Unit Plan 16 (Grade 5 Math): Dividing Unit Fractions and Whole Numbers

Focus: Divide unit fractions by whole numbers and whole numbers by unit fractions using models (tape/area, number lines, counters) and real-world contexts; explain why the results make sense.

Grade Level: 5

Subject Area: Mathematics (Number & Operations—Fractions)

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

I. Introduction

Students develop solid meaning for two special fraction–division cases:

1. Unit fraction ÷ whole number (for example, 1/3 divided among 4 people) and
2. Whole number ÷ unit fraction (for example, how many 1/4-cup scoops are in 3 cups?). They use equal-sharing and how-many-groups interpretations, moving from models to equations, and justify why (1/b) ÷ c = 1/(b×c) and a ÷ (1/b) = a×b are reasonable in context.

Essential Questions

• What does it mean to divide a unit fraction by a whole number in a real situation?
• How can we model how many 1/b’s fit into a (whole number divided by a unit fraction)?
• Why do some quotients get smaller (unit fraction ÷ whole number) while others get larger (whole number ÷ unit fraction)?
• How do models, equations, units, and estimates work together to tell the story of the quotient?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Model (1/b) ÷ c with equal shares (tape/area) and explain why the result is 1/(b×c).
2. Model a ÷ (1/b) with measurement division (how-many-groups) using number lines or repeated jumps to show there are a×b groups.
3. Choose a representation that fits the context and write a matching equation with units.
4. Predict the size of the quotient and check reasonableness with benchmarks and scaling logic.
5. Communicate mathematical thinking clearly, linking model → equation → labeled answer.

Standards Alignment — CCSS Grade 5

• 5.NF.7a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
• 5.NF.7b: Interpret division of a whole number by a unit fraction, and compute such quotients.
• 5.NF.7c: Solve real-world problems involving division of unit fractions by non-zero whole numbers and whole numbers by unit fractions.
• Mathematical Practices emphasized: MP.1 (make sense and persevere), MP.3 (justify/critique), MP.4 (model), MP.5 (use tools), MP.6 (precision), MP.7 (structure).

Success Criteria — Student Language

• I can explain what is being divided and what the answer represents.
• I can show (1/b) ÷ c with a model and state the quotient as 1/(b×c).
• I can show a ÷ (1/b) with a number line or jumps and explain why the answer is a×b.
• I can write an equation that matches my model and give a labeled answer.
• I can check that my answer is reasonable using benchmarks or scaling.