Unit Plan 12 (Grade 5 Math): Fractions as Division
5th graders interpret fractions as division by modeling a ÷ b with equal-sharing and measurement contexts. Students use tape diagrams, number lines, and area models to show how whole-number division creates fractions or mixed numbers, explaining units and remainder meaning clearly.
Focus: Interpret a/b as a ÷ b; use models (equal-sharing, measurement/tape diagrams, number lines, area) to solve real-world problems where whole-number division yields fractions or mixed numbers.
Grade Level: 5
Subject Area: Mathematics (Number & Operations—Fractions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students connect fractions to division by treating a/b as the quotient of a divided by b. They use equal shares and how-many-in-each or how-many-groups interpretations to model and solve problems that do not divide evenly. Contexts include sharing, measurement, area/length, recipes, and rates, emphasizing units and reasonableness. Students move flexibly among models, mixed numbers, and improper fractions, and explain why remainders can represent fractional parts of a whole.
Essential Questions
- What does a fraction mean if it comes from a ÷ b?
- How do I decide whether the quotient answers “how much in each group” or “how many groups”?
- When division doesn’t come out even, how do remainders become fractional parts in context?
- How do models help me explain and justify my answer and units?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Interpret a/b as a ÷ b and explain what the quotient means in context (amount per group or number of groups).
- Use tape diagrams, equal-sharing models, area/number lines to represent and solve quotient-as-fraction situations.
- Express answers as fractions or mixed numbers with correct units; convert between improper and mixed forms.
- Decide how to handle remainders (ignore, round, or convert to a fraction) depending on the situation; justify reasonableness.
- Communicate solutions clearly with models, equations, units, and explanations.
Standards Alignment — CCSS Grade 5
- 5.NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, using visual fraction models and equations to represent the problem.
- Mathematical Practices emphasized: MP.1 (make sense and persevere), MP.3 (justify/critique), MP.4 (model), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can explain that a/b means a divided by b and tell what that quotient represents in the problem.
- I can show my thinking with a model (tape diagram, number line, area) and a matching equation.
- I can write answers as fractions or mixed numbers and use correct units.
- I can decide what to do with a remainder and explain why that choice makes sense.
- I can check my answer with a quick estimate and a reasonableness statement.