# 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.

### Required Preparation

### CCSS Standards

### 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

### Suggested Centers

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