Lesson objective: Understand that the relationship between multiplication and division can be extended to dividing whole numbers and non-unit fractions.

Students bring prior knowledge of dividing whole numbers and unit fractions from 5.NF.7. This prior knowledge is extended to dividing whole numbers and non-unit fractions as students look for ways to use the relationship between multiplication and division. A conceptual challenge students may encounter is realizing that dividing by a number is equivalent to multiplying by the multiplicative inverse of the divisor.

The concept is developed through work with area models and number lines, which visually represents the relationship between multiplication and division.

This work helps students deepen their understanding of equivalence because dividing is equivalent to multiplying by the multiplicative inverse, or reciprocal of the divisor.

Students engage in Mathematical Practice 8 (look for and express regularity in repeated reasoning) as they interpret the division situations, and compare and contrast the roles of the dividend and divisor.

**Key vocabulary:**

- Dividend
- Divisor
- Multiplicative Inverse
- Quotient
- Remainder