Unit 6, Lesson 18
Compare without Multiplying
Grade 5
Preparation
Lesson Narrative
In this lesson, students continue to compare the size of a product to the size of one of its factors, based on the size of its 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 with both factors as 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
- Justify (orally and in writing) why $A \times B > B$ if $A > 1$, and $A \times B < B$ if $A < 1$, when $A$ is a fraction and $B$ is a whole number.
- Let’s compare expressions without evaluating them.
Required Preparation
None
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 student convince themself that mathematics makes sense?