Unit Plan 19 (Grade 4 Math): Fraction Equivalence—Why It Works

Focus: Explain and generate equivalent fractions using visual models and number lines; justify with same-whole reasoning and scale factors.

Grade Level: 4

Subject Area: Mathematics (Number & Operations—Fractions)

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

I. Introduction

Students build deep understanding of equivalent fractions by reasoning about the same whole, equal partitions, and scaling the numerator and denominator by the same number. Learners connect area models, fraction strips, and number lines to explain why fractions are equivalent and when simplifying is useful.

Essential Questions

• How do I know two fractions are equivalent, and how can I prove it?
• Why must equivalent fractions name parts of the same whole with equal-sized parts?
• How do number lines and area models help me see scale factors and benchmarks (0, 1/2, 1)?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Explain why a/b = (n × a)/(n × b) using visual fraction models and number lines.
2. Generate equivalent fractions by multiplying/dividing numerator and denominator by the same number.
3. Justify equivalence using the same whole, equal partitions, and corresponding points on a number line.
4. Use benchmarks (0, 1/2, 1) and reasonableness checks to verify equivalence.
5. Communicate thinking with labeled models, clear vocabulary, and concise written explanations.

Standards Alignment — CCSS Grade 4

• 4.NF.1: Explain why a/b = (n × a)/(n × b) by using visual fraction models; use this principle to recognize and generate equivalent fractions.

Success Criteria — Student Language

• I can show two fractions are equivalent with a model or number line and explain why.
• I can create equivalents by multiplying/dividing the numerator and denominator by the same number.
• I can check for the same whole and use benchmarks to decide if my answer makes sense.