Unit Plan 11 (Grade 5 Math): Subtracting Fractions & Mixed Numbers
5th graders subtract fractions and mixed numbers with unlike denominators using equivalent fractions and models. Students rename when needed, estimate with benchmarks, and solve word problems using clear unit reasoning and precise explanations.
Focus: Subtract fractions and mixed numbers with unlike denominators using equivalent fractions and models (strips, area, number lines); estimate with benchmarks and solve word problems with clear unit reasoning.
Grade Level: 5
Subject Area: Mathematics (Number & Operations—Fractions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students extend fraction addition work to subtraction, beginning with visual models and benchmark estimates to anticipate results. They create equivalent fractions to form a common denominator, subtract proper and improper fractions, and subtract mixed numbers by renaming (regrouping) wholes into fractional parts when needed. They apply strategies to comparison and word problems, checking results for reasonableness.
Essential Questions
- What does it mean to subtract fractions, and why do we need a common denominator?
- How do benchmarks (0, 1/2, 1, 2) help us estimate and check answers?
- When subtracting mixed numbers, how and why do we rename (regroup)?
- How do models and equations communicate the same subtraction story?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Use equivalent fractions to create a common denominator and subtract unlike denominators.
- Subtract mixed numbers, including cases requiring renaming a whole into fractional parts.
- Represent subtraction with fraction strips, area models, and number lines (take-away and comparison).
- Estimate differences with benchmarks and explain reasonableness.
- Solve word problems (single- and multi-step) and communicate steps with precise vocabulary.
Standards Alignment — CCSS Grade 5
- 5.NF.1: Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions to produce an equivalent expression with like denominators; use models/equations to represent.
- 5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including mixed numbers; use benchmark fractions and number sense to estimate and assess reasonableness.
- Mathematical Practices emphasized: MP.1 (persevere), MP.3 (justify/critique), MP.4 (model), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can find a common denominator using equivalent fractions and subtract correctly.
- I can rename a mixed number to subtract when the fractional part is smaller.
- I can estimate the difference with benchmarks and explain why my answer makes sense.
- I can show my work with a model and an equation and explain both clearly.
- I can solve word problems and label units carefully.