Lesson objective: Use fraction equivalence strategies to find the best expressions for adding fractions with different sized pieces.

Students bring prior knowledge of equivalent fractions from 3.NF.A.3a/bc. This prior knowledge is extended to to include sums and differences of fractions as students find sums and differences of fractions that are equivalent. A conceptual challenge students may encounter is the difference between the processes of adding whole numbers and adding fractions with different units.

The concept is developed through work with number line, which shows students that, without making pieces that are the same size (like denominators), the sums and differences of fractions cannot be named.

This work helps students deepen their understanding of equivalence because students are thinking deeply about the meaning of equivalent fractions and expressions and how they aid in finding sums and differences.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they make sense of quantities and their relationships in a problem situation when they reason about the magnitude of a sum. They will also exercise habits of quantitative reasoning by considering the units involved as they explore the meaning of the denominator and attend to the meaning of quantities. Rather than simply computing sums and differences with an algorithm, students will have the opportunity to contextualize the process of finding common denominators before performing the algorithm.

**Key vocabulary:**

- Sum
- Difference
- Equivalent
- Denominator

**Special materials needed:**

- Students may need fraction tape for intervention