Lesson objective: Understand that every non-unit fraction is a multiple of the unit fraction with the same denominator.

Students bring prior knowledge of adding fractions from 4.NF.B.3, as well as multiplication of whole numbers. This prior knowledge is extended to recognize that multiplication can be used with fractions, as well, as students represent situations using both repeated addition and multiplication. A conceptual challenge students may encounter is understanding why the denominator in a fraction does not change when the fraction is multiplied by a whole number.

The concept is developed through work with a number line, which allows students to see the connection between repeated addition and multiplication, and illustrates that the size of the fraction pieces remains constant, even when a multiplication problem results in more fraction pieces.

This work helps students deepen their understanding of operations because it highlights that the definition of multiplication remains constant, whether students are working with whole numbers or fractions. This work also helps students deepen their understanding of number as it reinforces their understanding that fractions are numbers.

Students engage in Mathematical Practice 8 (look for and express regularity in repeated reasoning) as they notice that instead of repeatedly adding the same unit fraction, they can multiply the unit fraction, and they begin to develop the algorithm \(a\times\frac1b=\frac{a}b\).

**Key vocabulary:**

- denominator
- multiple
- unit fraction