Lesson objective: Understand that equivalent fractions for whole numbers can be represented on a number line. Recognize equivalent fractions for whole numbers on a number line.

Students bring prior knowledge of recognizing fractions on a number line from 3.NF.A.1. This prior knowledge is extended to recognizing equivalent fractions for whole numbers as students use fractions to name whole numbers on a number line. A conceptual challenge students may encounter is understanding that different numbers may name the same location on a number line.

The concept is developed through work with a number line, which supports the concept of a fraction as a number.

This work helps students deepen their understanding of equivalence because equivalent fractions name the same position on a number line.

Students engage in Mathematical Practice 4 (model with mathematics) as they represent fractions on a number line and with numbers. Students count by unit fractions to determine equivalent fractions for whole numbers on the number line.

**Key vocabulary:**

- equivalent
- number line
- partition
- unit fraction
- position