# Lesson 18

Compare Without Multiplying

### Lesson Purpose

The purpose of this lesson is for students to compare the size of a product to the size of one factor on the basis of the size of the other factor.

### Lesson Narrative

In this lesson, students continue to compare the size of a product to the size of one of the factors based on the size of the other factor. They also continue to represent these comparisons on the number line. In this lesson there is no longer a context and students interpret the number line diagram in situations where both factors are fractions. Just as they observed in previous lessons, the size of a number becomes greater when multiplied by a fraction greater than 1 and smaller when multiplied by a fraction less than 1. In the next lesson, students will work toward giving a general explanation for these patterns.

• Representation
• MLR7

### Learning Goals

Teacher Facing

• Recognize that the product of a fraction and a whole number is less than, equal to, or greater than the whole number when the fraction is correspondingly less than, equal to, or greater than 1.

### Student Facing

• Let’s compare expressions, without evaluating them.

### 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

It is important that students convince themselves that mathematics makes sense. Today, students were noticing patterns and determining whether or not the patterns were generalizable. In what ways did each of your students convince themselves that mathematics makes sense?

### Suggested Centers

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