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Grade 3 Math Units

Unit Plan 21 (Grade 3 Math): Fraction Equivalence—Same Whole, Same Size

Grade 3 equivalent fractions: prove pairs like 1/2=2/4 with area and number line models, emphasizing same whole/same size reasoning, clear labels, and concise explanations.

Dr. Michael Kester-Haynes

• 5 min read
Unit Plan 21 (Grade 3 Math): Fraction Equivalence—Same Whole, Same Size

Focus: Explain and generate equivalent fractions (e.g., 2/4 = 1/2) using area and number line models; emphasize same whole and same size reasoning.

Grade Level: 3

Subject Area: Mathematics (Fractions—Equivalence)

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

I. Introduction

Students deepen their understanding of fractions as numbers by demonstrating when two fractions are equivalent—that is, they name the same size of the same whole or land at the same point on a number line. They use area models (strips, rectangles, circles) and number lines to create and justify examples like 1/2 = 2/4 or 2/3 = 4/6, and explain why equivalence works.

Essential Questions

  • What does it mean for two fractions to be equivalent?
  • Why must fractions use the same whole to make a fair comparison?
  • How do area and number line models show that 2/4 and 1/2 are the same size?

II. Objectives and Standards

Learning Objectives — Students will be able to:

  1. Explain fraction equivalence as same size of the same whole or the same point on a number line.
  2. Generate and label simple equivalent fractions (e.g., 1/2 ↔ 2/4, 2/3 ↔ 4/6) with area and number line models.
  3. Describe the structure (MP.7): partitioning each piece again creates more equal parts but the same total amount.
  4. Model solutions (MP.4) and present short justifications using precise vocabulary and representations.

Standards Alignment — CCSS Grade 3

  • 3.NF.3a: Understand two fractions as equivalent if they are the same size or the same point on a number line.
  • 3.NF.3b: Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3) and explain with models.
  • Mathematical Practices: MP.4 (Model with mathematics), MP.7 (Use structure).

Success Criteria — Student Language

  • I can show two fractions are equivalent with an area model or a number line.
  • I can explain that the whole stayed the same, and the size of the shaded/marked amount did not change.
  • I can create my own pairs like 1/2 and 2/4 and explain why they match.