Unit Plan 8 (Grade 6 Math): Divide Fractions by Fractions
6th graders model and compute fraction-by-fraction division using strips, number lines, and area models. They interpret real-world contexts, justify the reciprocal rule, estimate reasonableness, and explain results with units and clear mathematical reasoning.
Focus: Model and compute fraction–fraction division; interpret and solve word problems.
Grade Level: 6
Subject Area: Mathematics (Number System • Fraction Operations)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students build a deep understanding of fraction ÷ fraction by connecting meaning (how many groups? how much in each group?) to models (fraction strips, number lines, area models) and then to the procedure (multiply by the reciprocal) with clear reasoning. They solve real-world problems (recipes, measurement, rates) and defend answers with estimates and unit statements.
Essential Questions
- What does a/b ÷ c/d mean in a story: “how many groups of c/d fit in a/b,” or “how much is in each group”?
- How do fraction strips, number lines, and area models show fraction division?
- Why does “multiply by the reciprocal” make sense?
- How can I check if my answer is reasonable?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Interpret fraction ÷ fraction as “how many groups?” (measurement model) or “how much in each group?” (partitive model).
- Use visual fraction models (strips, number lines, area) and equations to represent and solve fraction division.
- Explain and apply the multiply-by-reciprocal rule, linking it to models or common denominators.
- Solve word problems involving division of fractions and mixed numbers; include units and estimates.
- Evaluate reasonableness using benchmarks (for example, dividing by less than 1 makes a larger result).
Standards Alignment — CCSS Grade 6
- 6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions; use visual fraction models and equations to represent the problem.
- Mathematical Practices emphasized: MP.1 (make sense), MP.2 (reason quantitatively), MP.3 (justify), MP.4 (model), MP.5 (tools), MP.6 (precision), MP.7 (structure), MP.8 (regularity).
Success Criteria — Student Language
- I can tell if the problem asks “how many groups?” or “how much in each group?”
- I can show fraction division with a model and an equation.
- I can compute a/b ÷ c/d correctly and explain why multiplying by d/c works.
- I can solve a word problem with units and an estimate to check.
- I can decide whether my answer should be greater than or less than the dividend based on the divisor.