Unit Plan 22 (Grade 3 Math): Comparing Fractions with Same Numerator/Denominator
Grade 3 fractions: compare with same numerator or denominator using area and number line models; record with <, >, = and justify clearly using same-whole reasoning.
Focus: Compare fractions by reasoning about size when they have the same numerator or the same denominator; record comparisons with symbols and justify.
Grade Level: 3
Subject Area: Mathematics (Fractions—Comparison)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students learn to compare fractions conceptually instead of “tricks.” With the same denominator, they compare how many unit fractions; with the same numerator, they compare the size of the unit fraction (denominator). They use area and number line models, ensure the same whole, and write statements using <, >, = with a brief justification.
Essential Questions
- How do I compare fractions that share the same denominator?
- How do I compare fractions that share the same numerator?
- Why must fractions refer to the same whole before comparing?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Compare fractions with the same denominator by reasoning about how many unit fractions (more parts of the same size → greater).
- Compare fractions with the same numerator by reasoning about the size of each part (larger denominator → smaller parts → lesser).
- Use area and number line models to support comparisons and write <, >, = correctly.
- Justify a comparison verbally and in writing (MP.3), referencing same whole and model evidence.
Standards Alignment — CCSS Grade 3
- 3.NF.3d: Compare two fractions with the same numerator or same denominator by reasoning about their size; record results with symbols and justify the conclusions.
- 3.NF.3c (concepts of whole): Explain that comparisons are valid only when the two fractions refer to the same whole.
- Mathematical Practices: MP.3 (Construct viable arguments & critique the reasoning of others).
Success Criteria — Student Language
- I can explain why one fraction is greater/less using a model and the same whole.
- I can compare same denominator by counting unit fractions, and same numerator by thinking about part size.
- I can write a correct statement with <, >, = and a short because sentence.