Lesson objective: Extend understanding of operation relationships by solving problems using patterns and the relationship between multiplication and division.

Students bring prior knowledge of division and multiplication from 3.OA.1 and 3.OA.2. This prior knowledge is extended to patterns and multiples as students use multiples and patterns to solve word problems. A conceptual challenge students may encounter is thinking that division is commutative.

The concept is developed through work with patterning and multiples which visually support students as they integrate this new knowledge.

This work helps students deepen their understanding of operations because they will use strategies such as the relationship between multiplication and division or properties of operations to multiply and divide.

Students engage in Mathematical Practice 2 (reason abstractly and quantitatively) as they represent word problems numerically.

**Key vocabulary:**

- Commutative Property
- Drawings
- Equations
- Inverse Operations
- Model
- Representation