Lesson 8

Previously, students generated equivalent fractions in any way that was intuitive to them. In this lesson, students use number lines to reason about and generate equivalent fractions. In particular, they experiment with partitioning a fractional part on the number line into smaller equal-size parts. Through repeated reasoning, students begin to notice regularity in the numerator and denominator of the equivalent fractions—namely, that the numbers are multiples of those in the original fraction. The experience of sub-partitioning number lines prepares students to formalize their observation and reason numerically about equivalent fractions in upcoming lessons. 

In this lesson, students take a closer look at the relationships between fractions with denominator 5, 10, and other multiples of 5. They begin to consider the meaning of fractions with denominator 100.

Activity 1: Handy Number Lines

• Consider creating a human number line by placing a strip of masking tape or painter’s tape, at least 25 feet long, on the floor of the classroom or a hallway.

In past lessons and in grade 3, students partitioned unit fractions such as \(\frac{1}{2}\), \(\frac{1}{3}\), and \(\frac{1}{4}\) (on fraction strips, tape diagrams, and number lines) into smaller fractional parts such as \(\frac{1}{6}\) and \(\frac{1}{8}\). How readily did students transfer those insights to work with fractions with larger denominators on the number line? What was intuitive to them and what wasn’t?