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Grade 3 Math Units

Unit Plan 31 (Grade 3 Math): Fractions Synthesis—Benchmarks, Equivalence, Compare

Learn to place fractions on number lines, prove equivalence, and compare using benchmarks and clear symbols to build flexible Grade 3 fraction reasoning.

Dr. Michael Kester-Haynes

• 5 min read
Unit Plan 31 (Grade 3 Math): Fractions Synthesis—Benchmarks, Equivalence, Compare

Focus: Bring together 3.NF: place fractions on number lines, explain equivalence, and compare with reasoning and clear symbols.

Grade Level: 3

Subject Area: Mathematics (Fractions)

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

I. Introduction

Students consolidate fraction understanding by connecting unit fractions to non-unit fractions, representing them on a number line, explaining equivalent fractions, and comparing fractions using benchmarks (0, 1/2, 1) and the idea of the same whole. They justify decisions with models and symbols.

Essential Questions

  • How does the number line help me understand and compare fractions?
  • What makes two fractions equivalent, and how can I prove it?
  • When I compare fractions, what benchmarks and models give the clearest evidence?

II. Objectives and Standards

Learning Objectives — Students will be able to:

  1. Represent unit fractions and a/b as a copies of 1/b using number lines and visual models.
  2. Place and label fractions on a number line, partitioning intervals into equal parts.
  3. Explain and generate equivalent fractions using area/strip models and number lines.
  4. Compare fractions using benchmarks (0, 1/2, 1), same numerator/denominator reasoning, and correct symbols (>, <, =).
  5. Justify conclusions by connecting models, benchmarks, and fraction structure.

Standards Alignment — CCSS Grade 3

  • 3.NF.1: Understand a unit fraction 1/b and a/b as a copies of 1/b.
  • 3.NF.2a–b: Represent fractions on a number line; mark off 1/b sized intervals; locate a/b.
  • 3.NF.3a–d: Explain equivalence of fractions; recognize/generate simple equivalents; compare fractions by reasoning about size (with the same whole); record comparisons with symbols.
  • Mathematical Practices: MP.2 (Reason abstractly & quantitatively), MP.3 (Construct arguments & critique).

Success Criteria — Student Language

  • I can show 1/b and a/b on a number line with equal parts and correct labels.
  • I can prove two fractions are equivalent using a model or number line.
  • I can compare two fractions and write >, <, or = with a reason (e.g., benchmark or same numerator/denominator logic).