# Lesson 19

Comparemos con 1

### Lesson Narrative

In previous lessons, students have compared the size of a product to the size of one factor by reasoning about the size of the other factor. They have done this using calculation, area diagrams, and number line diagrams. The goal of this lesson is to use the distributive property to explain why the comparisons work in all cases without calculating. The key observation is that a number greater than 1, such as $$\frac{5}{4}$$, can be written as $$1 + \frac{1}{4}$$ so multiplying by $$\frac{5}{4}$$ increases any number by $$\frac{1}{4}$$ of that number. In the same way multiplying by $$\frac{3}{4}$$ or $$1 - \frac{1}{4}$$ decreases any number by $$\frac{1}{4}$$ of that number.

• Engagement
• MLR8

Activity 1: Comparemos productos de fracciones en la recta numérica

### Learning Goals

Teacher Facing

• Explain what happens to a given fraction when multiplied by a fraction greater than or less than 1.

### Student Facing

• Expliquemos qué sucede cuando multiplicamos una fracción por una fracción que es mayor que, menor que o igual a 1.

Building Towards

### Lesson Timeline

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

### Teacher Reflection Questions

During the last two lessons, students have noticed and explained patterns and generalizations about multiplying by numbers greater than, less than, and equal to 1. What are some ways that you honored student language while strategically incorporating more precise academic language?

### Suggested Centers

• Rectangle Rumble (3–5), Stage 5: Fraction Factors (Addressing)
• Rolling for Fractions (3–5), Stage 4: Multiply Fractions (Supporting)