Unit Plan 20 (Grade 3 Math): Fractions on the Number Line—Benchmarks & Reasoning
Use benchmarks (0, 1/2, 1) to locate and compare fractions on number lines; partition equal intervals, label a/b precisely, and justify fraction size with clear >, <, = reasoning.
Focus: Locate and label fractions on a number line; use benchmarks 0, 1/2, and 1 to reason about size and make informal comparisons.
Grade Level: 3
Subject Area: Mathematics (Fractions & Number Line Reasoning)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students extend their understanding of fractions as numbers by placing them on number lines and using 0, 1/2, and 1 as benchmarks to reason about which fraction is closer to 0, around 1/2, or near 1. They justify placements and compare fractions (same numerator or same denominator) with short, clear arguments.
Essential Questions
- How do 0, 1/2, and 1 help me judge a fraction’s size on a number line?
- Why does the point for a/b belong at the end of a equal intervals of size 1/b starting at 0?
- How can I explain (and critique) a comparison like 3/8 vs 5/8 or 2/5 vs 2/7?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Partition 0–1 into b equal intervals and label unit fractions (1/b) and a/b accurately.
- Use benchmarks 0, 1/2, 1 to decide if a fraction is less than, about, or greater than 1/2.
- Compare fractions with the same denominator or the same numerator using number-line reasoning and record with >, =, <.
- Construct and present brief MP.3 arguments; ask clarifying questions and revise based on feedback.
Standards Alignment — CCSS Grade 3
- 3.NF.2a–b: Understand a fraction as a number on the number line; represent fractions by partitioning from 0 to 1 into b equal parts and locating a/b at the end of the ath interval.
- 3.NF.3d (informal comparison): Compare two fractions with the same numerator or the same denominator by reasoning about their size; record comparisons with >, =, < and justify conclusions.
- Mathematical Practices: MP.3 (Construct viable arguments and critique the reasoning of others) emphasized; MP.6 (precision) and MP.2 (reasoning) supportive.
Success Criteria — Student Language
- I can split 0–1 into equal intervals, label 1/b and a/b, and place a point correctly.
- I can use 0, 1/2, and 1 to say if a fraction is less than, about, or greater than 1/2.
- I can compare two fractions (same numerator/denominator) and explain why using a number line and symbols.