Lesson objective: Compare fractions with unlike denominators by finding common denominators.

Students bring prior knowledge of comparing two fractions with like denominators by reasoning about their size from (Grade 3, Unit 11; 3.NF.A.3). This prior knowledge is extended to unlike denominators by encouraging students to partition fractions into same-sized pieces and compare them that way. A conceptual challenge students may encounter is generating correct equivalent fractions and finding numbers that both denominators can be changed into.

The concept is developed through scaffolded work with unlike denominators that range from compatible numbers where one denominator goes into another evenly to denominators that are not compatible and where both fractions must be changed to a common multiple in order to be compared.

This work helps students deepen their understanding of equivalence because of the understanding that they should use common denomiators in order to compare same-sized pieces.

Students engage in Mathematical Practice 4 (model with mathematics) as they use fraction bar models and number lines to generate equivalent fractions and compare fractions.

**Key vocabulary:**

- denominator
- equivalent
- greater than
- less than
- like denominator
- numerator
- unlike