Lesson objective: Generate many equivalent fractions for the same point on a number line by repeatedly partitioning the number line.

This lesson helps to build procedural skill with generating equivalent fractions. A number line is used here because it supports the understanding that equivalent fractions name the same position on a number line. This work develops students' understanding that we can name numbers in infinitely many ways.

Students engage in Mathematical Practice 4 (model with mathematics) as they represent fractions as lengths on a number line, as numbers, and in equations. Students partition the number line to generate equivalent fractions. Students engage in Mathematical Practice 6 (attend to precision) as they partition the number line into equal parts and use precise vocabulary to communicate their understanding.

**Key vocabulary:**

- equivalent
- number line
- partition
- position