Lesson objective: Extend understanding that fractions can be compared using its comparison to a benchmark fraction.

Students bring prior knowledge of comparing fractions from 3.NF.A.3.a-d. This prior knowledge is extended to using a benchmark as students compare fractions. A conceptual challenge students may encounter is understanding a reasonable benchmark fraction depends on the fractions that are being compared.

The concept is developed through work with a number line, which shows a fraction's size in relation to a benchmark.

This work helps students deepen their understanding of number because students are reasoning about the size of a number based on its relationship to a benchmark.

Students engage in Mathematical Practice 3 (construct viable arguments and critique the reasoning of others) as they reason about the size of a fraction in comparison to its benchmark, and as they reason about the comparison of fractions because of their relationship to benchmark fractions.

**Key vocabulary:**

- benchmark fraction
- denominator
- equivalent
- half
- numerator
- relationship
- unit fraction