story?
- What information must appear in my equation so it matches the context and units?
- How do I explain whether an answer is reasonable using benchmarks and scaling?
- How can I communicate a clear solution path from story → model → equation → labeled answer?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Represent word problems that require fraction × whole or fraction × fraction with visual models and equations.
- Solve multi-step contexts, including portion-of-a-portion and area with fractional sides, and label units precisely.
- Use benchmarks and scaling logic to predict product size and check reasonableness.
- Explain and defend solution choices, critiquing others’ work with evidence from models and units.
- Convert between mixed numbers and improper fractions as needed to present clear final answers.
Standards Alignment — CCSS Grade 5
- 5.NF.6: Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
- Mathematical Practices emphasized: MP.1 (make sense and persevere), MP.3 (justify/critique), MP.4 (model), MP.5 (use tools strategically), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can choose a model that fits the story and write a matching equation.
- I can solve and give a labeled answer with correct units.
- I can predict if my product should be smaller, about the same, or larger using scaling.
- I can explain my steps and why my model and equation make sense.
- I can check reasonableness with a quick benchmark estimate.