Lesson objective: Apply choosing a reasonable benchmark that may not be half or 1 to make fraction comparisons.

This lesson provides an opportunity for students to apply their knowledge and understanding of comparing fractions with using a benchmark to a mathematical situation. Students are asked to choose reasonable benchmarks that are not half or 1 in order to make a comparison.

Key Concept students will use:

- We can compare two numbers indirectly by comparing them both to a common benchmark.

Skills students will use:

- Compare fractions with same numerators (Grade 3, Unit 11)
- Generate equivalent fractions (Grade 3, Unit 10)
- Choose a reasonable benchmark to make a comparison using <, >, or =

Students engage in Mathematical Practice 3 (construct viable arguments and critique the reasoning of others) as they choose a reasonable benchmark and explain their reasoning as well as why another benchmark is not reasonable. Students must also then justify their comparison of the numbers with that benchmark.

**Key vocabulary: **

- benchmark fraction
- denominator
- equivalent fraction
- numerator