Lesson objective: Understand that we can name numbers, including fractions, in an infinite number of ways.

Students bring prior knowledge of partitioning area models to create equivalent fractions 3.NF.A.3. This prior knowledge is extended to creating many equivalent fractions for the same number as students repeatedly partition the model. A conceptual challenge students may encounter is understanding that the model may be partitioned to infinity to generate an infinite number of equivalent fractions.

The concept is developed through work with a tape diagram, which illustrates the repeated partitioning of the figure.

This work helps students deepen their understanding of equivalence because they demonstrate that partitioning a model many times does not change its size.

Students engage in Mathematical Practice 4 (model with mathematics) as they represent fractions using the area model and numbers. They model equivalent fractions for one-half by folding the model and recording the fractions.

**Key vocabulary:**

- equivalent
- infinite
- partition

**Special materials needed:**

- rectangles for students to fold