# Lesson 13

Use Equivalent Fractions to Compare

### Lesson Purpose

The purpose of this lesson is for students to compare two fractions by rewriting one of them as an equivalent fraction with the same denominator as the other.

### Lesson Narrative

Previously, students used various strategies and representations to reason about the relative size of fractions. In this lesson, they focus on writing equivalent fractions as a way to compare fractions. Here the denominator of one fraction is a factor or a multiple of the denominator of the other fraction, making it likely for students to see one fraction in terms of the fractional part of the other. In a future lesson, students will compare fractions in which the denominators have no common factors.

• Representation
• MLR7

### Learning Goals

Teacher Facing

• Compare two fractions by rewriting one of them into an equivalent fraction with the same denominator as the other.

### Student Facing

• Let’s compare fractions by writing an equivalent fraction.

### Lesson Timeline

 Warm-up 10 min Activity 1 20 min Activity 2 15 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

How readily did students grasp the idea of writing equivalent fractions with a common denominator as a way to compare fractions? What evidence did you see of students connecting it to the reasoning they did about equivalent fractions on number lines? How could the connections be made more explicit?

### Suggested Centers

• Mystery Number (1–4), Stage 4: Fractions with Denominators 5, 8, 10, 12, 100 (Addressing)
• Compare (1–5), Stage 3: Multiply within 100 (Supporting)