Lesson objective: Extend fraction understanding by recognizing that equivalent fractions can be generated by partitioning or combining each equal share of a fraction. Students will understand that when naming equivalent fractions the denominator changes by *n* times and the numerator will also change by *n* times.

Students bring prior knowledge of recognizing and generating equivalent fractions from 3.NF.A.3.a-c. This prior knowledge is extended to include changing the denominator and numerator by *n *as students partition and combine each equal share of a fraction. A conceptual challenge students may encounter is decomposing or composing each equal share of the whole to represent the new denominator.

The concept is developed through work with area models and number lines, which visually and conceptually support fraction equivalence.

This work helps students deepen their understanding of equivalence because fractions are equivalent when they represent the same area or the same point on a number line.

Students engage in Mathematical Practice 3 (construct viable arguments and critique the reasoning of others) as they justify and reason about how partitioning each fractional piece generates an equivalent fraction.

**Key vocabulary:**

- area
- denominator
- equivalent
- numerator
- partition