Lesson objective: Extend understanding of equivalent fractions to see that writing equivalent fractions is useful for comparing sums of two fractions.

Students bring prior knowledge of decomposition of fractions to find sums and differences of fractions with the same denominators from 4.NF.B.3a and 4.NF.B3b. This prior knowledge is extended to include fractions that have different denominators as students work to combine lengths. A conceptual challenge students may encounter when combining fractions with different denominators is figuring out how to name the resulting length. Naming the final sum is not required in this lesson, but students may notice the usefulness of rewriting fractions with the same denominators as a step in that direction.

This work helps students deepen their understanding of addition because they work with putting lengths together just as they did previously with whole numbers and with fractions with like denominators.

Students engage in Mathematical Practice 5 (Use appropriate tools strategically) as they use number lines or tape diagrams to verify that it's possible to travel the same total distance even when the fractions are named with different denominators.

**Key vocabulary:**

- equivalent
- denominator
- sum
- expression

**Special materials needed:**

- fraction number lines
- fraction strips (optional)