Lesson objective: Extend understanding that the connection between division and multiplication can be extended to fraction division.

Students bring prior knowledge of dividing unit fractions from Grade 5 (5.NF.7). This prior knowledge is extended to dividing non-unit fractions as students use the connection between division and multiplication and multiplicative properties to understand dividing fractions. A conceptual challenge students may encounter is making sense that dividing by a number is equivalent to multiplying by the reciprocal.

The concept is developed through work with multiple fraction division strategies, which leads from the "common denominators" strategy (Susan's Way) to the "decompose the divisor" strategy (Diego's Way) to the "invert the divisor and multiply" strategy (Paige's Way).

This work helps students deepen their understanding of operations because the role of the dividend and divisor need to be recognized to implement the "invert the divisor and multiply" strategy.

Students engage in Mathematical Practice 3 (contruct viable arguments and critique the reasoning of others) as they analyze and apply the three strategies to fraction division problems.

**Key vocabulary:**

- dividend
- divisor
- factor
- multiplicative identity
- multiplicative inverse
- product
- quotient
- remainder