Lesson objective: Understand that multiplying both fraction components by the same number preserves the relationship between them and this is the same result as multiplying by one.

Students bring prior knowledge of multiplying fractions and whole numbers from 4.NF.B.4. This prior knowledge is extended to multiplying fractions by a fraction equivalent to one as students practice multiplying and drawing number lines to show their thinking. A conceptual challenge students may encounter is thinking that multiplication will always result in a product greater than both factors.

The concept is developed through work with equations and vertical number lines, which deepen students understanding of operating on fractions.

This work helps students deepen their understanding of equivalence because they will be operating on fractions and just as they learned to operate on whole numbers.

Students engage in Mathematical Practice 4 (model with mathematics) as they use number lines, as well as, words and equations to represent their mathematical thinking. Students will explain why the product of a number multiplied by a fraction equivalent to one will result in a prodcut equivalent to the given number.

**Key vocabulary:**

- equivalent
- scaling
- tape diagram
- vertical number line