Lesson objective: Identify and create equivalent sums and differences using fractions with unlike units.

This lesson helps to build fluency with computation of equivalent fractional values and deepen conceptual understanding that expressions composed of equivalent values are equal. Fraction tape is used here because it highlights the concept that fractions with difference sized pieces can still have equivalent values. This work develops students' understanding that If \(\frac ab=\frac{an}{bn}\) and \(\frac cd=\frac {cm}{dm}\), then \(\frac ab+\frac cd=\frac {an}{bn}+\frac {cm}{dm}\). This is why rewriting fractions as equivalent fractions produces the same sum.

Students engage in Mathematical Practice 2 (Reason Abstractly and Quantitatively) as they extend their understanding of equivalent fractions and addition and subtraction of fractions with like denominators (including mixed numbers) to create expressions that are equivalent using fractions with unlike denominators.

**Key vocabulary:**

- sum
- difference
- equivalent

**Special materials needed:**

- Students may need fraction tape to model equivalent sums and differences