Lesson objective: Recognize invariance of fractional distances on a number line.

Students bring prior knowledge of invariance of whole numbers on a ruler from 2.MD.D.9. This prior knowledge is extended to invariance of fractions on a number line and ruler as students explore lengths starting at different endpoints. A conceptual challenge students may encounter is measuring lengths that do not begin at 0 on a ruler.

The concept is developed through work with number lines and rulers, which are partitioned in the same manner.

This work helps students deepen their understanding of equivalence because they will begin to see that fractions remain the same size regardless of their location on a number line.

Students engage in Mathematical Practice 4 (model with mathematics) as they partition number lines and rulers and use copies of unit fractions to measure fractional lengths.

**Key vocabulary:**

- measure
- number line
- partition
- ruler
- unit fraction