Lesson 5

The purpose of this lesson is for students to explain why \(a \div b = \frac{a}{b}\) and apply their understanding to flexibly interpret division situations and equations where the unknown is the numerator, denominator, or the value of the quotient.

In this lesson, students generalize their understanding that a fraction can be interpreted as division of the numerator by the denominator. They interpret situations where a certain amount of pounds of blueberries is shared with a certain number of people when the pounds of blueberries each person gets is equal to 1, greater than 1, and less than 1. Then, they construct arguments about why an equation would make sense for any numerator and for any denominator. As they do so, they have a chance to use language precisely (MP6), explaining that the numerator \(a\) represents the number of objects being shared and the denominator \(b\) represents the number of equal shares.

How has your thinking about division changed since the beginning of the unit? What evidence did you see during this section of the unit that each of your students extended their understanding of the meaning of division?