Unit Plan 21 (Grade 4 Math): Fractions as Sums—Decompose & Compose
Understand a/b as the sum of unit fractions 1/b; decompose and compose fractions and mixed numbers in multiple ways using visual models and equations to justify equivalence.
Focus: Understand a/b with a > 1 as sums of unit fractions 1/b; decompose and compose fractions and mixed numbers with clear models and equations.
Grade Level: 4
Subject Area: Mathematics (Number & Operations—Fractions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students internalize that a fraction a/b can be seen as the sum of a unit fractions 1/b. They decompose fractions and mixed numbers in more than one way and compose them back, justifying with area models, fraction strips, and the number line. This week sets the stage for later operations with fractions by strengthening the meaning of parts, units, and equivalences.
Essential Questions
- How does thinking of a/b as a copies of 1/b help me understand and explain fractions?
- In how many ways can I decompose a fraction or mixed number, and how do I know each way is equivalent?
- How do models (area, strips, number lines) and equations work together to prove my decomposition?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Explain a fraction a/b (with a > 1) as a sum of unit fractions 1/b using models and equations.
- Decompose a fraction into sums of fractions with the same denominator in more than one way and justify the decompositions.
- Represent decompositions on area models, fraction strips, and number lines, labeling units precisely.
- Compose unit fractions back into a single fraction or mixed number, confirming equivalence.
- Communicate reasoning using mathematical language (e.g., unit fraction, decompose, compose, equivalent, sum, addends).
Standards Alignment — CCSS Grade 4
- 4.NF.3a: Understand a fraction a/b with a > 1 as a sum of unit fractions 1/b.
- 4.NF.3b: Decompose a fraction into a sum of fractions with the same denominator in more than one way; record each decomposition by an equation and justify decompositions (e.g., by using a visual fraction model).
Success Criteria — Student Language
- I can show a/b = 1/b + 1/b + … (a times) with a model and an equation.
- I can decompose a fraction (and mixed number) in more than one way and explain why each is equivalent.
- I can compose unit fractions back and check that my total matches the original fraction.